HK1224987A1

HK1224987A1 - Method and system for determination of at least one property of a manipulator

Info

Publication number: HK1224987A1
Application number: HK16113320.6A
Authority: HK
Inventors: 克拉斯．尼尔森; 亚当．尼尔森; 马蒂亚斯．哈格; 比约恩．奥洛夫松; 安德斯．罗伯特松; 奥洛夫．索恩莫
Original assignee: 康格尼博提克斯股份公司
Priority date: 2013-08-27
Filing date: 2014-08-25
Publication date: 2017-09-01

Description

Method and system for determining at least one characteristic of a robotic arm

Technical Field

The present invention relates to a method and system for determining at least one characteristic, such as compliance (compliance) of a robotic arm (manipulator), and a computer product for determining and utilizing the obtained at least one characteristic.

Background

Robots have found widespread use in many industrial fields. Some industrial fields include labor that is hazardous to human health, or labor that is done under conditions that a human cannot withstand. Other industrial areas include repetitive tasks that can be performed more efficiently and accurately by robots.

Most industrial robots comprise a robot arm designed to manipulate material, wherein the robot arm usually has an arm-like mechanism consisting of a series of segments, each segment being referred to as a link in the following. The movements of the robot arm may be generated either manually by the operator or automatically by executing instructions according to a user program defining the tasks of the robot. In the latter case, the robotic arm is controlled by a user program loaded or entered into the controller to achieve the programmed pose (position and orientation for desired tip placement). The controller is part of the robot, which controls the movement of the robotic arm by movement of the rods via the motor, drive system, and actuation of the articulated mechanism forming a mechanism with a certain kinematic structure.

The number of independent parameters that determine the position state of a rigid body (stiff rod) or mechanism is called the degree of freedom (DOF, also used in complex numbers as a degree of freedom complex). One free rigid body has 6DOF (three translations and three rotations) in three-dimensional (euclidean) space. Rigid or stiff rods include such rigid bodies. Each kinematic pair of rods is connected via a joint (joint), which is usually sliding (which in the following may also be referred to as a cylindrical, linear, or translational joint) or articulated (which in the following may also be referred to as a swivel joint or a rotary joint). One such joint constrains five of the six possible DOF of one rod relative to the other rod of the pair, which adds one DOF to the last rod of the robotic arm (ending with the end flange of the installation tool) in the non-singular configuration of the robotic arm. By virtue of the kinematic structure of the rods and joints, the DOF of the robotic arm (robotic arm-DOF) can be considered to be the minimum number of coordinates required to specify the kinematic configuration.

Since the tool, called the end-effector of the robot (or an equivalent tool changer that allows the end-effector to be changed manually or without manual assistance), is another object to be moved in euclidean space, 6DOF robotic arms are the most common, since 6DOF robotic arms include the fewest degrees of freedom for full movement of the end-effector, which requires 6 of the above-mentioned joints for a normal, non-singular configuration. There are also other types of joints, such as ball joints and cylindrical joints, but these types of joints can be considered as a combination of the more simple joints mentioned above, and these types of joints are referred to below as joints. As mentioned, the joint may be rotational or translational, but both cases are equally covered below. This corresponds to the established concept of generalized joint coordinates in the robot literature. The robotic arm-DOF joint coordinates define the motion configuration, which also defines the pose of the endpointer, but cannot be unique.

The joints are typically actuated by feedback controlled motors via a drive system that includes gears for reducing motor rotation to low speed joint rotation. The drive system is then essentially a transmission, but we assume that the ideal motor and any associated actuator/motor dynamics are included in the drive system. The drive system is avoided in so-called direct drive joints, but due to the practicality and fundamental problems of direct drive, almost all robots are configured with a drive system for each joint. However, the following description also covers a direct drive coupling as a special case of a known and ideal drive system having a gear ratio of one. The drive system is referred to herein as a typical device of joints and rods, including its motor for actuation and any drive system that is a shaft(s).

When joint motions are coupled in a robot arm, the complete kinematic structure of the robot arm usually comprises internal joint motions, which are very common for wrist motions, which is the case for the axes 5 and 6 of the robot arm 2 in fig. 1. While this internal joint movement may be relevant to the practice of the present invention, in the following we may ignore internal joint movement, since the principles of the present invention are related to following the movement of the joint torque as if each joint were originally of the direct drive type. Thus, kinematically we here refer to the joints and the bars forming the arm structure of the robot arm.

The common arm mechanism mentioned including a robotic arm is often referred to as a pure tandem motion robotic arm or mechanism (SKM, in this document referring to the equivalent concept of tandem motion machine), meaning that each rod is behind a joint, and then the next rod forms a tandem chain from the foot (or mobile base) of the robot to the end flange. Alternatively, the rods may also be arranged in parallel, thus forming a Parallel Kinematic Manipulator (PKM). A large number of combinations of SKM and PKM can be constructed.

In robotic applications, such as those used for manufacturing, it is highly desirable that the physical pose created be consistent with the programmed pose within a certain tolerance. To support efficient pose specifications for the end-effector, either manually or in a user program and possibly from CAD data, the controller thus contains a motion model of the robotic arm. The kinematic model includes the geometrical relationships of the joints to the rods and to them in the robotic arm, assuming that these parts comprise rigid bodies. Because the robotic arm is not very rigid, there will be deflection due to the offset mass and handling forces at the location of the tip. The deviation between the programmed pose and the physical pose may be at a single location or multiple locations along the path, or at any used location of the robot. Managing the deviation by the user in the user program via adjustment or by self-learning slightly off the programming pose limits the reuse of the robot tasks and increases the cost for robot programming and deployment.

In the first decade of the robot, major deviations are due to lack of control, such as inadequate trajectory generation (e.g., joint torque saturation is not considered) and overly primitive feed forward compensation (e.g., with path errors due to joint servo control errors). Knowing the detailed robot arm parameters would not be useful in earlier systems since there were no control functions to utilize them. The widespread use of model-based control to then utilize knowledge about the mechanical arm characteristics to optimize control is caused by large performance improvements and robots that perform the program approximately as programmed from the mid-eighties and beyond. Due to the lack of control compensation for several special robot arm characteristics, the robots still deviate from their programmed motion. Modern controllers typically have suitable structure and functionality for such compensation, but lack actual robot specific data due to lack of a viable method for obtaining and maintaining this data. In order to obtain as few deviations from the programmed pose as possible, it is therefore necessary to deal with these deviations and therefore a viable method for determining the relevant robot arm characteristics is required.

There are several reasons for deviation from the programming pose. One reason may be the inaccuracy of the rod and joint geometry, i.e. due to motion errors. The motion error may be managed by motion correction, which is typically available from robot manufacturers. Another cause of deviation relates to inaccuracies in the dynamic control of the joint and arm mechanism and/or arm during high speed motion, e.g. torque saturation caused by joint mode or multi-body action. Typically, such deviations are managed by model-based controls provided by the robot manufacturer. Yet another reason for deviation from the programmed pose arises from inaccuracies caused by the interaction of forces between the end-effectors of the robotic arm and the workpiece, but also by gravity and other forces acting on the robotic arm. As such, such deviations are also related to joint dynamics around or along joint motion due to tolerances of the bearings and other joint portions.

Lightweight robots and smart robots with highly optimized control are becoming increasingly popular in industrial applications. Since another source of deviation is the deflection caused by the compliance of the robotic arm, this puts new requirements on the control-based model. A flexible rod may be defined as a non-rigid rod, i.e. a rod that exhibits a certain degree of elasticity. Another source of misalignment is the compliance of the robot joint in directions other than the direction of joint rotation, e.g., perpendicular to the direction of joint rotation. Industrial robots have a higher flexibility for the machining operation than conventional machine tools. This gives the robot a higher requirement on the elastic model to calculate the actual Tool Center Point (TCP) position when forces act on the robot.

Attempts have been made to develop a rod and joint compliance model using quasi-static and dynamic models of robotic arms such as described in "simulation and control of flexible robotic arms" published in 2010 of mobergs. As shown in fig. 2, the publication is characterized by a flexible joint as the spring-mass system 25 having four rods: rod 1-rod 4, three motors: M1-M3 and different mass and spring rates. The rod elasticity is then simulated by means of a stiffness matrix. However, as Moberg has acknowledged, the simulation of the number of non-actuated joints and their positions is not obvious. (Mobergs references to non-braking joints will be captured below by our more general concept representing the elastic-DOF of joints and rods that can be deformed according to an elastic model.)

There are several types of solutions that deal with some of the aforementioned types of biases, with optical systems for pose measurement and tracking being the most common. Such a system, referred to as an external calibration system, may be used to compensate the motion of the tip on-line without requiring parameters for the source of the deviation, or such a system may be used to calibrate parameters of the motion model. Although today's calibration systems do not capture parameters describing deflection due to forces, high-end robots in common applications are relatively rigid and thus useful. In many other cases, either the robot is less rigid or the application requires more precision, and external sensing or improved compensation is highly desirable. Although a large number of robots are suitable for larger scale production facilities, the cost of the mentioned external calibration systems often exceeds the cost of a single robot. In smaller scale production facilities that rely on the operation of one or several robots, such external calibration systems are not suitable due to excessive cost. An example of an external calibration system is described in WO 9912082. In addition to calibration, external sensors that detect torque or the position of joints or tool exchanger can be used to improve robustness against unknown variations in the robot arm or in the manufacturing process if there is an interaction force between the tool and the workpiece.

Another method of calibration was proposed in Bennet, Hollerbach and Henri's article "KinematicicalnationbyDirectmationJacobianamatrix", Niss appearing on ICRA in France 1992. In this article, the parameters in the jacobian matrix of a robot are estimated by first gripping the robot in a predetermined pose and then actuating the joints of the robot. The unknown kinematic parameters may then be determined based on information from a force/torque sensor attached to the exterior of the end bar near the clamping location. The jacobian matrix expresses the correlation between endpoint velocity and joint velocity, or corresponds to force/torque. The data obtained from a set of such actuations yields a set of such matrices, which are used to calculate the kinematic parameters. Even with the kinematic corrections being performed, and also with force/matrix-based methods that ignore the dynamics of the actuator to the joint, the deviations caused by dynamic forces and the interaction of the forces with the workpiece still exist.

Therefore, it makes sense to determine the coefficients of the stiffness matrix described by Moberg using the conventional robotic arm calibration system described earlier, or such calibration systems are not simply designed to measure and compensate for rod and joint compliance in directions other than the primary direction.

The article "cartesian com-plicated models for industrial robot using virtual joints", published in 2008 by e.abele et al, and the identification of parameters of a robot structure, is described. In fig. 3a, a common approach to the primary connection 30 is shown, wherein the drive side (θ)_z) And the output side (q) of the gear₂) The torsion between is shown, which is applied if the overall elasticity can be mainly attributed to the elasticity of the gears. The robot rod and the connection from joint to rod are considered inflexible. In fig. 3b, a virtual joint 31 having more than two DOF compared to the primary joint in fig. 3a is shown, and thus the compliance in more than two DOF may be taken into account when building a model of the robot structure. However, to be able to measure joint compliance, only one joint is loaded at a time. That is, when measuring axis (i), all axes from the base to the aforementioned axis (i-1) must be clamped so that the identified axis acts as the first free moving joint, thus creating a rather time consuming process of determining any compliance of the robot.

Therefore, in order to reduce the deviations by compensation based on a correction model comprising compliance, the limitations of the prior art mean that a more accurate, simple and inexpensive method of determining such robot stem and joint parameters is required.

SUMMARY

The object of the present invention is to address at least some of the aforementioned disadvantages of the prior art.

According to a first aspect, the object is at least partly achieved using a method of determining at least one characteristic associated with a selected axis of a robot arm, wherein the robot arm is configured to be controlled by a controller and the robot arm comprises at least one axis comprising a joint and a link connected to the joint, wherein the joint is configured to be actuated by an actuator. The method comprises the following steps:

-securing a movable part of the robot arm to a position in space by controlling the robot arm such that the robot arm achieves a gripping motion configuration;

-selecting an identified joint set comprising at least one joint of the robot arm, wherein at least one joint of the identified joint set is configured to control and monitor the selected axis for which the associated at least one characteristic is to be determined;

-selecting an excitation joint set comprising at least one joint of the robot arm, the excitation joint set configured for a gripping motion configuration of the robot arm to excite at least one rod connected to the at least one joint of the identification joint set;

-selecting a gripping formation joint set of the robot arm;

-actuating the firing joint set such that the selected axis is fired while controlling the gripping configuration joint set such that the gripping motion configuration is maintained;

-monitoring one or more quantities related to actuator torque and/or joint position for at least one joint of the identified joint set and/or the excited joint set;

-determining at least one characteristic of the selected axis based on the one or more monitored quantities.

Using this method it is possible to determine characteristics such as the rod and joint compliance of the robot arm and thereafter use this characteristic to obtain more accurate robot arm control. It is not necessary to disassemble any part of the robot arm to determine this characteristic, and therefore a faster and more cost effective method is achieved than before.

According to one embodiment, the method comprises determining at least one characteristic of the selected axis based on a combination of the monitored one or more quantities related to actuator torque and/or joint position. Thus, a greater number of characteristics may be determined.

According to one embodiment, the method includes determining at least one characteristic of a plurality of selected axes each for a robotic arm. Thus, several features may be determined.

According to a further embodiment, the method comprises repeating the method, wherein the gripping motion configuration of the robot arm obtained in the method is different from the previously obtained gripping motion configuration of the robot arm, and determining at least one characteristic of the selected axis based on the determined characteristic of the selected axis in the different gripping motion configuration. By varying the gripping motion configuration, a number of quantities may be obtained to more accurately determine the at least one characteristic.

According to another embodiment, the step of determining the at least one characteristic comprises determining a stiffness matrix for the robotic arm based on the one or more monitored quantities. The stiffness matrix of the robot arm consists of one or several component stiffness matrices, e.g. a bar stiffness matrix, in order to determine the stiffness characteristics of the complete robot arm.

According to one embodiment, the method includes organizing the characteristics according to the structure of the stiffness matrix of the robotic arm that relates the potentially unknown displacements of the rod and joint to torque and force, such that any combination of series and parallel links can be considered for simulation, thereby facilitating the determination of these characteristics. The characteristic may be a robot arm stiffness parameter.

According to a further embodiment, the step of determining the at least one characteristic comprises performing an optimization based on the one or more monitored quantities. The robot arm may be provided with a sensor configured to generate a sensor signal having sensor data when in the gripping motion configuration, and wherein the method further comprises including the sensor data from the robot arm in said optimizing. The sensor may be a force sensor configured to generate a sensor signal having force data.

According to one embodiment, the at least one joint of the set of gripping formation joints is not part of the set of identification joints and the set of excitation joints. Thus, gripping a splice in a constructed splice set will not affect other splice sets, nor will it affect the quantity being monitored. According to one embodiment, the set of gripping configuration joints is controlled such that the set of gripping configuration joints does not substantially affect the determination of the at least one characteristic associated with the selected shaft.

According to one embodiment, the method comprises comparing the at least one characteristic with a previously obtained characteristic value or with a predefined characteristic value, determining a difference between the at least one characteristic and the previously obtained characteristic value or the predefined characteristic value, comparing the difference with a difference threshold and determining the wear of the robot arm based on the result of the comparison. Thus, if the determined characteristic differs from any previously obtained characteristic value, or represents a predefined characteristic value having a characteristic, e.g. substantially no wear, the wear of the robot arm may be determined by analysis.

According to one embodiment, the robotic arms are parallel motion robotic arms. And the robot arm may be a tandem motion robot arm. Thus, the method can be used in any case.

According to a further embodiment, the method comprises obtaining specific motion parameters by means of a motion correction of the robot arm, and updating the motion parameters of the robot arm based on at least one determined characteristic of the selected axis. Thus, the robot arm may be better calibrated using the obtained at least one characteristic. The motion parameters to be updated may be nominal parameters of the robot arm or motion parameters obtained by conventional calibration methods.

The present disclosure also relates to a use of the determined at least one characteristic determined according to any of the method steps disclosed herein for updating nominal motion parameters of a robot arm. Furthermore, the method relates to the use of the determined at least one characteristic determined according to any of the method steps disclosed herein for updating a robot program or motion control parameters of a robot arm. Therefore, the control accuracy of the robot arm can be improved.

According to a second aspect, the object is at least partly achieved with a system for determining at least one characteristic associated with a selected axis of a robotic arm. The system includes a robotic arm having at least one shaft including a joint and a link connected to the joint. The system also includes at least one actuator configured to actuate the joint and a controller configured to control the robotic arm, wherein the controller includes a control unit and a computer-readable storage unit including instructions configured to cause the control unit to:

-clamping the movable part of the robot arm to a position in space by controlling the robot arm such that the robot arm achieves a clamping motion configuration;

-selecting a gripping formation joint set of the robot arm;

-actuating the firing joint set such that the selected shaft is fired while controlling the gripping configuration joint set such that the gripping motion configuration is maintained;

-determining at least one characteristic of the selected axis based on the one or more monitored quantities;

-generating a characteristic signal indicative of the at least one characteristic.

According to a third aspect, the disclosure relates to a computer program (P) associated with the system, wherein the computer program (P) comprises instructions configured to cause a control unit to perform the method according to any one of the steps disclosed herein.

According to a fourth aspect, the present disclosure relates to a computer program product comprising computer instructions stored on a computer readable storage medium to perform a method according to any of the steps disclosed herein. The disclosure also relates to a computer program product comprising at least one characteristic obtained when performing a method according to any of the steps disclosed herein, wherein the at least one characteristic is stored on a computer readable storage medium.

Brief Description of Drawings

The invention will be described in detail below with reference to the attached drawings, in which:

figure 1 illustrates a system for determining rod and joint characteristics of a robotic arm, according to one embodiment of the present invention.

Figure 2 shows a prior art model of a robotic arm with rod and joint compliance.

Figure 3a shows a prior art model of a substantially flexible joint.

Fig. 3b shows a prior art model of a joint with compliance in directions other than the DOF of the joint.

Figure 4 shows in a simplified manner a robot arm with a flexible joint and a lever.

Fig. 5 shows a beam of ideal compliance.

Figure 6a shows a portion of a robot arm with a flexible shaft and adjacent joints of the robot arm having the indicated compliance.

Fig. 6b shows the two-dimensional perspective view of fig. 6a with the indicated joint compliance.

Fig. 6c shows the direction of gravity on the flexible rod.

Fig. 6d shows how the gravity of fig. 6c can be represented by two parts, so that the following equation is simplified.

Fig. 6e shows a specific example of joint compliance.

Figure 7 shows a motion diagram of the robotic arm of figure 1.

Figure 8 shows an example of a representation of a deflection due to compliance corresponding to a certain kinematic configuration of the robot arm in figure 1.

Figure 9 shows a flow chart of an embodiment of a method according to the present invention.

Fig. 10 shows an example of a deformation of the rod and the joint.

Fig. 11a shows an example of a set of global stiffness matrices for the example shown in fig. 10.

FIG. 11b illustrates an example of a set of global total Jacobian matrices for the example illustrated in FIG. 10.

Figures 12a-12d show a robot arm with two joints and three levers in different gripping motion configurations according to the present method, and the resulting compliance when the robot arm is actuated.

Fig. 13a-13b show several load cycles of the axes 2 and 3 of another robot.

Detailed Description

Definition of features

The robot comprises: combination of a robotic arm configured to control movement of one or more axes of the robotic arm and a controller

Mechanical arm: comprising a robot arm forming one or several axes of one or several kinematic chains.

Axis (plural: axis): including joints and linkages for actuation and any drive train.

Connecting rods: one or several rods interconnected by joints.

Rigidity: is the rigidity of the object, defined asFor elastic objects with one DOF, where F is the force applied to the object and is the displacement resulting from that force along the same DOF, orDefining a rotational stiffness, where M is an applied torque or torque and θ is a rotational displacement resulting from the applied torque, orDescribing how the torque produces translation, orDescribing how the force produces the displacement.

Flexibility: the inverse of the stiffness.

Flexible rod: a non-rigid rod. A flexible rod has its mass distributed between two joints it connects, and due to the physical nature of the distributed mass, the flexible rod thus formally has an infinite DOF and an infinite number of resonant modes. For the present invention, only the lowest resonance frequency is relevant as an indication of the compliance of a rod with a certain mass. This frequency can be measured in free motion and can also be used as a performance limit, but is not a central part of the method. Accordingly, the inertia of the rod may approach the concentrated mass at the center of gravity. Furthermore, the elastic dynamic model determined in the clamping configuration is a corresponding quasi-static model which is sufficient for compensating for errors resulting from process forces. With this simplification, a flexible rod is considered to have six additional DOF that specify the end of the rod (the pose of the next joint in the kinematic chain) relative to the beginning of the rod (the pose of the aforementioned joint).

Component stiffness matrix: a matrix for simulating component deformation, such as stem deformation due to joint forces and/or torques. Assuming that the rod deformation is small compared to the rod size and motion, the stiffness matrix is used as a linear mapping. The rod deformation may be defined in the local coordinate system of the rod and then converted to the global coordinate system.

Mechanical arm rigidity matrix: given that the part stiffness matrix may be constant, the stiffness of the robotic arm varies with the configuration defined by the joint coordinates (with the robotic arm-DOF elements). Since even large drive train influences have a rather small influence on the translation, the difference between the motor and the rod translation is here negligible in practice. That is, the motor angle sufficiently well represents the joint angle, in addition to the single pose. For each individual configuration, the rod stiffness matrices may be put together to form a larger mechanical arm stiffness matrix (MSM). MSM also refers to the global stiffness matrix.

Orthogonal joint compliance: the compliance of the rod in any direction, which is orthogonal to the motion described by the free coordinates of the joint representing the joint motion.

Non-orthogonal joint compliance: compliance of the shaft along or around the motion coordinate. Non-linear compliance is included in the characteristics of the drive train of the joint (non-linear compliance may be determined first and therefore may be compensated for grip pose configuration, or alternatively avoided by selecting an appropriate grip pose configuration) and therefore for understanding the invention it may be assumed that the non-orthogonal joint compliance is linear.

Rod gravity: for SKM, the rod mass causes gravity, which needs to be balanced by the joint torque adjacent the shaft. For PKM, a corresponding set of parallel bars needs to balance the gravity. In both cases, potentially for any joint depending on the kinematic configuration, a (process or gravity) force acting on the end flange (e.g., the gravity of the installed terminator, or the force due to the clamped position) may be added to the force acting on each axis. A feature of the clamping experiment is that gravity can be balanced from the end flange side, thus enabling a small/zero joint torque (e.g. for determining the clearance (backlash)) despite the large gravity. Although the description focuses on the case of SKM for clarity and common industrial use, any of the above cases is covered by the following.

The influence of joint gravity: in general, for virtually all robots currently on the market, the greatest influence of gravity is the influence on the corresponding rigid body of the preceding joint in the kinematic chain. This gravitational effect is most practically measured optimally in free space friction measurements (but taking into account the average torque during slow bi-directional motion, rather than a hysteresis reflecting friction) in free space motion, using a sufficient number of motion configurations to determine the actuation torque required to counteract the gravitational force. The gear ratios are known (from data tables or from measurements that are trivial to the technician) and therefore the linear conversion between joint torque and rod torque is known and therefore the (rigid) rod gravity can equally be considered at the motor side of each joint. Asymmetric friction may be detrimental to the accuracy of gravity identification, so in this case several different payloads (changing gravity instead of friction) may be used.

Influence of rod gravity: in addition to the effect of the joint gravity, the gravity of the flexible rod affects the shape of the rod itself (see fig. 8 describing the 2D case), which means that gravity increases the bending of the rod.

The clamping movement structure comprises: a configuration of a robotic arm in which the robotic arm (or any movable part of the robotic arm) is clamped in a well-defined pose.

Identifying a joint group: the joint set comprising at least one joint in a certain gripping configuration is configured to control and monitor the shaft or shafts relating to the respective set of rods having the characteristics to be determined. The control and monitoring of the configuration is effected by means of controllers which thus control the set of joints driving the rods having the characteristics to be determined.

Excitation joint group: a set of joints, at a minimum and usually one (for example the one that is used to exert a force to enable identification in view of the best case), which, for the current gripping motion configuration, excites the rod or rods driven by the joint or joints belonging to the identification joint set. "firing" here means affecting the lever or levers driven or actuated by the joints belonging to the identified joint group.

Clamping structure joint group: the joints that do not belong to either the excitation or identification joint groups. The joints are controlled such that the kinematic configuration is achieved such that the joints do not substantially affect the identification of the shaft characteristic and such that the clamping pose is maintained.

The characteristics are as follows: the characteristic is any of a linear compliance of the joint or the rod, an orthogonal compliance of the joint, a non-linear compliance of the rod, or an orthogonal gap of the joint. The characteristics may be determined as stiffness values for the rod and joint.

System for controlling a power supply

In fig. 1, a system 1 according to one embodiment is shown and will now be described with reference to this figure. The system 1 comprises a robot arm 2, here shown with six joints 3, 5, 7, 8, 11, 12 and six bars 4, 6, 9, 10, 13, 14. Each joint 3, 5, 7, 8, 11, 12 is configured to be actuated by an actuator, e.g. a motor (not shown), directly or indirectly via a transmission (here a transmission system, not shown), such that the motor rotation is converted into a low speed motion as indicated by the thick arrow. The thick arrows show how each rod 4, 6, 9, 10, 13, 14 can be moved around the joint 3, 5, 7, 8, 11, 12 to which it is connected. The joint 3 constitutes the shaft 1 together with the rod 4 to which it is connected. The direction of movement of the shaft 1 when the rod 4 is rotated about the joint 3 is indicated by the thick arrow representing the shaft 1. Moreover, the joint 5 is connected to a rod 6, thus forming the shaft 2. The direction of movement of the shaft 2 when the link 6 rotates about the joint 5 is indicated by the thick arrow representing the shaft 2. The shaft 3 is the movement of the rod 9 around the joint 7, but the actuation comes from the transmission system affecting the rod 23, the rod 23 we call the parallel joint of the shaft 3. Joint 8 forms shaft 4 together with rod 10, joint 11 forms shaft 5 together with rod 13, and joint 12 forms shaft 6 together with rod 14, in the following order. The directions of their movements are indicated in the figure by arrows, respectively. For simplicity, and since the present invention relates to arm side joints and lever mechanisms, the actuator/motor and drive train that are part of each shaft are not shown or referenced.

A tool exchanger 16 (shown separated in fig. 1) may be mounted to the flange 15 of the installation tool along with its robotic arm side, and various tools or endrs may be attached to the tool exchanger 16 on its tool side.

Such a six-joint robot arm 2 is also referred to as a DOF robot arm, since it can be positioned in the working area of the robot arm 2 with an attached endstop attached to the flange 15 of the installation tool in six DOF. The system 1 may comprise any number of joints, i.e. one or more joints, and any number of rods connected to the one or several joints, and this number is not critical for the completion of the invention.

As will be described herein, the system 1 further comprises a controller 19, the controller 19 comprising a control unit 20 and a computer readable storage unit 21, the readable storage unit 21 having instructions configured to perform a method according to any one of the embodiments. More specifically, the system 1 is configured to determine at least one characteristic associated with a selected axis of the robotic arm 2, and the controller 19 is configured to generate a characteristic signal indicative of the at least one characteristic.

The controller 19 is configured to control the movement of the robot arm 2 and optionally the dock 18. Depending on preference, the controller 19 may be an external controller 19 (or digital computer) in the form of a manual or automatic operation, or internal, i.e. built into the robot arm 2 itself.

The robotic arm 2 may comprise built-in sensors, such as encoders or resolvers or the like attached to the motor shafts to sense the actuator positions of the joints 3, 5, 7, 8, 11, 12, in order to sense the endpointer position relative to an internal coordinate system spanning the joint space and to associate the endpointer position with an external coordinate system (typically spanning cartesian space). These sensors, which are typically used for feedback control of the robotic arm, may also be used in accordance with the present invention to determine data that may be used to determine characteristics of the joint and the rod, such as compliance. Parameters such as speed of motion, force, or stiffness may be transformed between rod space and cartesian space. In a similar manner, a parameter describing actuator space, such as joint motor angle driven by force or torque, may be transformed into a parameter describing joint space, such as correcting a known joint position based on motion. Thus, data from sensing the number of motors may be expected to contain information about the overall characteristics of the robotic arm, such as the compliance of the rod and the resultant tip position deviation due to payload and external forces, in view of appropriate control conditions.

The robot arm 2 may be docked or attached to the gripper 18 shown in the figures or another gripper so that the robot arm 2 achieves a gripping movement configuration. One way to obtain a gripping motion configuration is to have the controller 19 control (automatically or by manual command) the robot arm 2 so that the movable part of the robot arm 2 reaches a position in the space where the gripper 18 is located. The movable part is usually an end flange at the last bar of the robot arm 2, preferably equipped with a tool exchanger 16. The tool exchanger 16 is mounted on its tool side using mating parts of the clamp 18, e.g. a protrusion 17. The position in space here is thus determined by the position of the projection 18. The controller 19 may also control the gripper 18 to provide a certain position in space for the robot arm 2 to dock onto. Any combination of robot arm movement and gripper movement may be used as long as the robot arm achieves the desired gripping state.

Depending on what properties are to be obtained, one or several fixed positions, defined for example by the tool side of the tool exchanger 16, may be provided in the working area of the robot. The use of a reconfigurable clamp 18 as shown in fig. 1 allows docking to occur at one location, for example, secured and flexible by an unlocked leg of the clamp 18 with a flexible end stop that allows high speed docking. Thereafter, the clamping takes place by locking the legs of the clamp 18 at the position set by the robot arm 2. The position may be controlled manually or automatically.

For simplicity, this position in space or clamp 18 is assumed to be rigid compared to the compliance of the robotic arm, but the method can be easily extended to a flexible clamp. That is, the holder 18 is not rigid, but has a known or predetermined stiffness. That is, the stiffness of the gripper 18 may be measured by position and force sensors and determined as an extension of the robot arm 2 by standard methods or according to the invention. A special case is a plurality of robot arms with one or several controllers, which are docked to each other and which apply the clamping force in an alternating manner. The dock 18 shown in fig. 1 is a parallel mechanism that includes an efficient way of providing a repositioned, but rigid gripping pose.

Another example of a parallel mechanism may be seen as part of the robot arm 2 in fig. 1, where the actuation of the joint 7, and thus the shaft 3, is connected to the lever 9 via a parallel bar 23. The bar can be considered a parallel link within the PKM as part of the overall SKM. Instead, the rod 9 can be considered as part of the joint 7. It is then assumed that the rod 9 transmits forces only in its reverse direction, i.e. the rod 9 transmits only tensile and/or thrust forces without significant bending and/or torsion, so that the elastic dynamics of the rod 9 may be included in the joint characteristics that may be determined according to the method described in WO2014065744a1, for example. This type of joint is called a parallel joint and a mechanical arm as SKM, satisfying this assumption.

Some high precision robots and/or machines have a parallel arrangement within the drive train, for example in the form of dual motors acting partially against each other to avoid the effects of backlash. The case where there are more motors and/or actuators than there are DOFs is referred to in the described example as over-actuation (over-actuation) of the joint. The characteristics of the two actuation branches can then be determined one by means of a double experiment of the drive train for the double motor actuation. Thus, over actuated joints are a special case of the method presented in WO2014065744a1 and are not further covered here. In the case of a parallel joint or parallel rod, over-actuation refers to loading some of the joints and rods against each other.

The reference to avoiding over-actuation means that some actuators or joints are passive, temporary during the identification of the property of interest. The robot may also include passive joints that are used for special purposes during normal operation or reconfiguration. Such a joint can be locked at a specific angle that makes the remaining kinematic configuration particularly well suited for the task at hand. The joint may be temporarily passive as part of a particular dynamic behavior (e.g., a swinging motion), or the joint may acquire a generated angle caused by some external mechanism. In any case, the passive joint may be part of a dynamic configuration described below. The robotic arm 2 is fully actuated by default and according to current industry practice, but an under-actuated robotic arm has a lower number of axes than DOF. Passive joints represent under-actuation. Those joints and the connected rods may then either be managed by the same method with sufficient locking and/or fixing, or such joints do not influence the movement via a property of interest, and thus passive joints are manageable, but not further described herein.

While another type of robotic arm is one that has a robotic arm DOF higher than the required endware DOF, in the case of applications and tools that themselves leave one or several DOFs in an unspecified state, the endware DOF may be less than six. Typical examples are welding and grinding. From an application point of view, a rotation axis is ideally therefore irrelevant, the tool being rotationally symmetrical. Therefore, many robots for arc welding have only five DOF, and in material processing, there are robots for palletizing having four DOF. However, most robots now have six DOF, thus resulting in, for example, one redundant DOF for arc welding and two redundant DOF for palletizers. A robot arm with at least one redundant DOF is a redundant robot arm that allows motion in a so-called null space; zero-space motion consists of moving joints and rods, but there is virtually no endstop. Although in principle such a robot arm is unnecessarily expensive (due to the additional shaft/shafts), kinematic redundancy is actually useful (e.g. for optimal stiffness during grinding, orientation of the hose relative to the welding gun, etc.). Since redundant motions of the tool are generally not consistent with the motions caused by any particular axis, all axes of the robotic arm need to be well controlled and thus characteristics of the robotic arm that are still present need to be identified.

Redundant robotic arms with two or more arms, each with seven or more DOF like a human arm, are becoming increasingly important as they are well suited for performing tasks in human workplaces. For example, such a robotic arm allows for the positioning of the elbow, making better tradeoffs between accessibility, force, stability, and space. A typical application is an assembly that generally requires six DOF for a workpiece and a tool for holding the workpiece, thus leaving one DOF forming a null space in a redundant state. The zero-space motion then consists of moving the joint and the rod, but without the endpieces. Also, if the end effector has the obtained gripping pose, a zero-space motion can be performed, thereby changing the motion configuration. However, this assumes that a completely rigid robot also has a completely correct motion model to avoid a physically impossible over-actuation configuration in some dimensions, or that a robot with some motion errors also has some compliance. The latter is a practical and typical case in the case of robots, which results in solving in practical applications the problems of variations and deviations caused by joint and rod compliance.

Flexibility

Fig. 4 schematically shows an elastic model of a robot arm 40 with elastic rods 43, 45 and 47 and elastic joints 42, 44 and 46. By simulating the robot arm structure using the elastic joint and the elastic rod, the following behavior of the robot arm 40 can be described. The robotic arm 40 is attached to a rigid base 41. Each of the resilient levers 43, 45 and 47 is represented by a linear spring element having a certain spring constant characterizing the inverse of the compliance of the lever. The elastic bars 43, 45, 47 are each considered to have a certain length. The elastic joints 42, 44 and 46 are each represented by a spring element as shown in the figures. Moreover, the spring element is believed to cause relatively little deflection. It will be described below how the elasticity shown results in a compliance of the bars and joints of the robot arm 2, and how this compliance can be determined as a characteristic of the bars and joints. The characteristic may include, for example, a linear compliance of the joint or the rod, an orthogonal compliance of the joint, a non-linear compliance of the rod, or an orthogonal gap of the joint.

Fig. 5 shows an ideal spring beam 50 under the influence of force and torque, one of its ends being rigidly held and the other free to move. An ideal resilient beam here means that the beam has a substantially linear behavior for small elastic deformations. When the beam 50 is no longer subjected to forces and torques, the beam 50 will return to its original shape and orientation and thus here extend uniformly along the main axis 51. The beam 50 thus extends along a main axis 51 and has a height a and a width b. The shaft of the robotic arm may be characterized as an ideal spring beam 50. As can be seen from the figure, the beam 50 flexes when a force and/or torque is applied to the beam by bending and twisting away from the principal axis 51 of the beam 50. Furthermore, the elastic dynamic model of the robot arm 2 determined in the gripping configuration of the robot arm is a corresponding quasi-static model which is sufficient for compensating for deviations caused by process forces. That is, a fully dynamic model with more accurate inertia and multiple resonances (each contributing some additional elastic DOF in form) can be used internally in the controller 19, but can be ignored below, as we deal with the accuracy for the robots to better perform their tasks, rather than the dynamics of joint control. With this simplification, we can consider a flexible rod with six additional elastic DOF that specify the end of the rod, i.e., the next relative to the beginning of the rodThe pose of the individual joint, i.e. the pose of the preceding joint. As shown in FIG. 5, the compliance of the beam 50 may use both translational and angular displacements_z、_y、_x、_yAnd_zcharacterized by the angular deviation from the main axis 51. The x-axis extends along the major axis 51 of the beam 50, the y-axis extends along the height a of the bar 50, and the z-axis extends along the width b of the bar 50. In the figure_zAnd_yrespectively representing elongation along the z-axis and y-axis,_xillustrating the twisting of the beam 50 and,_yrepresents rotation about the y-axis, and_zillustrating rotation of the beam 50 about the z-axis.

Fig. 6a shows the resilient bar 60 in a three-dimensional coordinate system, defined by axes x, y and z, corresponding to the coordinate system in fig. 5. The spring bar 60 essentially has the spring characteristics of the ideal beam 50 shown in fig. 5, and here a corresponding force and/or torque is applied with respect to the ideal beam 50. The curved shape of the rod 60 will of course depend on the shape of the rod and the material from which it is made. In general, the curved shape may be calculated using the well-known Finite Element Method (FEM), and such analysis (e.g., of a single rod) may even be incorporated into the calculation scheme according to the present invention (which will be described based on the same theory on which the FEM is based). Reflecting the industrial requirements for the accuracy of the endpieces, however, we will from now on ignore the shape of the loaded rod and instead formulate an example framework that supports the identification of parameters that will yield the desired accuracy when used in compensation by means of the controller 19. The elastic rod 60 connects the first joint 61 and the second joint 62. The lever 60 forms a shaft 64 with the first joint 61, together with its transmission system, and the first joint 61 is configured to rotate the lever 60 about the z-axis. The rods 60 extend mainly along the x-axis, which is directed along the line connecting the joints 61 and 62, perpendicular to those two axes of rotation in their nominal unloaded state. The x-axis corresponds to the main axis 51 in fig. 5.

In fig. 6b, the bar 60 is shown in a two-dimensional view in the x-y plane for the case of simplified loading in this plane. In fig. 6a and 6b, θ k and θ k +1 denote the flexible connection of the joint 61 and the joint 62 from any previous position, respectivelyRotational displacement of the head and/or the rod about the z-axis, andandrespectively, the rotational displacement theta of the joints 61 and 62 caused by the rotational displacement of the joints themselves and the previous_kAnd theta_k+1Rotational displacement behind the z-axis. The rotational displacement of the first joint 61 is shown about the z-axis, thereby angular deviation in the x-y planeAt this point. The rotational displacement of the second joint 62 is shown about the z-axis, thereby angular deviation in the x-y planeAt this point. Bending of the rod 60 about the z-axis due to the elasticity of the rod 60 is shown as an angular deviationIs the resulting joint 62(θ)_k+1) Minus the rotation at joint 61Followed by rotation.

Fig. 6c shows the elastic bar 60 in the same two-dimensional view as in fig. 6b, but illustrating the influence of gravity. The center of mass 63 of the bar 60 is assumed here to be at the center of the bar 60. The mass of the rod 60 creates a gravitational force that is countered by a torque at the preceding joint (not shown) during normal free space motion. In the figure, this preceding joint is the left joint 61, which comprises the force F and the torque M acting on the second joint 62 and thus affects the torque balance of the joint 61 via the bending rod 60. The amount of rotation produced at the location of the joint 62 is defined by the angle θ_cDescribed, thereby rotated about the z-axis. The displacement of the rod 60 along the y-axis at the position of the joint 62 due to gravity is determined by the relative absence of load (here horizontal)The centerline (e.g., 51, not shown) represents. In fig. 6c, the lever 60 is also shown when in another possible position, indicated by the dashed line 65. Here, the same loads F and M expressed in the part coordinate system (rod 65 is shown by the dashed coordinate axis at joint 61) produce the same deviation from θ_c(for the rod 65, not labeled), but the direction of gravity will be different. This dependence on the nominal joint angle (here for joint 61) is straightforward to deal with, but it can be appreciated from fig. 6c that there is also a change in the direction of gravity caused by the compliance experienced. However, the deflection is small compared to the motion and the change in gravity due to compliance is small and negligible for the robotic arm (as follows).

Fig. 6d shows the same elastic rod 60 as in fig. 6c, wherein the mass of the rod 60 is represented by two respective halves of the mass gravity acting on the joint 61 and the joint 62. The effect of the mass of the bar 60 on the other joints and the bending of the bar 60 itself due to the effect of the mass can then be catered for. This distribution can be used in the following equation. The mass of the rod 60 may be predetermined or estimated by using the method explained for example in application WO2014065744a 1.

Fig. 6e shows the same resilient bar 60 as in the previous fig. 6a-6d, when a force and/or torque is applied to the bar 60 such that the position of the first and second joints 61, 61 is not substantially displaced, but the bar 60 itself is shown bent into another possible shape, which is the bar 66 shown in dashed lines. The rod 60 has been displaced rotationally about the Z-axis, and thus in the x-y plane, with an angle from the first joint 61And the rod 60 is rotationally displaced about the z-axis at the second joint, having an angle theta, as seen from the second joint 62_k+1. Angle of rotationAnd theta_k+1Corresponds to that in fig. 6bThis type of deviation can also be determined using existing methods.

In fig. 6a-6d, the separation of a bar 60 with two joints 61, 62 connected thereto has been shown, and the resulting compliance and angle in different directions has been parameterized. The following will describe how these parameters can be obtained, and also how more complex characteristics of the compliance of the robot arm 2 (fig. 1) can be obtained.

To explain this method, a movement diagram of the robot arm 2 is shown in fig. 7. The movement diagram shows the connection of the various rods and joints of the robot arm 2. As shown, the robotic arm 2 is connected to a rigid base with a rod 22. The base and the rod 22 correspond to the base to which the joint 3 is connected in fig. 1. The attachment of the base of the robotic arm to the ground plate or floor is not considered a docking operation and will not be so addressed in this description. In fig. 7 the remaining rods 4, 6, 9, 10, 13 and 14 and joints 3, 5, 7, 8, 11 and 12 also have their counterparts.

In fig. 8, a robot arm 80 is shown in a two-dimensional view, having a plurality of joints 5, 7, 11 and a plurality of bars 6, 81, 82, 83. The robotic arm 80 in the figures shows the robotic arm 2 in a kinematic configuration in which the axes 1, 4 and 6 (see fig. 1) are fixed such that the remaining axes move in one of the planes depicted. The named quantities represent one possible parameterization that facilitates identification of compliance based on the acquired sensor data. As the reference signs show, the joints 5, 7 and 11 have their direct counterparts in the robot arm 2 of fig. 1, and are thus the joints 5, 7 and 11. Furthermore, the lever 6 has its direct counterpart which is the lever 6 of the robot arm 2 of fig. 1. In this configuration, the remaining rods 81, 82 and 83 are rod and joint combinations. Thus, the rod 81 here represents the joint 3 and the rod 4, the rod 82 represents the joint 8 and the rod 10, and the rod 83 represents the joint 12 and the rods 9, 13 and 14 of the robot arm 2 of fig. 1 and 7. The quantities shown in fig. 8 belong to the different joints and rods. Thus, x_kIndicating joint associated alongX-axis displacement of (2), y_kRepresenting displacement, theta, along the y-axis of the associated joint_kIndicating the rotational displacement before the joint,representing the rotational displacement after the joint, and q_kIndicating the joint angle of the next bar in the chain. As mentioned, the joint angle is used in the conversion into overall coordinates.

Method of producing a composite material

In fig. 9, a flow chart shows the steps of a method for determining at least one characteristic associated with a selected axis of a robotic arm 2. As previously mentioned, a shaft is defined as a joint that includes a motor and transmission system for actuation and a linkage connected thereto. The linkage may comprise one or several rods. In the method, the robot arm 2 is controlled by the controller 19 to perform the different steps of the method manually or automatically. The method may be stored as machine instructions or computer instructions in a computer program P in a computer readable storage medium 21 and executed by the control unit 20. When explaining the method, reference will now be made to the flow chart. The flow chart should not be interpreted as a series of steps performed in a particular order; the steps shown may be performed in an order other than that shown.

According to the method, the robot arm 2 is caused to realize a kinematic configuration of clamping by controlling the robot arm 2 to clamp the movable portion of the robot arm 2 to a position in space (a 1). As already mentioned above, the position in space may be provided by the docking object 18 (fig. 1). The robotic arm 2 may be programmed to change its end effector to connect to a tool in the tool station by using a tool changer. The robot arm 2, which is not equipped with a tool exchanger during its normal operation, may be manually equipped with the same gripping equipment or any other gripping equipment to perform the method, and thus any robot arm 2 may be calibrated. The clamp kinematics configuration has previously been defined as a configuration of a robot arm, wherein the robot arm is docked in a predefined pose of at least one DOF of a fixed end-effector (or any movable part of the robot arm 2 to be clamped). Since clamping all six endr DOF (or end flange or tool exchanger DOF) is feasible, this is assumed below. Although the robot arm 2 is clamped to a position in space, the controller 19 is configured to read an output value from an internal sensor of a joint of the robot arm 2. These values may be transmission system parameters that may be converted to joint parameters, such as clearance, compliance, and possibly other parameters. This is explained in more detail in WO2014065744a1 in connection with figures 2-7 of the application on pages 13-22.

The method further includes selecting an identified joint set including at least one joint of the robotic arm 2, wherein the at least one joint of the identified joint set is configured to control and monitor a selected axis for which an associated at least one characteristic is to be determined (a 2). The identification joint set is a set of joints, the smallest and usually one, which during normal operation of the robot arm actuates a corresponding set of levers having the characteristics to be determined. For each axis in the set, to identify a rod that bends in the plane of joint motion (fig. 5), the motor control is such that a certain joint torque (compensating for the effects of the non-linear joint drive system) is applied and the position and torque of the joint (again compensating for the effects of the non-linear joint drive system) are measured. The control of the joints in the set is not relevant in order to identify other (orthogonal to the movement of the preceding joint) rod characteristics. The joint or joints in the group may thus be in an unaltered or uncontrolled state and may only be monitored so that certain assumptions are satisfied.

In addition, the method comprises selecting an excitation joint set comprising at least one joint of the robot arm 2, the excitation joint set being configured for a gripping motion configuration of the robot arm 2 to excite at least one rod connected to the at least one joint of the identification joint set (a 3). The method also selects a gripping formation joint group (a4) of the robot arm 2. The clamping configuration joint set typically includes joints that are neither in the excitation joint set nor in the identification joint set. The joints are controlled such that the kinematic configuration is achieved such that the joints do not substantially affect the identification of the shaft characteristics and such that the clamping pose is achieved and maintained. For the latter, the docking attitude provided by the gripping device usually needs to be adjusted, but the joint (usually PKM) of the gripping device does not belong to (by definition) any configuration of joint set. The at least one joint of the joint set of the gripping construction according to one embodiment is not part of the identification joint set and the excitation joint set.

The different sets of taps explained above may be predetermined, may be calculated by the controller 19 taking into account a number of conditions, or may be randomly selected until the matrix involved has a sufficiently high rank (rank).

Thereafter, the method continues by actuating the firing joint set such that the selected shaft is fired while the gripping configuration joint set is controlled such that the gripping motion configuration is maintained (a 5). According to one embodiment, the set of gripping configuration joints is controlled such that the set of gripping configuration joints does not substantially affect the determination of the at least one characteristic associated with the selected shaft.

The actuator torque or torques used to actuate the firing joint set may be 10-15% of the maximum torque of the actuator(s). Upon actuation of the firing joint set, the one or more quantities are monitored with respect to actuator torque and/or joint position for at least one joint (a6) in the identification joint set and/or the firing joint set. Based on the monitored one or more quantities, the at least one characteristic of the selected shaft is determined (a 7). The at least one characteristic of the selected axis may be based on the monitored one or more quantities related to actuator torque and/or joint position combinations for determining at least one characteristic of a plurality of selected axes, each for the robotic arm 2.

Steps a1-a6 are advantageously repeated for a plurality of different gripping motion configurations to enable calculation of all characteristics of interest. For example, at least one characteristic of a plurality of selected axes, each for the robotic arm 2, may be determined. Thus, steps a1-a6 are repeated, wherein in the method the obtained gripping motion configuration of the robot arm 2 is different from the previously obtained gripping motion configuration of the robot arm 2, and the at least one characteristic of the selected axis is determined based on the determined characteristic of the selected axis in the different gripping motion configurations.

Step a7 may include using a matrix stiffness method. The matrix stiffness method utilizes the stiffness relationship of the rod and joint for deriving the rod and joint displacement of the robotic arm 2. As already shown in fig. 5-6e, the robot arm 2 may be modeled as a set of ideal bars interconnected at different joints of the robot arm 2. By using matrix mathematical methods, the stiffness characteristics of these elements can then be compiled into a single matrix equation that governs the behavior of the entire ideal structure. The matrix stiffness method will be described below with reference to a simple robotic arm 100 shown in fig. 10. The robot arm 100 comprises two levers connected by a joint AB: rod a and rod B. In this figure, one end of rod a is connected to joint AB, and the other end of rod a is rigidly connected to the base. Accordingly, one end of bar B is connected to joint AB, and the other end of bar B is shown rigidly connected to another base. This corresponds to gripping the robotic arm 100 in a certain gripping motion configuration. Rods a and B have their main extensions along the x-axis, and the y-axis is defined perpendicular to the x-axis. The end of lever a connected to the base forms a first node, the joint AB forms a second node, and the end of lever B connected to the second base forms a third node. In the figure, the displacement of the node is shown as x_k，x_kThe representation is a displacement along the x-axis, y_kThe expression is displacement along the y-axis, theta_kThe representation is a displacement along the axis of rotation (z-axis) of the joint AB before the joint AB, andthe representation is the displacement along the z-axis after the joint AB. The displacement of the first node is denoted x₀、y₀Andthus, when the first node is rigidly attached to the base, the initial displacement of the first node is zero. The displacement of the second node is denoted x₁、y₁、And theta₁And the displacement of the third node is represented as x₂、y₂And theta₂. Since the first and third nodes may not be shifted, x₂＝0、y₂0 and θ₂0. Reference is now made to fig. 8, which illustrates the corresponding displacement of the more complex robotic arm 80.

Let a representation of the part coordinates be given in the local coordinate system of the robot arm. In general, we can use functionsThe simulation hasThe function gives the force at the node to achieve the deformationThe component may be a joint or a rod of the robotic arm 100. When deformedWhen small, a common simplification is to assume linear elasticity, and the functionThis can then be expressed as:

wherein the content of the first and second substances,is the component stiffness matrix. The formula models what is used to represent elements in the FEM. We extend the model to deal with moving parts such as motors where forces or torques are generated in the part. Except for the component stiffness matrix which has already been determinedThe force on the part is also given by the force vector inside the partThe force can then be expressed as:

there are many different options for representing the bar structure and the bar stiffness matrix. For a planar robotic arm, it is feasible to give the rod six elastic DOF, three at each end. The bar stiffness matrix for each bar should be specified to capture the expected deformation at the component level. Rod stiffness matrixFor a rod k with six elastic DOF, and the linear behavior can be constructed as follows, as a variant of (4) below to emphasize the relationship of four independent parameters to them:

wherein the parameter a₁…a₄Typically representing an unknown stiffness parameter.

The six elastic DOFs of the flexible rod are not directly driven, but indirectly driven via forces from the joints involved, which depend on the stiffness of the rod in different directions. To perform simulations of stem deflection due to joint force/torque, it is convenient and standard (in solid mechanics) to use a component stiffness matrix (as a linear map, assuming that stem deflection is small compared to stem size and motion). To simplify the method according to the invention and the practical use involving identification and compensation, some stiffness matrix elements may be set to zero, which means that they are zero or that the compliance member is captured well enough by other stiffness elements. A known stiffness (e.g., from FEM analysis of the rod) may be set as the constant stiffness element. In practice, and in order to simplify this description, we assume that the rod bending according to fig. 6b means that the rod stiffness matrix (3) will contain only four parameters symmetrically distributed in a 6x6 matrix, to correspond to axial, lateral and rotational displacements in each end. Where the component has a constant cross-section, an example of a component stiffness matrix having an area A is as follows:

where L denotes the length of the rod, E denotes the tensile modulus of elasticity as known from hooke's law, and I denotes the moment of inertia of the cross-section.

The joint can also be represented in many different ways. Component stiffness matrixMay be configured as follows:

wherein, c_jThe stiffness of the axis of rotation of joint j is indicated. The joint is here assumed to be rigid in all directions except around the axis of rotation. The joint model also includes the motor that will produce the torque τ. The total force on the joint is then given by the following equation:

where θ is the rotational displacement before the joint, andis the rotational displacement behind the joint.

The global stiffness matrix (MSM) can now be combined using the component stiffness matrix for each rod and joint. Since the rod stiffness matrix is given in a local coordinate system where the rod stiffness matrix is constant, the matrix has to be converted into a global coordinate system in order to combine the global stiffness matrix. Such a transformation depends on the configuration defined by the joint coordinates with the robotic arm DOF elements. The transformation will rearrange the stiffness parameter positions in the component stiffness matrix; however, the stiffness parameters are still the same. Therefore, the rigidity of the robot arm varies with the configuration corresponding to the coordinate conversion. Here, the difference between the actuator/motor and the lever position caused by the influence of the transmission system is generally insignificant, since it is generally small compared to the joint angle, but in principle it is the joint angle that is relevant (and calculable according to WO2014065744a 1).

For each single clamping motion configuration, the bar stiffness matrix may be put together to form a larger MSM. For each clamping motion configuration, some MSM elements will be zero, and others will reflect constant rod stiffness elements. For another configuration, the other portion of the MSM will be non-zero and may be identified by measurements made in the clamping motion configuration. The contents of the MSM may thus be used to select a series of configurations such that all rod parameters of interest may be determined, for example, by non-linear optimization. Thus, the structure of the MSM is defined. The robotic arm 100 may be provided with sensors configured to generate sensor signals with sensor data to obtain sensor data to be used in the following optimization when in one or several gripping motion configurations. The sensor may be a force sensor configured to generate a sensor signal having force data.

The combination of MSMs will be described below with reference to fig. 11a-11 b. Using the enumerated displacement coordinates as shown on the left and top of the matrix K in fig. 11a, the MSM for SKM obtains an illustrative structure with bar blocks along and around the diagonal of the matrix, and joint blocks on the diagonal that overlap with the bars to which it is connected. Since there are more than two components connected to a common joint, for a PKM, or any robotic arm that includes any parallel linkage, there will be an MSM element formed from more than two overlapping component matrices. For example, if rod C were to be connected to joint AB (thereby causing displacement x)₁And y₁) This would mean more elements overlapping with the 2x2 block matrix, which in FIG. 11a is the overlap of rod A and rod B (for the overall displacement coordinate x)₁And y₁). The union joint or redundant robotic arm may also have an overlap of joint elements. Since the MSM is based on all the global displacements and any combination of links can be superimposed on the spanning structure at the displacement position according to the force/torque balance, it follows that any mechanical arm or mechanism can be represented. Thus, for any type of robot, it is advantageous to determine unknown parameters.

From newton's law, the sum of all forces is equal to zero in the rest state. This is therefore true for the nodes in our model, which is true anywhere else. We know that the force from part k isWherein the content of the first and second substances,depending on the defined configuration of the previously described components. We need to sum all forces in the same direction in each position. To do this, the local DOF of each stick needs to be converted into the global coordinate system of the robotic arm 2. This conversion can be described by equations (7) and (8) below. If the components in FIG. 10 are initially described in the coordinate system along rod A and rod B, we need to find the local DOFX_k、y_k、And theta_kMapping to a global coordinate system. We observe that this relationship is:

x_k＝cos(θ)u_x-sin(θ)u_y(7)

y_k＝sin(θ)u_x+cos(θ)u_y(8)

wherein x is_kAnd, y_kIs a displacement in the global coordinate system, u_xExtending along the main axis of the rod u_yExtending along the height of the rod. In the case of a plane, rotationAnd theta_kNot affected by coordinate changes, but for a general three-dimensional system there will also be a mapping between rotational coordinates. From the relationship in equations (7) and (8), we can form the coordinate transformation matrix L according to:

the coordinate transformation matrix transforms the component stiffness matrix in the local coordinate system to a global coordinate component stiffness matrix. In the three-dimensional case, where the rods may have any orientation, the transformation matrix will be more complex, but may be specified from a quaternion describing the rod direction. Global coordinate part stiffness matrix K for part K_kThen given as:

the force from component k on the node connected to component k is now given by:

we now sum all forces acting in each direction in each node. This is expressed in global coordinates by a component stiffness matrix K_kAdd to the corresponding location in k. This is similar to how the stiffness matrix is combined in the FEM. Furthermore, we have some boundary conditions at the robot base and the clamped end-piece, where the displacement is zero. The combination process is illustrated using fig. 11 a. As represented in fig. 11a, there is a rectangular block of MSM matrix k that is zero, i.e., is not part of any marked sub-matrix. The k-matrix illustrative block structure depends of course on how the displacements are enumerated. The enumeration used in this example is written on top and to the left of the k-matrix in fig. 11 a. Overlapping matrix blocks means that there is a sum of the effects from overlapping components, including the trigonometric functions necessary to convert from local displacement to global displacement according to the columns of the k-matrix, so that the force/torque balance is maintained at the location of the global coordinates. In this example, the elements of rod a that overlap the elements of rod B form here a 2x2 block matrix for the global displacement coordinates x1 and y 1. In a similar manner, the joint AB overlaps the rod to which it is connected. Since this is not a passive joint, the joint torque τ from actuation (by a motor via a transmission system, not shown in fig. 10) will produce non-zero elements on these columns of vector F. Additionally, for each clamping configuration, some of the MSM rod matrix elements will be zero, while other MSM elements will have values representing the rod and joint stiffness. In contrast to equation (1) for the part stiffness matrix in local coordinates including the rod, the slave equation(s) ((R)) depicted in FIG. 11a12) The system resulting from equation (13) refers to a global coordinate system, and thus a constant rod stiffness matrix appears in the MSM via a corresponding transformation, which includes a trigonometric function for each element. These functions may appear implicitly by means of a quaternion element representing the rod orientation corresponding to the joint angle q (see fig. 8).

The above simulations provide us with a system of equations for the form Ku-F. Let n be_aThe representation is the number of elastic DOF of the flexible robotic arm, which is equivalent to the number of rows and columns in K, and the same as the number of rows in u or F. The matrix K is formed by n_aUnknown stiffness parameterIs composed of n and the vector u is composed of n_u-6 unknown deformationsAnd six deformation components known as zero. The vector F is completely known. We define the function S as:

S＝S(X)＝Ku(12)

and isAll are unknown parameters. Thus, the DOF of the elastic portion of the system amounts to n_u. The goal is to minimize the residual norm (residual norm):

r＝‖S-F‖(13)

this can be done by using a conventional newton iterative solver. Thus, optimization is performed based on one or more monitored quantities. Specifically, the function S is linearized as:

S＝S₀+[J_kJ_u]X(14)

wherein S is₀＝S(X₀) And X₀Is an initial estimate of an unknown parameter, J_kIs a parameter of S (X) relative to stiffness_kJacobian matrix of, and J_uIs relative to the use in the phaseThe same initial guess is X₀Deformation u of_kThe jacobian matrix of. The vector X is solved by iteratively using the increment X obtained by solving equation (15):

S₀+[J_kJ_u]X＝F(15)

the Jacobian matrix has n_uRows and n_a+n_u-3 columns, and when n_a>At 6, the Jacobian matrix will typically be a singular matrix. To overcome this singularity, robotic arms are positioned in more configurations. For each new construct, we get n_uNew equation of (2), but n_uThe new equation of-6 is not known. Although the deformations are different, the stiffness parameters are the same in all configurations. Thus, vector X will follow n_u-6 additional deformation increase. The columns of the jacobian matrix will increase with the same number. The global stiffness matrix can then be solved and the stiffness parametersAnd deformation ofIs determined. Thus, the stiffness parameters of the mechanical arms, i.e. the properties to be determined by this method, are organized according to the structure of the MSM, which relates the possible unknown displacements of the levers and joints to the torque and force, so that any combination of series and parallel links can be represented. Thus, along with the underlying resolution strategy, the unknown properties are advantageously determined by the presented MSM structure.

The smallest possible number of constructions to obtain the nonsingular Jacobian matrix is:

equation (14) merely indicates that if the number of equations is less than n_CONFThe Jacobian matrix guarantees are singular, however, linear correlations between columns may still occur, and it may be useful to add more constructs. For each construct, the two Jacobian matrices are computed and combined into the global overall Jacobian matrix shown in FIG. 11 b.

The method has been shown here in connection with the simplified example of fig. 10, but it should be understood that the method can be applied to any robot arm, such as the robot arm 2 in fig. 1.

The robot arm 2 is subjected to the influence of gravity and the mass of the robot arm 2 will thus influence the shape of the rod and cause flexing of the robot arm parts. This means that gravity increases the bending of the rod. The influence of gravity can be decomposed into the influence of the rod gravity and the influence of the joint gravity. According to one embodiment, the method includes determining a gravitational effect value acting on the selected axis, and compensating the determined at least one characteristic of the selected axis for the determined gravitational effect value. The explained bar stiffness matrix (3) in principle simulates this bending caused by gravity, but the difference is that when the bar stiffness matrix (3) captures the bending caused by force F and torque M, gravity exerts an influence on another unknown position on the bar. To compensate for the main dynamic effects, a reasonable model assumes that the mass of the rod is a point mass in the center of gravity of the rod as already shown in fig. 6c, and that the rod has a uniform distribution of this bending between adjacent joints as already shown in fig. 6 d. On the one hand, this seems to be a contradiction, since distributed and uniform bending indicates distributed mass, which is contrary to the proposed simplified rod gravity influence model. On the other hand, such simplification is consistent and has several advantages:

● the complete Jacobian matrix after all required experiments will be part of an over-determined equation or system of equations to be solved by pseudo-inverse or non-linear optimization, and then the inaccuracies will be suppressed.

● this assumption is consistent with how most robots today are constructed.

● a more detailed model may require FEM analysis of the rod (or similar non-rigid body simulations) that can be done, but requires engineering that this method of the invention avoids in practice.

● stiffness parameter for the bar stiffness matrix (3)Can be used to also capture the rod gravitational effect, which can be managed within the framework of the method of the invention, as shown in fig. 6 d.

● there is (after a separate free space experiment to determine the gravitational effects of the joint) a clear and automatic way to include the gravitational effects of the rod in the identification of the rod characteristics. Even if these effects are not entirely true effects, these effects are a suitable simplification for the compensation using the rod characteristics.

● the quasi-static assumption used for the elastic dynamic model indicates that the rod inertia around its centroid is negligible.

According to one embodiment, the method comprises comparing the at least one characteristic with a previously obtained characteristic value or a predefined value, determining a difference between the at least one characteristic and the previously obtained characteristic value or the predefined characteristic value, comparing the difference with a difference threshold and determining the wear of the robot arm based on the result of the comparison. Thus, if the determined characteristic differs from any previously obtained characteristic value, or a predefined characteristic value representing a characteristic of the selected shaft, for example, having substantially no wear, or allowable wear, the wear of the robot arm may be determined by analysis. For example, the values of the characteristics may be determined and compared at different points in time. If the difference between the values is greater than the difference threshold, then it may be determined that the selected shaft is worn and a portion of the shaft needs to be replaced.

According to one embodiment, the robotic arms are parallel kinematic robotic arms.

According to another embodiment, the robot arm is a multi-arm robot arm, or a plurality of robots with a common workspace. The method may then be performed by passing the gripping motion configuration through the arm of one robot arm (or any selected moveable part of a robot arm) gripping the robot arm to the arm of any other robot arm (or any selected moveable part of a robot arm) of the robot arm.

According to one embodiment, the method comprises obtaining specific motion parameters by means of motion correction of the robot arm 2 and updating the motion parameters based on at least one determined characteristic of the selected axis.

The determined at least one characteristic of the robotic arm 2 may be used for a number of applications and aspects. For example, the at least one characteristic may be used to update nominal motion parameters of the robotic arm 2. The at least one characteristic may be used for motion correction of the robotic arm 2. According to another embodiment, the at least one characteristic is used for updating robot programs or motion control parameters of the robot arm 2.

The invention also relates to a computer program P associated with the system 1, wherein the computer program P comprises computer instructions configured to cause the control unit 19 to perform a method according to any one of the steps shown previously. The invention also relates to a computer program product comprising computer instructions stored on a computer readable storage medium 21 to perform a method according to any one of the steps shown above. Furthermore, the present invention relates to a computer program product comprising at least one characteristic obtained when executing the method according to any of the steps shown above, wherein the at least one characteristic is stored on a computer readable storage medium 21.

The illustrated method may be performed for multiple robots of the same series in order to obtain a nominal average for the rods and joints that may be used to determine a statistical distribution of these characteristics across the series of robots using statistical data. This data can then be used to compensate for rod compliance and joint compliance in the same type of robot.

The above explained method provides a more accurate way of determining the compliance of the robot than previously known solutions. Costs can be reduced since, for example, no calibration system or removal of the robot or locking of certain parts is required for performing the method, which also makes the method easier to perform than previously known solutions.

Examples of the invention

An example will now be explained with reference to fig. 12a-12d, which show the robotic arm 80 (fig. 8) in an undeformed (R1) and deformed state (R2) in a plurality of gripping motion configurations used in this example. The distortion is scaled in the figure for easier viewing. The robotic arm 80 includes three joints and four levers. Each rod has four stiffness parameters and each joint has one stiffness parameter. The motor torque is applied at the joint that produces the deformation of the mechanical arm. The joint values where the robotic arm is simulated to grip are randomly selected to be a number between-2 radians and the motor torque is randomly selected to be a number between-1 Nm and +1Nm, and we use 16 configurations to form the equation, four of which are shown in fig. 12.

In a certain kinematic configuration, the robotic arm 80 is a plan view of the robotic arm 2. That is, the joints 1, 4, and 6 of the robot arm 2 form a clamping structure joint group. In this example, random firing is used, with all other joints belonging to both the identification joint set and to the firing joint set. This method is useful if there is no high level of knowledge about the known robot structure, but a skilled operator can choose to have configurations of joints split into different groups (typically with more right angles), which would require fewer configurations to determine all the properties.

The motor torque values and force values are used as if the force/torque sensors were used at the endpieces (assuming that the gravity and motor torque are known, then the base force is also generated) to obtain the individual stiffness parameters of the robot arm. Thus, the forces at any end of the robot arm are known (i.e., F and R in fig. 11a are known). When performing the method, the end-effector of the robot arm is clamped to a set of fixed positions, but without additional clamping between the joint and the rod, no disassembly of any parts is necessary. This example and numerical solution are for the serial robot arm described, but the same principles can be applied to parallel moving robot arms. The elasticity is simulated using a stiffness matrix for each component that is combined in a manner similar to the combination of elements in the FEM into an overall stiffness matrix for all components of the robotic arm system. As stated earlier, the rod compliance may be characterized as bending, elongation and torsion of the rod due to movements of the joints affecting the rod, but also due to rod and joint gravity. Conventional motion models of robotic arms are used to determine new positions and orientations of components in the stiffness model due to compliance, etc. The deformation is then assumed to be small and then we can approximate the elastic behavior with a linear model in the non-deformed state. The output from the motion model is then the necessary information to convert each part stiffness matrix (3) into a global coordinate system, along with a mapping description between local part DOFs to global DOFs. In the case of future over-compliant robotic arms, which are not supported for their assumption of minor deformation, the global stiffness matrix will depend on the component position and orientation (i.e., the robotic joints) and the component deformation.

This example should be considered as merely an illustrative example of the method of the present invention and should not be considered as limiting the invention, which simply extends to other kinematic configurations, to three dimensions, and/or robotic arms with more DOF.

Practice of

According to a further embodiment, the method comprises determining one or several characteristics or the presence of such characteristics that do not satisfy the assumptions of the described model. The residual norm r, calculated according to equations (12), (13) and (14) as mentioned above, will actually be zero, satisfying the model assumption and with sufficient numerical conditions. By scaling by an appropriate amount, the numerical condition is improved and the equations are solved only by a few iterations. However, if the solution does not converge to a smaller residual, the robot arm has some un-simulated characteristics, such as a damaged bearing in the joint, or some other mechanical defect resulting from an improper design or some link production. As an example, fig. 13a and 13b show data from a method for determining drive train parameters of a robotic arm using the method described in WO2014065744a1, in this case for a six DOF robotic arm with a maximum payload of 185Kg, but loading about 15% of the maximum torque of shaft 2 and shaft 3 in a clamped configuration. The robot (not shown) has axes similar to those shown in fig. 1, but does not have a parallel portion 23 of the axis 3.

Fig. 13a shows the measured quantity position and torque of the shaft 2. The motion starts at the center and then moves for several cycles using a practically repeatable behavior. The vertical difference between the curves is twice the joint friction (joint frictionstimestwo) and the slope is the stiffness of the joint. Slight variations of these two parameters are clearly repeatable and can therefore be compensated within the joint control, so that the assumptions of the rod and joint models are satisfied very well.

Fig. 13b corresponds to fig. 13a with several load cycles, but for axis 3 it exhibits a non-ideal behavior. Primarily, the slope (of the line across the zero torque level) corresponding to the joint stiffness depending on the loading direction, and the vertical clearance exhibiting twice the joint friction, are not consistent with any well-defined parameter values. Using values from more than one cycle, to engage that splice in either the excitation splice set or the identification splice set will result in an excessively large residual and the largest element of that residual can be used to determine what splice is misbehaving.

The position versus torque curves of fig. 13a and 13b should be the same for each cycle for the applied cyclic load. In contrast, while the load curve in FIG. 13a shows the expected repeatability, the curve in FIG. 13b is different for different cycles. This is due to mechanical defects of the elbow of the robot and in such cases, if the measured quantities are obtained from such a number of cycles, the residual r is still larger than expected. The non-zero element of r then contains information of what part of the robot arm is problematic, although there will be no value representing a certain characteristic since it is outside the range of the model representing a well-behaved robot arm. Thus, such a situation can be determined by the current method.

By separating the joints so that for the mentioned robot only the non-ideal axis of the axis 3, having their joints in the set of clamped configuration joints with consistent loads during the determination of the characteristics of all other rods, the residual for this optimization (axis 3 parameters not determined) will be very close to zero. Only the second set of experiments in which shaft 3 was studied will confirm this inconsistency. The technician can observe this problem by learning fig. 13b, but the numerical inspection of the residuals of the present invention is more suitable for robotic analysis itself.

The present invention is not limited to the preferred embodiments described above. Various alternatives, modifications, and equivalents may be used. For example, clamping is preferably done by limiting one or several DOF in both directions of the respective motion, but by dividing it into two parts for each DOF, a double experiment covering each side can in principle be performed and then mounted together. This means that a robot contacting any object that is rigid or has a known flexibility will be able to determine the characteristics of some joints and/or rods. Accordingly, the above embodiments should not be taken as limiting the scope of the invention, which is defined by the appended claims.

Claims

1. A method for determining at least one characteristic associated with a selected axis of a robotic arm (2), wherein the robotic arm (2) is configured to be controlled by a controller (18) and the robotic arm (2) comprises at least one axis comprising a joint and a link connected to the joint, wherein the joint is configured to be actuated by an actuator, the method comprising:

-clamping a movable part of the robot arm (2) to a position in space by controlling the robot arm (2) such that the robot arm (2) achieves a clamping motion configuration;

-selecting an identified joint set comprising at least one joint of the robot arm (2), wherein at least one joint of the identified joint set is configured to control and monitor the selected axis for which an associated at least one characteristic is to be determined;

-selecting an excitation joint set comprising at least one joint of the robot arm (2), the excitation joint set being configured for the gripping motion configuration of the robot arm (2) to excite at least one rod connected to the at least one joint of the identification joint set;

-selecting a gripping configuration joint group of the robot arm (2);

-determining the at least one characteristic of the selected axis based on the monitored one or more quantities.

2. The method of claim 1, comprising determining the at least one characteristic of the selected axis based on a combination of the monitored one or more quantities related to actuator torque and/or joint position.

3. A method according to any one of the preceding claims, comprising determining at least one characteristic of a plurality of selected axes each for the robotic arm (2).

4. The method of any of the preceding claims, further comprising:

-repeating the method, wherein the obtained gripping motion configuration of the robot arm (2) is different from the gripping motion configuration of the robot arm (2) previously obtained in the method; and

-determining at least one characteristic of the selected axis based on the determined characteristics of the selected axis in different gripping motion configurations.

5. A method according to any of the preceding claims, wherein the step of determining the at least one characteristic comprises determining a robot stiffness matrix for the robot (2) based on the one or more monitored quantities.

6. The method of claim 5, comprising organizing properties according to the structure of the robotic arm stiffness matrix that relates potentially unknown displacements of levers and joints to torques and forces, such that any combination of series and parallel links can be represented, facilitating determination of these properties.

7. The method of any one of the preceding claims, wherein the step of determining the at least one characteristic comprises performing an optimization based on the one or more monitored quantities.

8. A method according to claim 7, wherein the robot arm (2) is provided with a sensor configured to generate a sensor signal with sensor data when in the gripping motion configuration, and wherein the method further comprises including sensor data from the robot arm (2) in the optimization.

9. The method of claim 8, wherein the sensor is a force sensor configured to generate a sensor signal having force data.

10. The method of any one of the preceding claims, wherein the at least one joint of the clamping configuration joint set is not part of the identification joint set and the excitation joint set.

11. The method of any preceding claim, wherein the clamping configuration joint set is controlled such that it does not substantially affect the determination of the at least one characteristic associated with the selected axis.

12. The method according to any of the preceding claims, comprising comparing the at least one characteristic with a previously obtained characteristic value or with a predefined characteristic value, determining a difference between the at least one characteristic and the previously obtained characteristic value or predefined characteristic value, comparing the difference with a difference threshold and determining the wear of the robot arm (2) based on the result of the comparison.

13. A method according to any of the preceding claims, wherein the robotic arms are parallel kinematic robotic arms.

14. The method of any one of the preceding claims, comprising

-obtaining specific motion parameters by means of motion correction of the robot arm (2); and

-updating a motion parameter of the robot arm (2) based on the at least one determined characteristic of the selected axis.

15. Use of the determined at least one characteristic determined according to any one of claims 1 to 14 for updating nominal motion parameters of a robot arm (2).

16. Use of the determined at least one characteristic determined according to any one of claims 1 to 14 for updating a robot program or a motion control parameter of a robot arm (2).

17. A system (1) for determining at least one characteristic associated with a selected axis of a robotic arm (2), the system (1) comprising a robotic arm (2) having at least one axis comprising a joint and a link connected to the joint; the system further comprises at least one actuator configured to actuate the joint and a controller configured to control the robotic arm (2), wherein the controller (19) comprises a control unit (20) and a computer-readable storage unit (21) comprising instructions configured to cause the control unit (20) to:

-selecting a set of identification joints comprising at least one joint of the robot arm (2), wherein the set of identification joints is configured to actuate a lever of the selected axis whose associated at least one characteristic is to be determined;

-selecting a gripping configuration joint group of the robot arm (2);

-determining the at least one characteristic of the selected axis based on the one or more monitored quantities; and

18. A computer program (P) associated with a system (1), wherein the computer program (P) comprises computer instructions configured to cause a control unit (19) to perform the method according to any one of claims 1 to 14.

19. A computer program product comprising computer instructions stored on a computer readable storage medium (21) to perform the method according to any one of claims 1 to 14.

20. A computer program product comprising the at least one characteristic obtained when performing the method according to any one of claims 1 to 14, wherein the at least one characteristic is stored on a computer readable storage medium.