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CN112847430B - Intrinsic safety design method for cooperative robot - Google Patents

Intrinsic safety design method for cooperative robot Download PDF

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CN112847430B
CN112847430B CN201911169657.XA CN201911169657A CN112847430B CN 112847430 B CN112847430 B CN 112847430B CN 201911169657 A CN201911169657 A CN 201911169657A CN 112847430 B CN112847430 B CN 112847430B
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CN112847430A (en
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王洪光
于海斌
潘新安
胡明伟
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Shenyang Institute of Automation of CAS
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Abstract

本发明涉及协作机器人领域,具体地说是一种协作机器人本质安全设计方法,包括:步骤一、对协作机器人工作性能分析;步骤二、协作机器人上层设计;步骤三、对协作机器人进行风险分析,确定安全风险类型和安全性评价指标;步骤四、进行机器人工作性能与安全性能相关性分析,确定对协作机器人工作性能与安全性能存在耦合影响的指标;步骤五、建立人机交互撞击模型并绘制基于人体生物力学限制指标危险等级安全表,根据所述安全表确定耦合指标参数范围;步骤六、根据步骤五中获得的耦合指标参数范围,在步骤二优化后的协作机器人基础上进安全设计。本发明能够均衡相互耦合的协作机器人安全性能指标和工作性能指标,使两者同时最大化。

Figure 201911169657

The invention relates to the field of collaborative robots, in particular to an intrinsic safety design method for a collaborative robot, comprising: step 1, analyzing the working performance of the collaborative robot; step 2, designing the upper layer of the collaborative robot; and step 3, performing risk analysis on the collaborative robot, Determine the types of safety risks and safety evaluation indicators; Step 4, carry out the correlation analysis between the working performance and safety performance of the robot, and determine the indicators that have a coupled impact on the working performance and safety performance of the collaborative robot; Step 5. Establish and draw a human-computer interaction impact model Based on the human biomechanical limit index danger level safety table, the coupling index parameter range is determined according to the safety table; step 6, according to the coupling index parameter range obtained in step 5, the safety design is carried out on the basis of the optimized collaborative robot in step 2. The invention can balance the safety performance index and the working performance index of the mutually coupled collaborative robot, so as to maximize the two at the same time.

Figure 201911169657

Description

Intrinsic safety design method for cooperative robot
Technical Field
The invention relates to the field of cooperative robots, in particular to an intrinsic safety design method of a cooperative robot.
Background
The cooperative robot is a robot capable of directly interacting with a person in a designated cooperative area, and has the characteristics of man-machine fusion, safety, easiness in use, sensitivity, accuracy, flexibility, universality and the like. The cooperative robot breaks through the limit of man-machine separation, shares a working space with people, is suitable for man-machine cooperation tasks in non-structural environments, and improves the automation level of medium and small enterprises.
Different from a traditional industrial robot which seeks working performance maximization and works in a closed structure environment, the cooperative robot needs to seek the maximization of the working performance under the constraint of safety, namely the safety of physical man-machine interaction, and how to simultaneously achieve the working performance and the safety performance maximization of the cooperative robot is a difficult point of the design of the conventional cooperative robot.
Disclosure of Invention
The invention aims to provide an intrinsic safety design method for a cooperative robot, which can balance the safety performance index and the working performance index of the cooperative robot coupled with each other, maximize the safety performance index and the working performance index of the cooperative robot at the same time and provide a basis for the mechanical design and the control system design of the cooperative robot.
The purpose of the invention is realized by the following technical scheme:
a collaborative robot intrinsic safety design method comprises the following steps:
the method comprises the following steps: analyzing the working performance of the cooperative robot, and determining a working performance index parameter value of the robot according to the working task of the robot;
step two: the cooperative robot is designed in an upper layer, and the robot is optimized according to the working performance index parameter value determined in the step one;
step three: performing risk analysis on the cooperative robot, and determining a safety risk type and a safety evaluation index;
step four: performing correlation analysis of the working performance and the safety performance of the robot, and determining indexes which have coupling influence on the working performance and the safety performance of the cooperative robot;
step five: establishing a human-computer interaction impact model, drawing a safety table based on human body biomechanics restriction index danger level according to the human-computer interaction impact model, and determining an index parameter range with coupling influence in the fourth step according to the safety table;
step six: and according to the coupling index parameter range obtained in the fifth step, safety design is carried out on the basis of the optimized cooperative robot in the second step, and safety evaluation is carried out through safety evaluation indexes in the third step after the design is finished.
In the first step, the robot is divided into a low-load robot, a medium-load robot and a high-load robot according to the operation type of the robot.
And in the second step, the configuration optimization is firstly carried out on the cooperative robot, and then the precision optimization is carried out on the cooperative robot.
In step three, the safety risk type analysis comprises an impact type, a personnel stress type and a injured part of the personnel.
The safety performance evaluation indexes in the third step are as follows:
Figure BDA0002288359470000021
in the formula (1), N is a safety performance parameter of the designed robot, and N isCIs a human body biomechanical limiting parameter.
And in the fourth step, determining optimized parameters of the robot speed and the effective quality by constructing a coupling matrix diagram of the working performance and the safety performance of the cooperative robot.
And step five, obtaining the relation between the relative speed of the robot and the effective mass of the robot by establishing a human-computer interaction impact model:
Figure BDA0002288359470000022
in the above formula (9), vrelIs the relative speed, F, of the robot before collision with a personlimM is a biomechanical limit index of the human bodyRIs the effective mass of the robot, mHIs the effective mass of the human impact site, k is the hooke coefficient, where Flim、k、mHAnd obtaining the numerical value according to the safety risk type determined in the third step, drawing a safety table based on the human body biomechanical limit index danger level according to the formula (9), and selecting the range of the effective quality and speed performance parameters of the robot according to the safety table as a combination point of the effective quality and speed performance of the robot on the boundary of the design interval.
The human-computer interaction impact model establishment process comprises the following steps:
the transfer energy generated during the human-computer interaction impact is as follows:
Figure BDA0002288359470000023
Figure BDA0002288359470000024
in the above formulas (2) and (3), μ is the effective mass of both at the time of a human-machine collision, vrelIs the relative speed of the robot before collision with a person, CRIs the elastic recovery coefficient.mRIs the effective mass of the robot, mHIs the effective mass of the human impact site.
Assuming inelastic contact between the robot and the person at impact, i.e. CRWhen the energy is equal to 0, the transfer energy generated during the man-machine interaction impact is as follows:
Figure BDA0002288359470000031
assuming that the collision part of the human body is an undamped linear spring, the elastic potential energy stored by the linear spring is as follows:
Figure BDA0002288359470000032
in the above formula (5), Δ x is the amount of compression by contact, k is the hooke's coefficient, and F is the impact force by contact.
Assuming that the transfer energy generated by the collision is all stored in the linear spring in the form of elastic potential energy, then:
ΔW=E (6);
namely, it is
Figure BDA0002288359470000033
The relationship between the relative speed and the impact force in the human-computer interaction process is as follows:
Figure BDA0002288359470000034
the relation between the relative speed and the effective mass of the robot is obtained by substituting the formula (3) for the formula (8)
Figure BDA0002288359470000035
The invention has the advantages and positive effects that:
1. the invention can balance the safety performance and the working performance of the mutually coupled cooperative robots, maximize the safety performance and the working performance of the cooperative robots at the same time, provide basis for the mechanical design, the control system design and the like of the cooperative robots, provide an important theoretical basis for the intrinsic safety design of the cooperative robots, and can be popularized to the safety design of robot systems such as service robots, exoskeleton robots and the like.
2. The invention has carried out the intrinsic safety design to the cooperative robot SHIR5, the robot is applied to the robot cooperative task such as 3C assembly, detection successfully, has realized the maximization of working property and security performance, has verified the validity of this method.
Drawings
Figure 1 is a flow chart of the method of the present invention,
FIG. 2 is a safety chart of risk level based on biomechanical restriction indicators of human body,
figure 3 is a diagram of the configuration and dimensional parameters of a cooperative robot according to embodiment 1 of the present invention,
figure 4 is a diagram of a robot working performance and safety performance coupling matrix,
fig. 5 is a safety chart based on the human hand safety index risk level according to embodiment 1 of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in fig. 1, the present invention comprises the steps of:
the method comprises the following steps: and analyzing the working performance of the cooperative robot, and determining the working performance index parameter value of the robot according to the working task of the robot.
According to the robot operation type, the robot is divided into a low-load robot, a medium-load robot and a high-load robot, wherein:
(1) the low-load robot mainly performs the work of circuit board assembly, visual inspection and the like, and the requirements on the working performance of the low-load robot are low load and high speed (the load is 0.5 Kg-20 Kg, and the tail end speed of the robot is more than 10 m/s);
(2) the medium-load robot mainly engages in the work of toy assembly, part transportation and the like, and the working performance requirements are medium load and medium speed (the load is 20 Kg-60 Kg, and the tail end speed of the robot is more than 5 m/s);
(3) the high-load robot is mainly used for automobile assembly, spot welding, stacking and the like, and the high-load robot has high load and low speed (the load is more than 60Kg, and the tail end speed of the robot is less than 5m/s) on the working performance.
According to the operation business engaged in by the cooperative robot, specific parameter values of the working performance index of the robot are determined, wherein the specific parameter values comprise load, robot tail end speed, robot freedom degree, working space, robot precision and the like.
Step two: and (4) cooperating the upper layer design of the robot, and optimizing the robot according to the working performance index parameter value determined in the step one.
And 2.1, carrying out configuration optimization on the cooperative robot, wherein the working performance indexes of the cooperative robot comprise the freedom degree and the working space of the robot.
In the step 2.1, according to a reference document ' Humingwei, Kinghonang, Panxinan ', and the like ', a cooperative robot motion performance analysis and simulation [ J ] is reported by an intelligent system, 2017,12(1):75-81.
And 2.2, performing precision optimization on the cooperative robot on the basis of the step 2.1, wherein the working performance indexes of the cooperative robot comprise robot pose repeatability and pose accuracy (robot precision).
Step 2.2 above can be optimized using MATLAB numerical analysis software according to the reference "HU M W, WANG H G, PAN X A, et al.
Step three: and carrying out risk analysis on the cooperative robot, and determining a safety risk type and a safety evaluation index.
And 3.1, risk analysis, and safety risk confirmation according to different operation conditions of the robot.
Risks generated in the physical human-computer interaction process mainly include various collision conditions, including unconstrained impact, partially constrained impact, secondary impact caused by the impact and the like, and the reasons for causing personal injuries include static force, static pinch point force, static contact pressure, dynamic impact force, impact pinch point force, impact contact pressure, energy transfer and the like, and the parts of the personal which are easy to be injured are different according to different operation tasks.
Step 3.2, determining a human body biomechanical limit index causing human body injury according to the safety risk type confirmed in the step 3.1, and determining a safety performance evaluation index, wherein the safety performance evaluation index formula is as follows:
Figure BDA0002288359470000051
in the formula (1), N is a safety performance parameter of the designed robot, and N isCIs a human body biomechanical limiting parameter. The above formula (1) can be obtained according to the reference "Ikuta K, Ishi i H, Nokata M.safe Evaluation Method of Design and Control for Human-carbon Robots [ J]The International Journal of Robotics Research,2003,22(5): 281-.
And fourthly, carrying out correlation analysis on the working performance and the safety performance of the robot, and determining indexes with coupling influence on the working performance and the safety performance of the cooperative robot.
Obviously, the working performance indexes of all robots cannot be improved on the premise of ensuring the safety of human-computer interaction. In fact, the safety design of the cooperative robot is that the safety of the robot is balanced with the working performance indexes, and the performance indexes are independent or coupled.
As shown in fig. 4, in this step, the optimized parameters are determined as the robot speed and the effective quality by constructing a coupling matrix diagram of the working performance and the safety performance of the cooperative robot.
The working performance index parameters of the cooperative robot mainly comprise dexterity (degree of freedom and working space), agility (terminal speed), precision (repeatability and accuracy of terminal pose of the robot), load (rated load), flexibility (force perception) and lightness (self weight of a mechanical arm), and in order to ensure the working performance of the robot, the indexes are improved or maximized as much as possible.
The safety performance indexes for measuring the safety of the robot mainly comprise static force, static pinch point force, static contact pressure, impact force, impact pinch point force, impact contact pressure and dead weight impact force, and the safety of the robot can be ensured only by reducing or minimizing the safety performance indexes as much as possible.
And strong coupling exists between certain working performance indexes and safety performance indexes, and how to balance the indexes is an important task for carrying out safety design on the robot.
As shown in fig. 4, the present invention constructs a robot performance and safety performance coupling matrix diagram according to the analysis of the cooperative robot performance and safety performance, wherein "+" represents that two design indicators are positively correlated, such as weight reduction (self weight of mechanical arm) and robot safety design limiting criterion are positively coupled, i.e. the smaller the robot quality is, both the work performance and the safety performance are better, "-" represents that two design indicators are negatively correlated, such as robot agility (robot end speed) and load are reversely coupled with the robot safety design limiting criterion, which means that the increase of the robot speed and load improves the work performance of the robot but sacrifices the safety performance, and blank represents that there is no correlation between two design parameters. The analysis of whether or not there is coupling between the various performance parameters described above is well known in the art.
According to the method shown in fig. 4, the design parameters of coupling and decoupling of the working performance and the safety performance of the robot can be obtained through correlation analysis, for the decoupling design parameters, the decoupling design parameters are optimized to ensure the improvement of the working performance of the robot, such as the maximization of the robot precision, the maximization of the robot dexterity and the like, and for the coupling design parameters, optimization calculation is performed through an optimization algorithm, and since the rated load of the robot is usually a set value during design, the parameters of the effective mass (light weight) and the terminal speed (agility) of the robot are selected to be optimized according to the method shown in fig. 4.
And fifthly, establishing a human-computer interaction impact model, drawing a safety table based on human body biomechanics limit index danger level according to the human-computer interaction impact model, and determining an index parameter range with coupling influence on the working performance and the safety performance of the cooperative robot according to the safety table.
The specific process is as follows:
the transfer energy generated during the human-computer interaction impact is as follows:
Figure BDA0002288359470000061
Figure BDA0002288359470000062
in the above formulas (2) and (3), μ is the effective mass of both at the time of a human-machine collision, vrelIs the relative speed of the robot before collision with a person, CRIs the elastic recovery coefficient. m isRIs the effective mass of the robot, mHIs the effective mass of the human impact site.
Assuming inelastic contact between the robot and the person at impact, i.e. CRWhen the energy is equal to 0, the transfer energy generated during the man-machine interaction impact is as follows:
Figure BDA0002288359470000063
assuming that the collision part of the human body is an undamped linear spring, the elastic potential energy stored by the linear spring is as follows:
Figure BDA0002288359470000071
in the above formula (5), Δ x is the amount of compression by contact, k is the contact stiffness, and F is the impact force by contact.
Assuming that the transfer energy generated by the collision is all stored in the linear spring in the form of elastic potential energy, then:
ΔW=E (6);
namely, it is
Figure BDA0002288359470000072
The relationship between the relative speed and the impact force in the human-computer interaction process is as follows:
Figure BDA0002288359470000073
the relation between the relative speed and the effective mass of the robot is obtained by substituting the formula (3) for the formula (8)
Figure BDA0002288359470000074
In the above formula (9), mRIs the effective mass of the robot, mHIs the effective mass of the human impact part, mu is the effective mass of the human impact part and the human impact part when the human is collided, vrelIs the relative speed of the robot before collision with the human, k is the hooke coefficient, FlimIs a biomechanical limit index of human bodies.
Determining the maximum limiting force F of the impact part of the operator not being injured during the collision according to the safety risk type determined in the step threelimAnd the effective mass and the elastic coefficient of the impact part of the operator, and a safety table based on the human body biomechanical limit index danger level is drawn according to the formula (9), the drawn safety table is shown in figure 2, and the effective mass and speed performance parameter range of the robot is selected according to the figure 2 to be the combination point of the effective mass and speed performance of the robot on the boundary of the design interval, so that the working performance and the safety performance of the robot can be maximized.
The above formulae (3) to (9) are obtained according to the reference "Intrasicality Safer Robots" and FIG. 2 can be drawn by MATLAB numerical analysis software.
And step six, according to the effective mass and speed performance parameter range of the robot obtained in the step five, carrying out safety design on the basis of the optimized cooperative robot in the step two, selecting a corresponding driving and transmission mode during design so that the effective mass and speed performance parameters of the robot meet the requirements in the step five, and additionally, following a series of existing safety design requirements during design, such as minimizing the mass and inertia of the robot, eliminating all pinch points, maximizing the clamping radius and the like, wherein the existing safety design requirements can refer to a document of 'Intra chair Safer Robots'.
After the cooperative robot is designed, the robot is required to be subjected to safety evaluation by establishing an impact model and according to the formula (1) confirmed in the step three. Specific evaluation procedures can be found in the references "Sangg-DuckLee, Byeong-SangKim, Jae-BokSong. human-robot compatibility model with effective mass and design for a specific tester [ J ]. Advanced robots, 2013, 27 (3): 189-: 357, 366 ", etc., may be implemented based on the numerical analysis software MATLAB.
The following example is provided to specifically describe the specific process of the present invention.
Example 1:
the specific flow of this embodiment is as follows:
the method comprises the following steps: and analyzing the working performance of the cooperative robot.
According to the requirement that the cooperative robots share the working space with people, the robot working tasks are selected, the working tasks (the load is 0.5 Kg-20 Kg, and the tail end speed of the robot is more than 10m/s) such as 3C assembly, detection, sorting and the like are mainly executed, and specific parameter values of relevant performance indexes of the robots, including the degree of freedom, the working space, the precision and the like of the robots, are determined according to the working tasks engaged by the cooperative robots. In the embodiment, the degree of freedom of the robot is 7, the working space is 900mm, the precision is +/-0.1 mm (repeatability and accuracy of pose of the end pose of the robot), and the load is 5 Kg.
Step two: and (4) collaborating the upper layer design of the robot, and optimizing the robot according to the index parameter value determined in the step one.
And 2.1, carrying out configuration optimization synthesis on the cooperative robot according to the performance parameters of the robot, such as the degree of freedom, the working space and the like, wherein the optimized robot parameters are shown in figure 3.
2.2, on the basis of the configuration optimization and integration of the robot, performing precision optimization on the cooperative robot according to performance parameters such as pose repeatability, pose accuracy and the like of the robot, wherein the random motion precision of each joint after optimization in the embodiment is as follows:
Δθ′1=Δθ′2=4.8×10-5rad
Δθ′3=Δθ′4=6.4×10-5rad
Δθ′5=Δθ′6=Δθ′7=1.2×10-4rad。
and thirdly, performing risk analysis on the cooperative robot, and determining a safety risk type and a safety evaluation index parameter.
Step 3.1, analyzing the collision situation generated by the cooperative robot in the physical human-computer interaction process in the embodiment, determining the most dangerous collision situation in the human-computer interaction process as constraint collision, and determining that the main reason for causing personnel injury is dynamic impact force, and the probability of hand injury is the largest in the human-computer interaction process.
Step 3.2, according to the safety risk analysis in the step 3.1, determining that the biomechanical limit index of the human body is Flim280N, k 75N/mm and m is the effective mass of the impact partH0.6 Kg. Wherein the biomechanical limit index of the human body is Flim280N is obtained from a reference "ISO/TS 15066Robots and viral devices-colorful Robots", with a hooke coefficient of 75N/mm and an effective mass of mH0.6Kg is a basic parameter for intrinsic safety design of cooperative robots, and can be obtained according to references of "investment of intellectual Properties of the Human Body", Physics of the Human Body ", and the like, and a safety evaluation index is obtained according to the above formula (1).
And fourthly, carrying out correlation analysis on the working performance and the safety performance of the robot, and determining design parameters with coupling influence on the working performance and the safety performance of the cooperative robot as the speed and the effective quality of the robot by constructing a coupling matrix diagram of the working performance and the safety performance of the robot.
And fifthly, establishing a human-computer interaction impact model, drawing a danger level safety table based on the human body biomechanical restriction index according to the human-computer interaction impact model, and selecting effective quality and speed performance parameters of the robot according to the danger level safety table of the human body biomechanical restriction index so as to maximize the working performance and safety performance of the robot.
Confirming the effective mass and the elastic coefficient of the part impacted by the operator during collision and the maximum limiting force F of the part which is not injured according to the third steplimAnd according to the relation between the relative speed and the effective mass of the robot, namely the above equation (9), a danger level safety table based on the human hand mechanics restriction index is drawn as shown in fig. 5, and the effective mass and speed performance parameter range of the robot is determined according to fig. 5.
And step six, according to the range of the effective quality and speed performance parameters of the robot obtained in the step five, performing safety design on the basis of the optimized cooperative robot in the step two, selecting corresponding driving and transmission modes to enable the effective quality and speed performance parameters of the robot to meet the range requirements in the step five, additionally, following a series of existing safety design requirements during design, and after the cooperative robot is designed, performing safety evaluation on the robot by establishing a collision model and according to the formula (1) confirmed in the step three.

Claims (6)

1. A collaborative robot intrinsic safety design method is characterized in that: the method comprises the following steps:
the method comprises the following steps: analyzing the working performance of the cooperative robot, and determining a working performance index parameter value of the robot according to the working task of the robot;
step two: the cooperative robot is designed in an upper layer, and the robot is optimized according to the working performance index parameter value determined in the step one;
step three: performing risk analysis on the cooperative robot, and determining a safety risk type and a safety evaluation index;
step four: performing correlation analysis of the working performance and the safety performance of the robot, and determining indexes which have coupling influence on the working performance and the safety performance of the cooperative robot; determining optimized parameters of robot speed and effective quality by constructing a coupling matrix diagram of the working performance and the safety performance of the cooperative robot;
step five: establishing a human-computer interaction impact model, drawing a safety table based on human body biomechanics restriction index danger level according to the human-computer interaction impact model, and determining an index parameter range with coupling influence in the fourth step according to the safety table;
obtaining the relation between the relative speed of the robot and the effective quality of the robot by establishing a human-computer interaction impact model:
Figure FDA0003510431440000011
in the above formula (9), vrelIs the relative speed, F, of the robot before collision with a personlimM is a biomechanical limit index of the human bodyRIs the effective mass of the robot, mHIs the effective mass of the human impact site, k is the hooke coefficient, where Flim、k、mHObtaining the numerical value according to the safety risk type determined in the third step, drawing a safety table based on the human body biomechanical limit index danger level according to the formula (9), and selecting the range of the effective quality and speed performance parameters of the robot as a combination point of the effective quality and speed performance of the robot on the boundary of a design interval according to the safety table;
step six: and according to the coupling index parameter range obtained in the fifth step, safety design is carried out on the basis of the optimized cooperative robot in the second step, and safety evaluation is carried out through safety evaluation indexes in the third step after the design is finished.
2. The collaborative robot intrinsic safety design method of claim 1, wherein: in the first step, the robot is divided into a low-load robot, a medium-load robot and a high-load robot according to the operation type of the robot.
3. The collaborative robot intrinsic safety design method of claim 1, wherein: and in the second step, the configuration optimization is firstly carried out on the cooperative robot, and then the precision optimization is carried out on the cooperative robot.
4. The collaborative robot intrinsic safety design method of claim 1, wherein: in step three, the safety risk type analysis comprises an impact type, a personnel stress type and a injured part of the personnel.
5. The collaborative robot intrinsic safety design method of claim 1, wherein: the safety performance evaluation indexes in the third step are as follows:
Figure FDA0003510431440000021
in the formula (1), N is a safety performance parameter of the designed robot, and N isCIs a human body biomechanical limiting parameter.
6. The collaborative robot intrinsic safety design method of claim 1, wherein: the human-computer interaction impact model establishment process comprises the following steps:
the transfer energy generated during the human-computer interaction impact is as follows:
Figure FDA0003510431440000022
Figure FDA0003510431440000023
in the above formulas (2) and (3), μ is the effective mass of both at the time of a human-machine collision, vrelIs the relative speed of the robot before collision with a person, CRM is an elastic recovery coefficientRIs the effective mass of the robot, mHEffective mass of the human impact site;
assuming that the robot is in collision with a personIn non-elastic contact, i.e. CRWhen the energy is equal to 0, the transfer energy generated during the man-machine interaction impact is as follows:
Figure FDA0003510431440000024
assuming that the collision part of the human body is an undamped linear spring, the elastic potential energy stored by the linear spring is as follows:
Figure FDA0003510431440000025
in the formula (5), Δ x is the compression amount generated by contact, k is the hooke coefficient, and F is the impact force generated by contact;
assuming that the transfer energy generated by the collision is all stored in the linear spring in the form of elastic potential energy, then:
ΔW=E (6);
namely, it is
Figure FDA0003510431440000031
The relationship between the relative speed and the impact force in the human-computer interaction process is as follows:
Figure FDA0003510431440000032
substituting the formula (3) for the formula (8) to obtain the relation between the relative speed and the effective mass of the robot as follows:
Figure FDA0003510431440000033
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