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CN114952860B - Repetitive motion control method and system for mobile robots based on discrete-time neural dynamics - Google Patents

Repetitive motion control method and system for mobile robots based on discrete-time neural dynamics Download PDF

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Publication number
CN114952860B
CN114952860B CN202210713454.8A CN202210713454A CN114952860B CN 114952860 B CN114952860 B CN 114952860B CN 202210713454 A CN202210713454 A CN 202210713454A CN 114952860 B CN114952860 B CN 114952860B
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mobile robot
time
motion control
vector
discrete
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CN114952860A (en
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邱斌斌
李晓东
郭津津
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Guangzhou Sizhi Lai Medical Technology Co ltd
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Sun Yat Sen University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/161—Hardware, e.g. neural networks, fuzzy logic, interfaces, processor
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J18/00—Arms
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1661—Programme controls characterised by programming, planning systems for manipulators characterised by task planning, object-oriented languages

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  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Automation & Control Theory (AREA)
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  • Artificial Intelligence (AREA)
  • Physics & Mathematics (AREA)
  • Fuzzy Systems (AREA)
  • Mathematical Physics (AREA)
  • Software Systems (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
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  • Feedback Control In General (AREA)

Abstract

The invention relates to the field of robot control, and provides a method and a system for controlling repeated motion of a mobile robot based on discrete time neural dynamics, wherein the method comprises the steps of constructing a position layer kinematics equation, a speed layer kinematics equation and a physical limit constraint of the mobile robot, and converting the physical limit constraint into a speed layer double-end inequality constraint; constructing a repeated motion control scheme of the mobile robot based on a time-varying quadratic form optimization problem; constructing a continuous time zero nerve dynamics model; and constructing a discrete time zero nerve dynamics model according to a five-step explicit linear multi-step rule and the continuous time zero nerve dynamics model, calculating a control variable of the mobile robot, and performing repeated motion control on the mobile robot. The invention can realize the real-time repeated motion control of the mobile robot with physical limit constraint, and improves the motion instantaneity, path tracking precision and physical limit constraint processing capacity of the mobile robot.

Description

Mobile robot repetitive motion control method and system based on discrete time neural dynamics
Technical Field
The invention relates to the field of robot control, in particular to a method and a system for controlling repetitive motion of a mobile robot based on discrete time neural dynamics.
Background
The mobile robot mainly comprises a mobile platform and a mechanical arm fixed on the mobile platform. The repetitive motion control of the mobile robot requires that the final state of both the mobile platform and the robot arm remain consistent with the initial state after the closed path tracking is completed. If the mobile platform and the mechanical arm are not restored to the initial state, namely, a non-repeated motion phenomenon occurs, additional configuration adjustment or self-motion process is required to be carried out on the mobile robot, so that the task execution efficiency is greatly reduced.
The existing high-performance redundancy mechanical arm repetitive motion planning method and device comprises the steps of designing a quadratic type repetitive motion performance index and generating a quadratic type optimized redundancy analysis scheme; converting the quadratic form optimizing redundancy analysis scheme of the step into a quadratic form; and solving the quadratic programming by using a quadratic programming solver and transmitting a solving result to a lower computer controller to drive the redundant manipulator to move.
However, the above method expresses the problem of repetitive motion control of the mobile robot as a time-varying quadratic optimization problem, and solves the problem by applying a continuous time neuro-dynamics method or a numerical algorithm, which has low calculation accuracy and is difficult to be directly applied to a discrete time system, and the numerical algorithm needs to repeatedly perform a large number of iterative calculations at each calculation time point to obtain an optimal solution, so that efficient real-time repeatable motion control of the mobile robot cannot be performed.
Disclosure of Invention
The invention provides a method and a system for controlling the repetitive motion of a mobile robot based on discrete time neural dynamics, which are used for overcoming the defect that the mobile robot cannot be efficiently controlled in real time and repeatedly in the prior art.
In order to solve the technical problems, the technical scheme of the invention is as follows:
In a first aspect, the present invention provides a method for controlling repetitive motion of a mobile robot based on discrete-time neural dynamics, comprising the steps of:
s1: collecting motion data of a mobile robot;
S2: constructing a position layer kinematics equation, a speed layer kinematics equation and a physical limit constraint of the mobile robot, and converting the physical limit constraint into a speed layer double-end inequality constraint;
s3: combining the position layer kinematics equation, the speed layer kinematics equation and the speed layer double-end inequality constraint to construct a repeated motion control scheme of the mobile robot based on a time-varying quadratic optimization problem;
S4: based on a zero-change neural dynamics design rule, introducing an exponential penalty strategy into a repetitive motion control scheme of the mobile robot based on the time-varying quadratic form optimization problem, and constructing a continuous time zero-change neural dynamics model;
s5: constructing a discrete time zero nerve dynamics model according to a five-step explicit linear multi-step rule and the continuous time zero nerve dynamics model;
s6: inputting the motion data of the mobile robot into the discrete time zero neural dynamics model, and calculating a control variable of the mobile robot;
S7: and carrying out repeated motion control on the mobile robot according to the control variable.
In a second aspect, the present invention proposes a mobile robot repetitive motion control system based on discrete-time neural dynamics, comprising:
the acquisition module is used for acquiring motion data of the mobile robot;
the first construction module is used for constructing a position layer kinematics equation, a speed layer kinematics equation and a physical limit constraint of the mobile robot and converting the physical limit constraint into a speed layer double-end inequality constraint;
The second construction module is used for constructing a repeated motion control scheme of the mobile robot based on a time-varying quadratic optimization problem by combining the position layer kinematics equation, the speed layer kinematics equation and the speed layer double-end inequality constraint;
The third construction module is used for introducing an exponential penalty strategy into the repeated motion control scheme of the mobile robot based on the time-varying quadratic optimization problem based on the zero-change neural dynamics design rule, and constructing a continuous time zero-change neural dynamics model;
The fourth construction module is used for constructing a discrete time zero-change nerve dynamics model according to a five-step explicit linear multi-step rule and the continuous time zero-change nerve dynamics model;
The calculation module is used for calculating a control variable of the mobile robot according to the motion data of the mobile robot and the discrete time zero neural dynamics model;
and the control module is used for carrying out repeated motion control on the mobile robot according to the control variable.
In a third aspect, the present invention provides an electronic device, including a processor and a memory; the memory is used for storing programs; the processor executes the program to implement steps of any of the aspects of mobile robot repetitive motion control as based on discrete time neurodynamics.
In a fourth aspect, the present invention proposes a computer-readable storage medium storing a program that is executed by a processor to implement steps of any one of aspects of mobile robot repetitive motion control as based on discrete-time neurodynamics.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that: according to the invention, by constructing a position layer kinematics equation, a speed layer kinematics equation and a speed layer double-end inequality constraint of the mobile robot, a repeated motion control scheme of the mobile robot based on a time-varying quadratic optimization problem is designed, an exponential penalty strategy and a five-step explicit linear multi-step rule are introduced on the basis of the repeated motion control scheme of the mobile robot, a discrete time zero neuro-dynamics model is constructed, and a solving result of the next time point can be accurately predicted in each calculation time interval only by updating and calculating based on current and previous known data information once, so that the high-precision real-time repeated motion control of the mobile robot containing physical limit constraint is realized, the non-repeated motion phenomenon is effectively eliminated, and the motion instantaneity, the path tracking precision and the physical limit constraint processing capability of the mobile robot are effectively improved.
Drawings
Fig. 1 is a flowchart of a method for controlling repetitive motion of a mobile robot based on discrete-time neural dynamics.
Fig. 2 is a simplified model diagram of the mobile robot of the present invention.
Fig. 3 is a kinematic model diagram of the mobile platform of the present invention.
Fig. 4 is a diagram of the motion trajectory of the mobile robot and the actual trajectory and desired path of the end effector of the present invention.
Fig. 5 is a course angle diagram of the connection point between the mobile platform and the mechanical arm and the mobile platform according to the present invention.
Fig. 6 is an element trajectory diagram of a combined angle vector of the mobile robot of the present invention.
Fig. 7 is an element trajectory diagram of a combined velocity vector of the mobile robot of the present invention.
Fig. 8 is an element trace diagram of an end effector tracking error vector of the mobile robot of the present invention.
Fig. 9 is a diagram of a mobile robot repetitive motion control system architecture based on discrete-time neurodynamics.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the present patent;
The technical scheme of the invention is further described below with reference to the accompanying drawings and examples.
Example 1
Referring to fig. 1, the present embodiment provides a method for controlling repetitive motion of a mobile robot based on discrete time neural dynamics, which includes the following steps:
S1: and collecting motion data of the mobile robot.
S2: and constructing a position layer kinematics equation, a speed layer kinematics equation and a physical limit constraint of the mobile robot, and converting the physical limit constraint into a speed layer double-end inequality constraint.
S3: and constructing a repeated motion control scheme of the mobile robot based on the time-varying quadratic optimization problem by combining the position layer kinematics equation, the speed layer kinematics equation and the speed layer double-end inequality constraint.
In this embodiment, by uniformly converting the combination angle vector and the physical limit constraint of the combination speed vector of the mobile robot into an expression based on the combination speed vector, that is, the speed layer double-end inequality constraint, a repetitive motion control scheme of the mobile robot with a decision variable being the combination speed vector is constructed, so that the repetitive motion control scheme is re-expressed as a standard time-varying quadratic optimization problem resolved on the speed layer.
S4: and introducing an exponential penalty strategy into the repeated motion control scheme of the mobile robot based on the time-varying quadratic form optimization problem based on the zero-change neurodynamics design rule, and constructing a continuous time zero-change neurodynamics model.
S5: and constructing a discrete time zero nerve dynamics model according to a five-step explicit linear multi-step rule and the continuous time zero nerve dynamics model.
S6: and inputting the motion data of the mobile robot into the discrete time zero neural dynamics model, and calculating the control variable of the mobile robot.
S7: and carrying out repeated motion control on the mobile robot according to the control variable.
The method comprises the steps of constructing a position layer kinematics equation, a speed layer kinematics equation and a speed layer double-end inequality constraint of a mobile robot, designing a repeated motion control scheme of the mobile robot based on a time-varying quadratic form optimization problem, introducing an exponential penalty strategy and a five-step explicit linear multi-step rule on the basis of the repeated motion control scheme of the mobile robot, constructing a discrete time zero-change neural dynamics model, and accurately predicting a solving result of the next time point in each calculation time interval only by updating and calculating the current and previous known data information once, thereby realizing high-precision real-time repeated motion control of the mobile robot containing physical limit constraint, effectively eliminating non-repeated motion phenomenon, and effectively improving the motion instantaneity, path tracking precision and physical limit constraint processing capacity of the mobile robot.
Example 2
Referring to fig. 2-8, the present embodiment provides a method for controlling repetitive motion of a mobile robot based on discrete time neural dynamics, which includes the following steps:
s1: collecting motion data of a mobile robot;
In this embodiment, the motion data of the mobile robot includes a combined angle vector of the mobile robot, an actual position vector of the end effector, rotation angles of a left driving wheel and a right driving wheel of the mobile platform, a joint angle vector of a six-joint redundancy mechanical arm fixed on the mobile platform, a heading angle of the mobile platform, a combined speed vector of the mobile robot, and an expected path of the end effector.
S2: constructing a position layer kinematics equation, a speed layer kinematics equation and a physical limit constraint of the mobile robot, and converting the physical limit constraint into a speed layer double-end inequality constraint:
S2.1: determining a discrete time point of the motion of the mobile robot, and constructing a positional layer kinematics equation at the discrete time point.
In the present embodiment, at discrete points in timeIn the method, a position layer kinematic equation is constructed, and the expression is as follows:
Φ(Θk+1)＝ractual,k+1
where k is the update index, For a time step, t final is the final point in time of the entire calculation time interval,As an array of non-linear mapping functions,For a real set, Θ k+1 is the combined angle vector of the mobile robot, r actual,k+1 is the actual position vector of the end effector,For the rotation angle set of the left driving wheel and the right driving wheel of the mobile platform, theta k+1 is the joint angle vector of the six-joint redundancy mechanical arm fixed on the mobile platform.
Discrete time pointsFrom the sum of kThe value determination is generally referred to as the next discrete point in time, while t k is generally referred to as the current discrete point in time. The expression at the discrete time point t k+1 can better illustrate that the solution and problem to be solved is for the next discrete time point.
S2.2: and constructing a velocity layer kinematic equation according to the position layer kinematic equation.
In this embodiment, to monitor and control the process of the end effector tracking the desired path, the positioning error vector of the end effector is defined as e k+1＝ractual,k+1-rdesired,k+1, where r desired,k+1 is the desired path of the end effector.
By introducing the end effector positioning error described above as error feedback, the expression of the velocity layer kinematic equation is as follows:
Wherein phi k+1 is the course angle of the mobile platform, For a combined velocity vector of the mobile robot,For a set of rotational speeds of the left and right drive wheels of the mobile platform,For the joint velocity vector of the six-joint redundancy mechanical arm fixed on the mobile platform, J (phi k+1,θk+1) is a matrix related to jacobian; ζ k+1 is a vector containing end effector position error feedback,R desired,k+1 is the desired path of the end effector, lambda 1 is a settable parameter, which is the time derivative of the desired path of the end effector.
S2.3: the physical limit constraint is constructed by a set of discrete time-varying double-ended inequalities.
In this embodiment, the expression of the physical limit constraint of the mobile robot is as follows:
Wherein Θ - represents the lower limit of the combined angle vector of the mobile robot, Θ + represents the upper limit of the combined angle vector of the mobile robot, Representing the lower limit of the combined velocity vector of the mobile robot,The upper limit of the combined velocity vector of the mobile robot is represented.
S2.4: based on an exponential limit conversion strategy, the physical limit constraint is converted into a speed layer double-end inequality constraint, and the expression is as follows:
Where α k+1 represents the lower limit of the double-ended inequality constraint, β k+1 represents the upper limit of the double-ended inequality constraint, the i-th element α i,k+1 of α k+1 (i=1, 2, …, n), and the i-th element β i,k+1 of β k+1 (i=1, 2, …, n), respectively, are defined as follows:
Wherein exp (·) represents an exponential function; σ 1 >0 is a settable parameter for adjusting the deceleration amplitude; the parameter sigma 2 epsilon (0, 1) is a settable parameter for adjusting the critical area range where deceleration is required, i.e And
S3: and constructing a repeated motion control scheme of the mobile robot based on a time-varying quadratic optimization problem by combining the position layer kinematics equation, the speed layer kinematics equation and the speed layer double-end inequality constraint:
S3.1: and designing a repeated motion control scheme of the mobile robot by combining a position layer kinematics equation, a speed layer kinematics equation and a speed layer double-end inequality constraint, wherein the expression is as follows:
Wherein D k+1 represents a coefficient matrix of the repetitive motion performance index, D k+1 represents a coefficient vector of the repetitive motion performance index, and expressions of D k+1 and D k+1 are respectively as follows:
Wherein, C k+1 represents an auxiliary matrix related to the course angle of the mobile platform, and lambda 2、λ3 and lambda 4 are positive design parameters; p connection,k+1＝[xconnection,k+1;yconnectioh,k+1 is the connection point between the mobile platform and the mechanical arm, X connection,k+1 represents the coordinate of the connection point on the X axis, and Y connection,k+1 represents the coordinate of the connection point on the Y axis; p connection (0) represents the initial state of a connection point between the mobile platform and the mechanical arm, phi (0) is the initial state of a course angle of the mobile platform, theta (0) represents the initial state of a joint angle vector of the mechanical arm, and a is the distance from the left driving wheel and the right driving wheel to the midpoint of two wheel shafts; b is the distance from the midpoint of the two wheel shafts to the connecting point p connection,k+1, and gamma is the radius of the left driving wheel and the right driving wheel; 0 represents a zero matrix and I represents an identity matrix.
S3.2: and converting the repeated motion control scheme into a time-varying quadratic optimization problem to obtain the repeated motion control scheme based on the time-varying quadratic optimization problem, wherein the expression is as follows:
s.t.Gk+1xk+1＝gk+1
Hk+1xk+1≤hk+1
where T represents the transpose operator of the vector or matrix, For the decision variable vector to be solved for,For a positive definite symmetric coefficient matrix in the objective function,For the coefficient vector in the objective function,For a row-full rank coefficient matrix in the constraint of equations,For the coefficient vector in the constraint of the equation,As a coefficient matrix in the inequality constraint, Is a coefficient vector in the inequality constraint.
S4: based on a zero-change neural dynamics design rule, introducing an exponential penalty strategy into a repetitive motion control scheme of the mobile robot based on a time-varying quadratic form optimization problem, and constructing a continuous time zero-change neural dynamics model:
S4.1: introducing an exponential penalty strategy into a repetitive motion control scheme based on a time-varying quadratic optimization problem, eliminating inequality constraint in the repetitive motion control scheme, and obtaining the repetitive motion control scheme with the equality constraint only, wherein the expression is as follows:
s.t.Gk+1xk+1＝gk+1
Wherein, Is an exponential penalty function, the expression of which is as follows:
Where σ i(xk+1,tk+1)＝-Hi,k+1xk+1+hi,k+1 represents the ith auxiliary variable in the penalty function, H i,k+1 represents the row vector made up of the ith row element of matrix H k+1, H i,k+1 represents the ith element of vector H k+1, μ and ν represent positive design parameters.
S4.2: according to the Lagrangian multiplier method, the repetitive motion control scheme with only equality constraint is converted into a time-varying equation set problem, and the expression is as follows:
Uk+1yk+1+ω(xk+1,tk+1)＝0
wherein the expressions of U k+1、yk+1 and ω (x k+1,tk+1) are respectively as follows:
Wherein, Is a lagrange multiplier vector.
S4.3: carrying out continuous operation on the time-varying equation set problem to obtain a continuous time-varying equation set problem, wherein the expression is as follows:
U(t)y(t)+ω(x(t),t)＝0
s4.4: defining an error function of the continuous time-varying equation set problem as epsilon (t) =U (t) y (t) +omega (x (t), t) and combining a zero-ized neurodynamics design rule A continuous time nulling neuromotor model was obtained, the expression of which is as follows:
wherein η is a positive design parameter for adjusting the convergence rate; An array of monotonically increasing odd stimulus functions; m (x (t), t) represents a coefficient matrix, P (x (t), t) represents a time derivative matrix, u (x (t), t) represents a time derivative vector, and the expressions of M (x (t), P (x (t), t) and u (x (t), t) are respectively as follows:
s5: and constructing a discrete time zero nerve dynamics model according to a five-step explicit linear multi-step rule and the continuous time zero nerve dynamics model, and calculating a control variable of the mobile robot according to the discrete time zero nerve dynamics model.
In this embodiment, the five-step explicit linear multi-step rule is derived from a linear multi-step method, and can be used for discrete time solution of a differential equation form dynamics system. The model based on the five-step explicit linear multi-step rule can predictively calculate the solution of the next discrete time point through an explicit linear combination form by only using the results and derivative values of the current and previous five discrete time points, without using information of the next discrete time point. The five-step explicit linear multi-step rule involves six adjacent discrete points in time, i.e., includes five progressive steps, and is therefore referred to as five steps. And is called explicit since the five-step explicit linear multi-step rule does not need to use information to the next discrete point in time.
In this embodiment, the expression of the five-step explicit linear multistep rule is as follows:
Combining a five-step explicit linear multi-step rule with the continuous time zero-change neural dynamics model to obtain a discrete time zero-change neural dynamics model, wherein the expression is as follows:
Wherein, Calculating a value operator; The truncated error of the discrete time zero neural dynamics model is expressed as that the discrete time zero neural dynamics model has six-order calculation accuracy.
S6: and inputting the motion data of the mobile robot into the discrete time zero neural dynamics model, and calculating the control variable of the mobile robot.
S7: and carrying out repeated motion control on the mobile robot according to the control variable.
In this embodiment, the lower computer controller is used to drive the mobile robot to execute the repetitive motion control task according to the control variable.
In a specific implementation process, in order to ensure the convergence rate of the discrete-time thermodynamic model, a power-S-shaped function is selected as an excitation function.
In conducting numerical experiments, the end effector of a mobile robot is expected to track a complex lissajous pattern path, expressed as follows:
Where δ 1、δ2 and δ 3 are three constants that determine the desired path position.
Setting a time stepThe duration of the single repetition movement is t final =10s, the distance a between the left and right driving wheels and the middle point of the two wheel shafts is 0.32m, the distance b between the middle point of the two wheel shafts and the connecting point between the mobile platform and the mechanical arm is 0.1m, the radius gamma of the left and right driving wheels is 0.1025m, other parameters are set to be eta=25, mu=0.004, v=300 and sigma 1＝9,σ2＝0.1,λ1＝10,λ2＝λ3＝λ4 =30.
Furthermore, an initial position p connection(0)＝[xconnection(0);yconnection (0) = [ 0] of the connection point between the mobile platform and the robot arm; 0]m, initial heading angle phi (0) =0.1 rad of the mobile platform, combined angle vector Θ (0) = [0, pi/12, pi/3 ] T rad of the mobile robot. The physical limit constraints of the mobile robot are set as follows:
Θ+＝[∞,∞,0.524,2.356,1.088,6.283,6.283,6.283]Trad
Θ-＝-[∞,∞,0.524,0.175,6.283,6.283,6.283,6.283]Trad
Finally, the discrete time zero neural dynamics model is utilized to calculate and obtain a control variable, so that the high-precision real-time repetitive motion control of the mobile robot with physical limit constraint is realized.
As shown in fig. 4, the motion track of the mobile robot and the actual track and the expected path of the end effector of the present invention, it can be seen from fig. 4 that the actual track of the end effector coincides with the expected lissajous figure path, and the final state and the initial state of the mobile robot coincide after the path tracking task is completed. Fig. 5 is a diagram of a connection point between a mobile platform and a mechanical arm and a course angle of the mobile platform, fig. 6 is a diagram of element trajectories of combined angle vectors of the mobile robot, and fig. 5 and 6 show that three important variables for realizing repeated motion, namely, a connection point p connection,k+1 between the mobile platform and the mechanical arm, a course angle phi k+1 of the mobile platform and a combined angle vector Θ k+1 of the mobile robot, are returned to their initial states finally, so that the aim of coordinated repeated motion control of the mobile robot can be realized after the closed path tracking task of an end effector is completed. Fig. 7 is an element trajectory diagram of the combined velocity vector of the mobile robot according to the present invention, fig. 8 is an element trajectory diagram of the end effector tracking error vector of the mobile robot according to the present invention, and it can be seen from fig. 7 and 8 that the combined velocity vector of the mobile robotThe element tracks of the end effector converge to zero after the task execution is finished, and the X, Y, Z axis component of the end effector positioning error vector epsilon k+1＝ractual,k+1-rdesired,k+1 is smaller than 7×10 -6 m, so that the tracking precision of the end effector is obviously high enough. In addition, as can be seen from fig. 6 and 7, all elements of the combined angle vector and the combined speed vector of the mobile robot are limited within the given physical constraint upper and lower limits. In particular, the time-varying trajectory of the third joint angle θ 3,k+1 of the robotic arm of the mobile robot reaches the upper bound of the physical limit multiple times, but never crosses the upper bound. Obviously, when the angle theta 3,k+1 of the third joint is about to reach the upper limit of the physical limit, the double-end inequality constraint of the speed layer obtained based on the exponential limit conversion strategy is successfully activated, so that the speed of the third joint is further enabledDeceleration is performed to achieve avoidance of physical limits. It is worth noting that the average calculation time per update of the discrete time nulled neuro-dynamics model is about 9.3X10 -4 s, which is much smaller than the time step employedThereby meeting the requirement of strict real-time motion control of the mobile robot. In summary, these results well demonstrate high precision real-time repetitive motion control for mobile robots containing physical limit constraints.
Example 3
Referring to fig. 9, the present embodiment provides a mobile robot repetitive motion control system based on discrete time neural dynamics, including:
and the acquisition module is used for acquiring the motion data of the mobile robot.
The first construction module is used for constructing a position layer kinematics equation, a speed layer kinematics equation and a physical limit constraint of the mobile robot and converting the physical limit constraint into a speed layer double-end inequality constraint.
In this embodiment, a discrete time point is determined according to the update index and the time step, and a positional layer kinematic equation is constructed at the discrete time point.
In this embodiment, a velocity layer kinematic equation is constructed according to the position layer kinematic equation.
In this embodiment, the physical limit constraint is constructed by a set of discrete time-varying double-ended inequalities.
In this embodiment, the physical limit constraint is converted into a speed layer double-ended inequality constraint based on an exponential limit conversion strategy.
And the second construction module is used for constructing a repeated motion control scheme of the mobile robot based on the time-varying quadratic optimization problem by combining the position layer kinematics equation, the speed layer kinematics equation and the speed layer double-end inequality constraint.
In this embodiment, a repetitive motion control scheme of the mobile robot is designed in combination with a positional layer kinematic equation, a velocity layer kinematic equation, and a velocity layer double-end inequality constraint.
In this embodiment, the repetitive motion control scheme is converted into a time-varying quadratic optimization problem, and a repetitive motion control scheme based on the time-varying quadratic optimization problem is obtained.
And the third construction module is used for introducing an exponential penalty strategy into the repeated motion control scheme of the mobile robot based on the time-varying quadratic optimization problem based on the zero-change neural dynamics design rule, and constructing a continuous time zero-change neural dynamics model.
In this embodiment, an exponential penalty strategy is introduced into a repetitive motion control scheme based on a time-varying quadratic optimization problem, and inequality constraint in the repetitive motion control scheme is eliminated, so as to obtain a repetitive motion control scheme with only equality constraint.
The repetitive motion control scheme with only equality constraints is converted to a time-varying system of equations problem according to the Lagrangian multiplier method. And carrying out continuous operation on the time-varying equation set problem to obtain a continuous time-varying equation set problem, providing an error function of the continuous time-varying equation set problem, and combining a zero-change neural dynamics design rule to obtain a continuous time zero-change neural dynamics model.
And the fourth construction module is used for constructing a discrete time zero-change nerve dynamics model according to a five-step explicit linear multi-step rule and the continuous time zero-change nerve dynamics model, and calculating a control variable of the mobile robot according to the discrete time zero-change nerve dynamics model.
And the calculation module is used for calculating the control variable of the mobile robot according to the motion data of the mobile robot and the discrete time zero neural dynamics model.
And the control module is used for carrying out repeated motion control on the mobile robot according to the control variable.
In this embodiment, the lower computer controller is used to drive the mobile robot to execute the repetitive motion control task according to the control variable.
The method comprises the steps of constructing a position layer kinematics equation, a speed layer kinematics equation and a speed layer double-end inequality constraint of a mobile robot, designing a repeated motion control scheme of the mobile robot based on a time-varying quadratic form optimization problem, introducing an exponential penalty strategy and a five-step explicit linear multi-step rule on the basis of the repeated motion control scheme of the mobile robot, constructing a discrete time zero-change neural dynamics model, and accurately predicting a solving result of the next time point in each calculation time interval only by updating and calculating the current and previous known data information once, thereby realizing high-precision real-time repeated motion control of the mobile robot containing physical limit constraint, effectively eliminating non-repeated motion phenomenon, and effectively improving the motion instantaneity, path tracking precision and physical limit constraint processing capacity of the mobile robot.
The terms describing the positional relationship in the drawings are merely illustrative, and are not to be construed as limiting the present patent;
it is to be understood that the above examples of the present invention are provided by way of illustration only and are not intended to limit the scope of the invention. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the invention are desired to be protected by the following claims.

Claims (7)

1.基于离散时间神经动力学的移动机器人重复运动控制方法，其特征在于，包括：1. A method for controlling repetitive motion of a mobile robot based on discrete-time neural dynamics, comprising: S1：采集移动机器人的运动数据；S1: Collect motion data of mobile robot; S2：构建移动机器人的位置层运动学方程、速度层运动学方程和物理极限约束，并将所述物理极限约束转换为速度层双端不等式约束，包括：S2: Construct the position layer kinematic equation, velocity layer kinematic equation and physical limit constraints of the mobile robot, and convert the physical limit constraints into double-end inequality constraints of the velocity layer, including: S2.1：确定移动机器人运动的离散时间点，并在离散时间点中，构建位置层运动学方程，其表达式如下所示：S2.1: Determine the discrete time points of the mobile robot's motion and In the above example, the kinematic equation of the position layer is constructed, and its expression is as follows: 其中，为更新索引，为时间步长，为整个计算时间区间的最终时间点，为非线性映射函数阵列，为实数集合，为移动机器人的组合角度向量，为末端执行器的实际位置向量，为移动平台左驱动轮和右驱动轮的旋转角度集，为固定在移动平台上六关节冗余度机械臂的关节角度向量；in, To update the index, is the time step, is the final time point of the entire calculation time interval, is the nonlinear mapping function array, is the set of real numbers, is the combined angle vector of the mobile robot, is the actual position vector of the end effector, is the rotation angle set of the left and right driving wheels of the mobile platform, is the joint angle vector of the six-joint redundant manipulator fixed on the mobile platform; S2.2：根据所述位置层运动学方程，构建速度层运动学方程，其表达式如下所示：S2.2: According to the position layer kinematic equation, construct the velocity layer kinematic equation, the expression of which is as follows: 其中，为移动平台的航向角，为移动机器人的组合速度向量，为移动平台左驱动轮和右驱动轮的旋转速度集，为固定在移动平台上六关节冗余度机械臂的关节速度向量，为与雅可比相关的矩阵为含末端执行器位置误差反馈的向量，为末端执行器的期望路径的时间导数，为末端执行器的期望路径，为可设定的参数；in, is the heading angle of the mobile platform, is the combined velocity vector of the mobile robot, is the rotation speed set of the left and right driving wheels of the mobile platform, is the joint velocity vector of the six-joint redundant manipulator fixed on the mobile platform, is the matrix associated with the Jacobian is the vector containing the position error feedback of the end effector, is the time derivative of the desired path of the end effector, is the desired path of the end effector, is a configurable parameter; S2.3：通过离散时变双端不等式组，构建物理极限约束，其表达式如下所示：S2.3: The physical limit constraint is constructed by discrete time-varying two-terminal inequalities, which are expressed as follows: 其中，表示移动机器人的组合角度向量的下限，表示移动机器人的组合角度向量的上限，表示移动机器人的组合速度向量的下限，表示移动机器人的组合速度向量的上限；in, represents the lower limit of the combined angle vector of the mobile robot, represents the upper limit of the combined angle vector of the mobile robot, represents the lower limit of the combined velocity vector of the mobile robot, represents the upper limit of the combined velocity vector of the mobile robot; S2.4：基于指数型极限转换策略，将所述物理极限约束转换为速度层双端不等式约束，其表达式如下所示：S2.4: Based on the exponential limit conversion strategy, the physical limit constraint is converted into a velocity layer double-end inequality constraint, the expression of which is as follows: 其中，表示双端不等式约束的下极限，表示双端不等式约束的上极限，的第个元素)，以及的第个元素)，分别有如下定义：in, represents the lower limit of the two-ended inequality constraint, represents the upper limit of a double-ended inequality constraint, No. Elements ),as well as No. Elements ), respectively, are defined as follows: 其中，表示指数函数；为可设定的参数，用于调节减速幅度；参数为可设定的参数，用于调节需要减速的临界区域范围，即和；in, represents the exponential function; It is a settable parameter used to adjust the deceleration range; parameter It is a configurable parameter used to adjust the critical area range that needs to be decelerated, that is, and ; S3：结合所述位置层运动学方程、速度层运动学方程和速度层双端不等式约束，构建基于时变二次型优化问题的移动机器人的重复运动控制方案，包括：S3: Combining the position layer kinematic equation, velocity layer kinematic equation and velocity layer double-end inequality constraints, a repetitive motion control scheme of a mobile robot based on a time-varying quadratic optimization problem is constructed, including: S3.1：结合位置层运动学方程、速度层运动学方程和速度层双端不等式约束，设计移动机器人的重复运动控制方案，其表达式如下所示：S3.1: Combining the position layer kinematic equation, velocity layer kinematic equation and velocity layer double-end inequality constraints, design a repetitive motion control scheme for the mobile robot, which is expressed as follows: min. min. s.t. st 其中，表示重复运动性能指标的系数矩阵，表示重复运动性能指标的系数向量，和的表达式分别如下所示：in, The coefficient matrix representing the performance index of repeated motion, The coefficient vector representing the performance index of the repetitive motion, and The expressions are as follows: 其中，表示与移动平台航向角相关的辅助矩阵，、和均为正的设计参数；为移动平台与机械臂之间的连接点，表示所述连接点在X轴的坐标，表示所述连接点在Y轴的坐标； 表示移动平台与机械臂之间的连接点的初始状态，为移动平台的航向角的初始状态，表示机械臂的关节角度向量的初始状态，为左驱动轮和右驱动轮到两轮轴中点的距离；为两轮轴中点到连接点的距离，为左驱动轮和右驱动轮的半径；，表示单位矩阵；in, represents the auxiliary matrix related to the heading angle of the mobile platform, , and are all positive design parameters; is the connection point between the mobile platform and the robotic arm. represents the coordinate of the connection point on the X axis, Represents the coordinate of the connection point on the Y axis; represents the initial state of the connection point between the mobile platform and the robotic arm, is the initial state of the heading angle of the mobile platform, represents the initial state of the joint angle vector of the robot arm, is the distance from the left driving wheel and the right driving wheel to the midpoint of the two wheel axles; From the midpoint of the two axles to the connection point The distance is the radius of the left and right driving wheels; , represents the identity matrix; S3.2：将所述重复运动控制方案转换为一个时变二次型优化问题，得到基于时变二次型优化问题的重复运动控制方案，其表达式如下所示：S3.2: Convert the repetitive motion control scheme into a time-varying quadratic optimization problem, and obtain a repetitive motion control scheme based on the time-varying quadratic optimization problem, the expression of which is as follows: min. min. s.t. st 其中，表示向量或矩阵的转置运算符，为待求解的决策变量向量，为目标函数中的正定对称系数矩阵，为目标函数中的系数向量，为等式约束中的行满秩系数矩阵，为等式约束中的系数向量，为不等式约束中的系数矩阵，为不等式约束中的系数向量；in, represents the transpose operator of a vector or matrix, is the decision variable vector to be solved, is the positive definite symmetric coefficient matrix in the objective function, is the coefficient vector in the objective function, is the row full rank coefficient matrix in the equality constraint, is the coefficient vector in the equality constraint, is the coefficient matrix in the inequality constraints, is the coefficient vector in the inequality constraint; S4：基于零化神经动力学设计法则，将指数型惩罚策略引入所述基于时变二次型优化问题的移动机器人的重复运动控制方案，构建连续时间零化神经动力学模型；S4: Based on the zeroing neurodynamics design rule, an exponential penalty strategy is introduced into the repetitive motion control scheme of the mobile robot based on the time-varying quadratic optimization problem to construct a continuous-time zeroing neurodynamics model; S5：根据五步显式线性多步法则与所述连续时间零化神经动力学模型，构建离散时间零化神经动力学模型；S5: constructing a discrete-time annulization neural dynamics model based on the five-step explicit linear multi-step rule and the continuous-time annulization neural dynamics model; S6：将所述移动机器人的运动数据输入所述离散时间零化神经动力学模型，计算出移动机器人的控制变量；S6: inputting the motion data of the mobile robot into the discrete time annulization neural dynamics model to calculate the control variables of the mobile robot; S7：根据所述控制变量对移动机器人进行重复运动控制。S7: Performing repeated motion control on the mobile robot according to the control variables. 2.根据权利要求1所述的基于离散时间神经动力学的移动机器人重复运动控制方法，其特征在于，S4的具体步骤包括：2. The method for controlling repetitive motion of a mobile robot based on discrete-time neural dynamics according to claim 1, wherein the specific steps of S4 include: S4.1：将指数型惩罚策略引入基于时变二次型优化问题的重复运动控制方案，消除所述重复运动控制方案中的不等式约束，得到仅带等式约束的重复运动控制方案，其表达式如下所示：S4.1: An exponential penalty strategy is introduced into the repetitive motion control scheme based on the time-varying quadratic optimization problem, and the inequality constraints in the repetitive motion control scheme are eliminated to obtain a repetitive motion control scheme with only equality constraints, which is expressed as follows: min. min. s.t. st 其中，为指数型惩罚函数，其表达式如下所示：in, is an exponential penalty function, and its expression is as follows: 其中，表示惩罚函数中的第i个辅助变量，表示由矩阵的第行元素所构成的行向量，表示向量的第个元素，和表示正的设计参数；in, represents the i- th auxiliary variable in the penalty function, Represented by the matrix No. The row vector composed of row elements, Representation vector No. elements, and represents a positive design parameter; S4.2：根据拉格朗日乘子法，将所述仅带等式约束的重复运动控制方案转换为一个时变方程组问题，其表达式如下所示：S4.2: According to the Lagrange multiplier method, the repetitive motion control scheme with only equality constraints is converted into a time-varying equation system problem, which is expressed as follows: 其中，、和的表达式分别如下所示：in, , and The expressions are as follows: 其中，为拉格朗日乘子向量；in, is the Lagrange multiplier vector; S4.3：将所述时变方程组问题进行连续化操作，得到连续时间时变方程组问题，其表达式如下所示：S4.3: The time-varying equations are continuous-operated to obtain a continuous-time time-varying equations, the expression of which is as follows: S4.4：将所述连续时间时变方程组问题的误差函数定义为，并结合零化神经动力学设计法则，得到连续时间零化神经动力学模型，其表达式如下所示：S4.4: The error function of the continuous-time time-varying equations problem is defined as , and combined with the zeroing neurodynamic design principle , we get the continuous-time zeroing neural dynamics model, which is expressed as follows: 其中，为正的设计参数，用于调节收敛速率；为由单调递增的奇激励函数所构成的阵列；表示系数矩阵，表示时间导数矩阵，表示时间导数向量，且、和的表达式分别如下所示：in, is a positive design parameter used to adjust the convergence rate; is an array of monotonically increasing odd excitation functions; represents the coefficient matrix, represents the time derivative matrix, represents the time derivative vector, and , and The expressions are as follows: 。 . 3.根据权利要求2所述的基于离散时间神经动力学的移动机器人重复运动控制方法，其特征在于，S5中，根据五步显式线性多步法则与所述连续时间零化神经动力学模型，构建离散时间零化神经动力学模型，其表达式如下所示：3. The method for repetitive motion control of a mobile robot based on discrete-time neural dynamics according to claim 2 is characterized in that, in S5, a discrete-time annihilation neural dynamics model is constructed according to a five-step explicit linear multi-step rule and the continuous-time annihilation neural dynamics model, and its expression is as follows: 其中，为计算赋值运算符；in, is the calculation assignment operator; )，；为离散时间零化神经动力学模型的截断误差，表示离散时间零化神经动力学模型具有六阶的计算精度。 ), ; is the truncation error of the discrete-time annihilation neural dynamics model, indicating that the discrete-time annihilation neural dynamics model has a sixth-order computational accuracy. 4.根据权利要求1~3任一项所述的基于离散时间神经动力学的移动机器人重复运动控制方法，其特征在于，S7中，采用下位机控制器根据所述控制变量，驱动移动机器人执行重复运动控制任务。4. The method for repetitive motion control of a mobile robot based on discrete-time neural dynamics according to any one of claims 1 to 3 is characterized in that, in S7, a lower computer controller is used to drive the mobile robot to perform repetitive motion control tasks according to the control variables. 5.基于离散时间神经动力学的移动机器人重复运动控制系统，应用于权利要求1~4任一项所述的基于离散时间神经动力学的移动机器人重复运动控制方法，其特征在于，包括：5. A mobile robot repetitive motion control system based on discrete time neural dynamics, applied to a mobile robot repetitive motion control method based on discrete time neural dynamics as claimed in any one of claims 1 to 4, characterized in that it comprises: 采集模块，用于采集移动机器人的运动数据；A collection module, used to collect motion data of the mobile robot; 第一构建模块，用于构建移动机器人的位置层运动学方程、速度层运动学方程和物理极限约束，并将所述物理极限约束转换为速度层双端不等式约束；The first building module is used to build the position layer kinematic equation, velocity layer kinematic equation and physical limit constraints of the mobile robot, and convert the physical limit constraints into velocity layer double-end inequality constraints; 第二构建模块，用于结合所述位置层运动学方程、速度层运动学方程和速度层双端不等式约束，构建基于时变二次型优化问题的移动机器人的重复运动控制方案；The second building module is used to construct a repetitive motion control scheme of the mobile robot based on a time-varying quadratic optimization problem by combining the position layer kinematic equation, the velocity layer kinematic equation and the velocity layer double-end inequality constraint; 第三构建模块，用于基于零化神经动力学设计法则，将指数型惩罚策略引入所述基于时变二次型优化问题的移动机器人的重复运动控制方案，构建连续时间零化神经动力学模型；The third building block is used to introduce an exponential penalty strategy into the repetitive motion control scheme of the mobile robot based on the time-varying quadratic optimization problem based on the zeroing neural dynamics design rule, and to build a continuous-time zeroing neural dynamics model; 第四构建模块，用于根据五步显式线性多步法则与所述连续时间零化神经动力学模型，构建离散时间零化神经动力学模型；A fourth construction module is used to construct a discrete-time annulization neural dynamics model according to the five-step explicit linear multi-step rule and the continuous-time annulization neural dynamics model; 计算模块，用于根据所述移动机器人的运动数据和所述离散时间零化神经动力学模型，计算出移动机器人的控制变量；A calculation module, used for calculating the control variables of the mobile robot according to the motion data of the mobile robot and the discrete time annulization neural dynamics model; 控制模块，用于根据所述控制变量对移动机器人进行重复运动控制。The control module is used to perform repetitive motion control on the mobile robot according to the control variables. 6.一种电子设备，其特征在于，包括处理器以及存储器；所述存储器用于存储程序；所述处理器执行所述程序实现如权利要求1~4中任一项所述的基于离散时间神经动力学的移动机器人重复运动控制方法。6. An electronic device, characterized in that it includes a processor and a memory; the memory is used to store programs; the processor executes the program to implement the repetitive motion control method of a mobile robot based on discrete-time neural dynamics as described in any one of claims 1 to 4. 7.一种计算机可读存储介质，其特征在于，所述存储介质存储有程序，所述程序被处理器执行实现如权利要求1~4中任一项所述的基于离散时间神经动力学的移动机器人重复运动控制方法。7. A computer-readable storage medium, characterized in that the storage medium stores a program, and the program is executed by a processor to implement the repetitive motion control method of a mobile robot based on discrete-time neural dynamics as described in any one of claims 1 to 4.
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