A method for suppressing flexible vibration of space manipulator

Abstract

The present invention relates to a method for suppressing flexible vibration of a space manipulator, the steps of which include: discretely obtaining the end motion trajectory; setting the coefficient of the zero space term and the optimization algorithm parameters; constructing the inverse kinematics relationship between the end trajectory of the space manipulator and the joint trajectory containing the zero space term at the velocity level and the acceleration level; constructing a dynamic motion model of a flexible manipulator driven by the joint trajectory motion to describe the flexible vibration of the end of the manipulator; obtaining the amplitude of the flexible vibration of the end of the manipulator through the flexible vibration calculation of the end of the manipulator, and comparing it with the amplitude of the flexible vibration of the end of the manipulator before optimization to determine whether the requirements for flexible vibration suppression are met. The present invention realizes the conversion of the desired end trajectory into the joint motion trajectory containing the zero space term based on the polynomial end trajectory difference and the minimum norm method inverse kinematics relationship.

Description

Technical Field

[0001] The invention relates to a method for suppressing flexible vibration of a space manipulator, and belongs to the technical field of robots. Background Art

[0002] The space manipulator has the characteristics of light weight, large structure size and obvious joint flexibility. It is a complex flexible multi-body system with strong coupling and high nonlinearity. How to effectively improve the positioning accuracy of the manipulator system and reduce elastic vibration at the same time is one of the important problems that need to be solved urgently. The research on this issue has received widespread attention from many scholars at home and abroad.

[0003] Without adding other equipment, the main method of flexible vibration suppression is to optimize the design by adding vibration suppression equipment to the robot arm or shaping the input signal (weight cost or computing resource cost). The existing method uses input signals of special frequencies to complete vibration suppression, which is completely decoupled from the dynamic characteristics of the robot arm, has poor robustness, consumes a lot of computing resources, and is difficult to achieve rapid expansion and application. Summary of the invention

[0004] The technical problem solved by the present invention is: to overcome the deficiencies of the prior art and to propose a method for suppressing flexible vibration of a space manipulator, which is used to suppress the flexible vibration of the manipulator when the weight of the robot or manipulator is limited and the computing resources in the control system are limited.

[0005] The solution of the present invention is:

[0006] A method for suppressing flexible vibration of a space manipulator, comprising the steps of:

[0007] S1. Discrete the terminal motion trajectory. According to the expected terminal position, the expected terminal trajectory is discretized by a quintic polynomial function, and the terminal motion trajectory X in the time domain is decomposed;

[0008] S2, setting the null space term coefficients and optimization algorithm parameters;

[0009] S3, initialization calculation of joint motion trajectory, constructing the inverse kinematics relationship between the end trajectory of the spatial manipulator and the joint trajectory including the zero space term at the velocity level and the acceleration level;

[0010] S4, flexible manipulator dynamics model construction, constructing a flexible manipulator dynamics motion model driven by the above joint trajectory motion to describe the flexible vibration of the end of the manipulator;

[0011] S5. Obtain the flexible vibration amplitude of the end of the robotic arm through calculation of the flexible vibration of the end of the robotic arm, and compare it with the flexible vibration amplitude of the end of the robotic arm before optimization to determine whether it meets the requirements of flexible vibration suppression.

[0012] Furthermore, in S1,

[0013]

[0014] In the formula, t represents the current movement time, t f represents the total planning time, r 0 and r f They represent the initial position and the expected final position of the end of the robot arm respectively.

[0015] Furthermore, the terminal speed It can be solved as:

[0016]

[0017] Furthermore, the terminal acceleration It can be solved as:

[0018]

[0019] Furthermore, in S3, based on the minimum norm method, the inverse kinematics relationship between the end trajectory of the spatial manipulator and the joint trajectory including the zero space term is constructed as follows:

[0020]

[0021] In the formula, is the joint angular velocity, is the joint angular acceleration; J is the Jacobian matrix of the robot arm, is the derivative of the Jacobian matrix, J + is the pseudo-inverse matrix of J, J + =J T (JJ T ) -1 ; I is the unit matrix.

[0022] Furthermore, the joint motion trajectory θ is:

[0023]

[0024] Δt is the calculation step size.

[0025] Furthermore, in S4, the flexible vibration of the end of the robot arm is described as:

[0026]

[0027] Where q is the generalized coordinate, and the joint motion angle θ is selected. is the second-order derivative of the generalized coordinates M is the system mass matrix; C is the constraint equation, which is related to the generalized coordinates q and time t; C qrepresents the partial differential matrix of the constraint equation with respect to the generalized coordinate q; λ is the Lagrange multiplier; F is the elastic force matrix, which is related to the generalized coordinate q; Q is the generalized external force matrix, which is also related to the generalized coordinate q.

[0028] Furthermore, the flexible vibration is δ max =max(|X act -X|), X act is the actual end position under the current motion trajectory.

[0029] Furthermore, in S5,

[0030] 5.1 If the flexible vibration control requirements are met,

[0031] The system optimization model is expressed as:

[0032]

[0033] in, and They are and The lower and upper boundaries of .

[0034] Each generation of particle swarm optimization generates null space term coefficients and If the minimum flexible vibration δ under the current algebra is calculated according to the dynamic equation max Less than the expected value δ limit , then the optimization ends, and the zero spatial term coefficient of the current velocity level and acceleration level is the optimal solution, θ, The final and optimal joint motion trajectory can be obtained accordingly;

[0035] 5.2 If the residual vibration control requirements are not met, if the flexible vibration δ calculated according to the dynamic equation max Greater than the expected value δ limit , then continue to iterate and solve.

[0036] Further, the iterative solution method is:

[0037] 5.2.1 Update group optimality and individual optimality:

[0038] Individual Optimum Update to make the current generation δ max Smallest and Group best gbest (t) Update to the smallest value among all generations and

[0039] 5.2.2 Update the null space term coefficients:

[0040] Update the null space term coefficients based on the particle swarm algorithm with shrinkage factor and The update formula is:

[0041]

[0042] Represents the update and value, Represents the updated and value; is the particle change speed before updating, is the updated particle change speed; the upper and lower limits of particle speed are [-1,1]; regenerate the new generation of null space term coefficients and

[0043] 5.2.3 Update joint motion trajectory:

[0044] According to the updated Re-use the inverse kinematics relationship to calculate the new θ, That is the updated motion trajectory.

[0045] 5.2.4 Update calculation of flexible vibration of the end of the robot arm:

[0046] Using the newly obtained joint motion trajectory θ, Recalculate the flexible vibration of the robot motion;

[0047] If the residual vibration control requirements are still not met, repeat steps 5.2.1 to 5.2.4 until the requirements are met. The θ, This is the optimal motion trajectory; this trajectory also meets the terminal motion requirements.

[0048] The beneficial effects of the present invention compared with the prior art are:

[0049] (1) The present invention realizes the conversion of the desired end trajectory into a joint motion trajectory containing a zero space term based on the polynomial end trajectory difference and the minimum norm method inverse kinematics relationship;

[0050] (2) The present invention uses a particle swarm optimization algorithm with a shrinkage factor to iteratively optimize the joint motion trajectory containing a zero space term, thereby obtaining a joint motion trajectory that meets the minimum flexible vibration requirements with low resource consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is the overall algorithm structure diagram of the present invention;

[0052] Figure 2 This is a flow chart of the particle swarm algorithm for shrinkage factor of the present invention;

[0053] Figure 3 is the variation curve of the optimal objective function (residual vibration amplitude) of the present invention;

[0054] Figure 4 The original planned trajectory and the optimized trajectory of the terminal of the present invention. DETAILED DESCRIPTION

[0055] The present invention will be further described below in conjunction with the embodiments.

[0056] like Figure 1 As shown in the figure, in the motion planning of the end trajectory of the robot arm, the end trajectory is first discretized by the fifth-order polynomial function, and the end motion trajectory X in the time domain is decomposed:

[0057]

[0058] Where, t f represents the planning time, r 0 and r f They represent the initial position and the expected final position of the end of the robot arm respectively.

[0059] The terminal velocity can be solved as:

[0060]

[0061] In the process of calculating the kinematics of the robot arm, there is a certain mapping relationship between its end velocity and the angular velocity of each joint, that is, the inverse kinematics relationship. Based on the minimum norm method, the inverse kinematics relationship between the end trajectory of the spatial robot arm and the joint trajectory containing zero spatial terms is constructed at the velocity level and the acceleration level:

[0062]

[0063] In the formula, and are orthogonal to and The null space term of is an arbitrary vector, i.e., the coefficient of the null space term. The null space term produces a configuration change on the robot arm without affecting the velocity of the end. By integrating the velocity, a discrete joint angle curve containing two null space term coefficients is obtained.

[0064] According to the first kind of Lagrangian equation, the dynamic motion model of the flexible manipulator driven by the above joint trajectory motion is constructed to describe the residual vibration at the end of the manipulator:

[0065]

[0066] Where q is the generalized coordinate, which can be selected as joint angle or angular velocity; M is the mass matrix; C is the constraint equation; F is the elastic force matrix; and Q is the external force matrix.

[0067] In order to speed up the convergence, a particle swarm algorithm with a shrinkage factor is designed, such as Figure 2 As shown, the speed and position of each particle change according to the following formula:

[0068]

[0069] where c 1 With c 2 is the learning factor, r 1 With r 2 is any value between [-1,1], χ is called the shrinkage factor, which is defined as:

[0070] The summarized optimization model can be expressed as:

[0071]

[0072] in, and They are and The lower and upper boundaries of .

[0073] Using the above inverse kinematics relationship with zero space term and particle swarm algorithm with shrinkage factor, a specific number of optimization iterations is set, as shown in the attached Figure 3 As shown, the analytical solutions of joint velocity and joint acceleration under the minimum state of flexible vibration can be obtained respectively, and then the analytical solution of joint motion trajectory can be obtained by differential form:

[0074]

[0075] According to the attached Figure 3 When the number of iterations is 20, the flexible vibration is reduced to less than 50% of the initial state, which requires low computing resources. The above joint motion trajectory is used as the input condition of the flexible manipulator motion, and the manipulator motion trajectory that satisfies the minimum flexible vibration can be obtained without changing the desired end motion trajectory. Figure 4 shown.

[0076] The present invention realizes the conversion of the desired end trajectory into a joint motion trajectory containing a zero space term based on the polynomial end trajectory difference and the minimum norm method inverse kinematics relationship;

[0077] The present invention adopts a particle swarm optimization algorithm containing a contraction factor to iteratively optimize the joint motion trajectory containing a zero space term, and obtains a joint motion trajectory that meets the minimum flexible vibration requirement.

[0078] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for suppressing flexible vibration of a space manipulator, characterized in that: include: The terminal motion trajectory is obtained by discretization. According to the expected terminal position, the expected terminal trajectory is discretized by the fifth-order polynomial function, and the terminal motion trajectory X in the time domain is decomposed; Set the null space term coefficients and optimization algorithm parameters; Initialize the calculation of joint motion trajectory, and construct the inverse kinematics relationship between the end trajectory of the spatial manipulator and the joint trajectory including the zero space term at the velocity level and the acceleration level; The flexible robotic arm dynamics model is constructed, and the flexible robotic arm dynamics motion model driven by the above-mentioned joint trajectory motion is constructed to describe the flexible vibration of the robotic arm end; By calculating the flexible vibration of the end of the robot arm, the flexible vibration amplitude of the end of the robot arm is obtained, and compared with the flexible vibration amplitude of the end of the robot arm before optimization to determine whether the requirements for flexible vibration suppression are met; According to the minimum norm method, the inverse kinematics relationship between the end trajectory of the spatial manipulator and the joint trajectory including the zero space term is constructed as follows: In the formula, is the joint angular velocity, is the joint angular acceleration; J is the Jacobian matrix of the robot arm, for The derivative of the Jacobian matrix, J + is the pseudo-inverse matrix of J, J + =J T (JJ T ) -1 ; I is the identity matrix, is the terminal speed, is the terminal acceleration; It is characterized in that the joint motion trajectory θ is: Δt is the calculation step length; The method for judging whether the requirements for flexible vibration suppression are met is: (5.1) If the flexible vibration control requirements are met, The system optimization model is expressed as: in, and They are and The lower and upper boundaries of Each generation of particle swarm optimization generates null space term coefficients and If the minimum flexible vibration δ under the current algebra is calculated according to the dynamic equation max Less than the expected value δ limit , then the optimization ends, and the zero spatial term coefficient of the current velocity level and acceleration level is the optimal solution, θ, The final and optimal joint motion trajectory can be obtained accordingly; (5.2) If the residual vibration control requirements are not met, if the flexible vibration δ calculated according to the dynamic equation max Greater than the expected value δ limit , then continue to iterate and solve; The iterative solution method is: (5.2.1) Update the group optimum and individual optimum: Individual Optimum Update to make the current generation δ max Smallest and Group best gbest (t) Update to the smallest value among all generations and (5.2.2) Update the coefficients of the null space terms: Update the null space term coefficients based on the particle swarm algorithm with shrinkage factor and The update formula is: Represents the update and value, Represents the updated and value; Value; is the particle change speed before updating, is the updated particle change speed; the upper and lower limits of particle speed are [-1,1]; regenerate the new generation of null space term coefficients and (5.2.3) Update joint motion trajectory: According to the updated Re-use the inverse kinematics relationship to calculate the new θ, That is, the updated motion trajectory; (5.2.4) Update the calculation of flexible vibration of the end of the robot arm: Using the newly obtained joint motion trajectory θ, Recalculate the flexible vibration of the robot motion; If the residual vibration control requirements are still not met, repeat steps 5.2.1 to 5.2.4 until the requirements are met. The θ, This is the optimal motion trajectory; this trajectory also meets the terminal motion requirements.

2. A method for suppressing flexible vibration of a space manipulator according to claim 1, characterized in that: End motion trajectory In the formula, t represents the current movement time, t f Represents the total planning time, r0 and r f They represent the initial position and the expected final position of the end of the robot arm respectively.

3. A method for suppressing flexible vibration of a space manipulator according to claim 2, characterized in that: The terminal speed It can be solved as:

4. A method for suppressing flexible vibration of a space manipulator according to claim 2, characterized in that: Terminal acceleration It can be solved as:

5. A method for suppressing flexible vibration of a space manipulator according to claim 1, characterized in that: Describe the flexible vibration of the end of the robot arm as: Where q is the generalized coordinate, and the joint motion angle θ is selected. is the second-order derivative of the generalized coordinates M is the system mass matrix; C is the constraint equation, which is related to the generalized coordinates q and time t; C q represents the partial differential matrix of the constraint equation with respect to the generalized coordinate q; λ is the Lagrange multiplier; F is the elastic force matrix, which is related to the generalized coordinate q; Q is the generalized external force matrix, which is also related to the generalized coordinate q.

6. A method for suppressing flexible vibration of a space manipulator according to claim 5, characterized in that: Flexible vibration is δ max =max(X act -X), X act is the actual end position under the current motion trajectory.

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