Parameter learning and synchronous control method for redundant robot arm

Abstract

The application provides a parameter learning and synchronous control method for a redundant manipulator, and belongs to the technical field of manipulator control, and comprises the following steps: S1: an iterative formula for estimating physical parameters of the redundant manipulator is established, and an estimated physical parameter vector is obtained; S2: a velocity layer control formula for an end effector is established according to the estimated physical parameter vector; S3: velocity layer inverse kinematics analysis is performed on motion planning of the redundant manipulator, and a quadratic optimization scheme is established; S4: the quadratic optimization scheme is converted into a quadratic programming; S5: a quadratic programming solver is used for solving; and S6: the redundant manipulator is controlled according to a solving result. The application can accurately learn the physical parameters of the redundant manipulator, and can synchronously control the redundant manipulator based on the estimated physical parameter information, so that the manipulator has self-adaptability and high efficiency during execution.

Description

TECHNICAL FIELD

[0001] The present application relates to a parameter learning and synchronous control method of a redundant manipulator, and belongs to the technical field of manipulator control, and is especially suitable for parameter learning and synchronous control of a redundant manipulator. BACKGROUND

[0002] A redundant manipulator is a kind of manipulator with more degrees of freedom than the dimension of the task space. Compared with ordinary manipulators, it has higher flexibility and adaptability, and can use its redundant degrees of freedom to realize obstacle avoidance and optimize path planning, etc., so as to more efficiently complete the given task. With the continuous development and progress of robot technology, the redundant manipulator has become one of the important technologies in the field of industrial automation and artificial intelligence, and has broad application prospects. However, most of the current redundant manipulator control algorithms are designed and implemented based on known physical parameters. In some special scenarios, the redundant manipulator needs to be modified to meet different task requirements, which will change the physical parameters of the manipulator. For example, the manipulator in medical surgery usually needs to replace the end effector with specific shape, size and material to perform fine and complex tasks; in search and rescue scenarios, the manipulator can be equipped with telescopic links to adapt to different buildings and terrain environments. In these scenarios, the redundant manipulator control algorithm based on known physical parameters is difficult to accurately control the manipulator.

[0003] Although the redundant manipulator has more degrees of freedom and flexibility, it can better meet the complex task requirements, but it also needs more kinematic parameters to describe its structural information. When the physical parameters of the redundant manipulator change, the changed physical parameters can be determined through the traditional offline calibration process. However, this calibration process is relatively cumbersome, time-consuming, and prone to errors. Therefore, it is urgent to design an efficient parameter learning and synchronous control method to improve the control accuracy and task efficiency of the redundant manipulator, reduce the failure rate, and shorten the debugging time. SUMMARY

[0004] Therefore, the present application proposes a parameter learning and synchronous control method of a redundant manipulator, which can effectively learn the physical parameters of the manipulator using its state information, and realize synchronous control based on the learned physical parameters, thereby improving the adaptability of the redundant manipulator system.

[0005] To achieve the above-mentioned purpose, the present application provides the following technical solutions:

[0006] A parameter learning and synchronous control method of a redundant manipulator, comprising the following steps:

[0007] S1: according to the parameterization equation of the redundancy manipulator end effector position and velocity, a physical parameter estimation iterative formula of the redundancy manipulator is established, and then an estimated physical parameter vector of the redundancy manipulator is obtained;

[0008] S2: according to the parameterization formula of the Jacobian matrix and the estimated physical parameter vector of the redundancy manipulator in step S1, a velocity layer control formula of the end effector is established;

[0009] S3: according to the velocity layer control formula of the end effector in step S2, a velocity layer inverse kinematics analysis of the motion planning of the redundancy manipulator is carried out, and a quadratic optimization scheme is established;

[0010] S4: the quadratic optimization scheme in step S3 is converted into a quadratic programming;

[0011] S5: the quadratic programming in step S4 is solved by using a quadratic programming solver;

[0012] S6: according to the solution result obtained in step S5, the redundancy manipulator is controlled.

[0013] Further, the parameterization equation of the end effector position in step S1 is p(θ, φ) = Hφ, wherein p is the position of the end effector of the redundancy manipulator; θ is the joint angle of the redundancy manipulator; a ≥ 7 represents the number of degrees of freedom of the redundancy manipulator; φ is the physical parameter vector of the redundancy manipulator; the matrix H is defined as the time derivative of the parameterization equation of the end effector position is taken to obtain the parameterization formula of the velocity wherein v is the velocity of the end effector of the redundancy manipulator; is the time derivative of the Jacobian matrix H and vi is the joint velocity of the i th joint of the redundancy manipulator;

[0014] Further, according to the parameterization equation of the end effector position and velocity, the physical parameter estimation iterative formula of the redundancy manipulator is established as

[0015]

[0016] wherein, represents the matrix s is the state after being disturbed by additional noise; i represents the zero-mean homoscedastic random noise applied on the i th joint velocity of the redundancy manipulator; φ is the estimated physical parameter vector of the redundancy manipulator, and the time derivative thereof is is the convergence parameter; is the design parameter; superscript T denotes the transpose operation of a vector or a matrix; the iterative formula for estimating the physical parameters of the redundant manipulator can obtain the estimated physical parameter vector of the redundant manipulator by using the position and velocity information of the end effector.

[0017] Further, the Jacobian matrix parameterization formula in step S2 can be specifically described as wherein denotes the Jacobian matrix of the end effector position of the redundant manipulator with respect to the joint angle; matrix M i is defined as φ i denotes the i-th element of the physical parameter vector φ; further, by using the estimated physical parameter vector of the redundant manipulator, the velocity layer control formula of the end effector can be expressed as wherein denotes the i-th element of the estimated physical parameter vector φ of the redundant manipulator; is the joint angular velocity of the redundant manipulator; denotes the design parameter; denotes the desired end effector position; denotes the desired end effector velocity.

[0018] Further, the quadratic optimization scheme in step S3 can be expressed as follows: the minimized performance index of the design is a quadratic function of the joint angular velocity of the redundant manipulator, which is subject to the velocity layer control formula of the end effector and the joint physical constraint; that is, the minimized performance index is the constraint condition is and wherein, is a positive definite diagonal matrix; is the performance index to be optimized, and Ψ is the joint angular velocity feasible region set of the redundant manipulator.

[0019] Further, the quadratic optimization scheme in step S4 is converted into a quadratic programming, which is specifically described as follows: the original variable is replaced by introducing a vector u the quadratic optimization scheme is rewritten as follows: the minimized performance index is u T Ωu / 2+w T u, the constraint condition is Au=c and u - ≤u≤u + wherein, u + and u - respectively denote the upper limit and the lower limit of the joint angular velocity feasible region of the redundant manipulator.

[0020] Further, in step S5, the quadratic programming is solved by a quadratic programming solver, so as to obtain an optimal solution of the redundant manipulator parameter learning and synchronous control.

[0021] Further, step S6 is specifically converting the quadratic programming result solved by the solver into a corresponding control signal required by motor driving of the redundant manipulator through a control relationship, so as to drive the redundant manipulator to realize the control task.

[0022] The present application has the beneficial effects that the present application provides a redundant manipulator parameter learning and synchronous control method, establishes a physical parameter estimation iteration formula of the redundant manipulator, can effectively learn the physical parameters, and controls the redundant manipulator based on the estimated physical parameter vector, and is more adaptive and efficient. BRIEF DESCRIPTION OF DRAWINGS

[0023] In order to further illustrate the purposes and technical schemes of the present application, the present application provides the following drawings for illustration:

[0024] Figure 1 It is a redundant manipulator parameter learning and synchronous control method flow chart;

[0025] Figure 2 It is a motion process diagram of the redundant manipulator of the embodiment of the present application, and the unit of the coordinate axis is meter;

[0026] Figure 3 It is a joint angular velocity diagram of the embodiment of the present application, the horizontal coordinate is time (unit: second), and the vertical coordinate is angular velocity (unit: radian / second);

[0027] Figure 4 It is a position error diagram of the end effector in x, y and z directions of the embodiment of the present application, the horizontal coordinate is time (unit: second), and the vertical coordinate is error size (unit: meter);

[0028] Figure 5 It is an estimated physical parameter change diagram in the task process of the embodiment of the present application, the horizontal coordinate is time (unit: second), and the vertical coordinate is the size of the estimated physical parameter (unit: meter);

[0029] Figure 6 It is a physical parameter learning error of the embodiment of the present application, the horizontal coordinate is time (unit: second), and the vertical coordinate is error size (unit: meter). DETAILED DESCRIPTION

[0030] For the purposes of the present invention and technical solutions are more clear and explicit, below in conjunction with the drawings and examples of the present invention are described in detail. Embodiment: assume a redundant robot arm (seven degrees of freedom Franka Emika Panda robot arm) control scenario, set the actual physical parameters of the redundant robot arm φ = [0.333, 0.316, 0.0825, 0.0825, 0.384, 0.088, 0.1070] T (unit: meters) is unknown, known: the degree of freedom of the redundant robot arm and the dimension of the physical parameter vector is 7, the initial angle of each joint of the redundant robot arm is θ(0) = [0, -π / 4, 0, -3π / 4, 0, π / 2, 0] T (unit: radian), the upper and lower limits of the joint angular velocity of the redundant robot arm are u + = u - = [0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5] T (unit: rad / s), now set in 10 seconds, the task is a Chinese knot trajectory tracking task. For this scenario, the present invention proposes "a parameter learning and synchronous control method for redundant robot arm", combined with Figure 1 , including the following steps:

[0031] S1: according to the parameterized equation of the end effector position and velocity of the redundant robot arm, the physical parameter estimation iterative formula of the redundant robot arm is established, and then the estimated physical parameter vector of the redundant robot arm is obtained;

[0032] The parameterized equation of the end effector position is p(θ, φ) = Hφ, wherein is the position of the end effector of the redundant robot arm; is the joint angle of the redundant robot arm; is the physical parameter vector of the redundant robot arm; the matrix H is defined as The time derivative of the parameterized equation of the end effector position can obtain the parameterized formula of its velocity wherein is the velocity of the end effector of the redundant robot arm; is the time derivative of the Jacobian matrix H and is the joint velocity of the i-th joint of the redundant robot arm;

[0033] Further, according to the parameterized equation of the end effector position and velocity, the physical parameter estimation iterative formula of the redundant robot arm is established as

[0034]

[0035] wherein, representation matrix state disturbed by additional noise; s i represents the zero-mean independent and identically distributed random noise applied on the i-th joint velocity of the redundant manipulator; is the estimated physical parameter vector of the redundant manipulator, whose time derivative is is the convergence parameter; is the design parameter; the superscript T represents the transpose operation of a vector or a matrix; the physical parameter estimation iteration formula of the redundant manipulator can obtain the estimated physical parameter vector of the redundant manipulator by using the position and velocity information of the end effector.

[0036] In this embodiment, the initial value of is set to [0.300, 0.294, 0.049, 0.0720, 0.338, 0.041, 0.177] T (unit: meter), η is set to 50000, α is set to 1, and the absolute value of the noise s i is set to be less than 0.05.

[0037] Step S2: According to the Jacobian matrix parameterization formula and the estimated physical parameter vector of the redundant manipulator in step S1, the velocity layer control formula of the end effector is established.

[0038] The Jacobian matrix parameterization formula can be specifically described as wherein represents the Jacobian matrix of the end effector position of the redundant manipulator with respect to the joint angle; the matrix M i (θ) is defined as φ i represents the i-th element of the physical parameter vector φ; further, by using the estimated physical parameter vector of the redundant manipulator, the velocity layer control formula of the end effector can be represented as wherein represents the i-th element of the estimated physical parameter vector of the redundant manipulator ; is the joint angular velocity of the redundant manipulator; represents the design parameter; represents the desired end effector position; represents the desired end effector velocity.

[0039] In this embodiment, β is set to 5.

[0040] Step S3: According to the velocity layer control formula of the end effector in step S2, the velocity layer inverse kinematics analysis of the motion planning of the redundant manipulator is performed to establish a quadratic optimization scheme;

[0041] The minimum performance index is a quadratic function of the joint angular velocity of the redundant manipulator, which is subject to the velocity level control equation of the end effector and the physical constraints of the joints; that is, the minimum performance index is The constraint condition is and wherein, Ω is a positive diagonal matrix; Ψ is the performance index to be optimized, and Ψ is the feasible set of the joint angular velocity of the redundant manipulator.

[0042] In this embodiment, Ω is set as a unit matrix, and w is set as a zero vector.

[0043] Step S4: converting the quadratic optimization scheme in step S3 into a quadratic programming.

[0044] Specifically, a vector u is introduced to replace the original variable The quadratic optimization scheme is rewritten as follows: the minimum performance index is u T Ωu / 2+w T u, and the constraint condition is Au=c and u - ≤u≤u + wherein, u + and u - respectively represent the upper limit and the lower limit of the joint angular velocity feasible set of the redundant manipulator.

[0045] Step S5: solving the quadratic programming in step S4 by using a quadratic programming solver.

[0046] In this embodiment, the Karush-Kuhn-Tucker condition and the dual space method are used to equivalently solve the quadratic programming problem as a projection equation set. The specific projection equation set is

[0047]

[0048] wherein, is the Lagrange coefficient; δ>0 is a coefficient for controlling the convergence speed, which is set as 0.001 in this example; P ψ (·) is a projection function, which is specifically described as wherein and u i respectively represent the i-th element of the vector u + , u - and u; and the quadratic programming problem is solved by using the solver.

[0049] Step S6: converting the quadratic programming result solved by the solver into the control signal required by the motor drive of the corresponding redundant manipulator through a control relationship, so as to drive the redundant manipulator to achieve the control task.

[0050] The embodiment utilizes MATLAB software to perform simulation experiments to verify the correctness and superiority of the method of the application. The specific experimental results are shown in Figure 2 、 Figure 3 、 Figure 4 、 Figure 5 、 Figure 6 .

[0051] Further, it can be seen from Figure 2 that the redundant manipulator successfully completes the given Chinese knot trajectory tracking task.

[0052] It can be seen from Figure 3 that the joint speed starts from 0 rad / s in the whole task execution process, and the numerical change of each joint is smooth and stable.

[0053] It can be seen from Figure 4 that the trajectory tracking error of the end effector of the redundant manipulator is in the order of 10 -4 meters, which embodies the accuracy of the control aspect of the application.

[0054] It can be seen from Figure 5 that the estimated physical parameters quickly converge to the true values near 0 seconds, which embodies the effectiveness of the application in learning physical parameters.

[0055] It can be seen from Figure 6 that the learning error of the physical parameters quickly converges within 0.2 seconds, and converges to the order of 10 -4 meters after 2 seconds, which embodies the accuracy of the application in learning physical parameters.

[0056] Finally, it should be pointed out that the above preferred embodiments are only used to illustrate the technical solutions of the application and not to limit it. Although the application has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made in form and details without departing from the scope defined by the claims of the application.

Claims

1. A parameter learning and synchronization control method for a redundant robotic arm, characterized in that, The method includes the following steps: S1: Based on the parameterized equations of the position and velocity of the end effector of the redundant robot arm, establish the iterative formula for estimating the physical parameters of the redundant robot arm, and then obtain the estimated physical parameter vector of the redundant robot arm. The parameterized equation for the position of the end effector is p(θ, φ) = Hφ, where The position of the end effector of the redundant robotic arm; The joint angles of the redundant robotic arm; a≥7 indicates the number of degrees of freedom of the redundant robotic arm; The physical parameter vector of the redundant robotic arm; matrix H is defined as The parameterized formula for the velocity can be obtained by taking the time derivative of the parameterized equation for the position of the end effector. in For the speed of the redundant robotic arm end effector; matrix The time derivative of matrix H and Let be the joint angular velocity of the i-th joint of the redundant robotic arm; based on the parameterized equations of the end effector position and velocity, the iterative formula for estimating the physical parameters of the redundant robotic arm is established as follows: in, Representation matrix The state after being subjected to additional noise interference; s i This represents the zero-mean identically distributed random noise applied to the angular velocity of the i-th joint of the redundant robotic arm; Let be the estimated physical parameter vector of the redundant robotic arm, and its time derivative is: These are the convergence parameters; The design parameters are specified; the superscript T indicates the transpose of a vector or matrix; the iterative formula for estimating the physical parameters of the redundant robotic arm can utilize the position and velocity information of the end effector to obtain the estimated physical parameter vector of the redundant robotic arm. S2: Based on the Jacobian matrix parameterization formula and the estimated physical parameter vector of the redundant robotic arm in step S1, establish the speed layer control formula for the end effector. S3: Based on the velocity layer control formula of the end effector in step S2, perform velocity layer inverse kinematics analysis on the motion planning of the redundant robot arm and establish a quadratic optimization scheme. S4: Transform the quadratic optimization scheme in step S3 into a quadratic programming problem; S5: Solve the quadratic programming problem in step S4 using a quadratic programming solver; S6: Based on the solution obtained in step S5, control the redundant robotic arm.

2. The parameter learning and synchronization control method for a redundant robotic arm according to claim 1, characterized in that, The Jacobian matrix parameterization formula described in step S2 is specifically described as follows: in The Jacobian matrix representing the position of the end effector of the redundant robotic arm with respect to the joint angles; matrix M i (θ) is defined as φ i Let represent the i-th element of the physical parameter vector φ; further, using the estimated physical parameter vector of the redundant robotic arm, the velocity layer control formula for the end effector is expressed as: in Estimated physical parameter vector for redundant robotic arms The i-th element; The joint angular velocity of the redundant robotic arm; For design parameters; The desired end effector position; This indicates the desired end effector speed.

3. The parameter learning and synchronization control method for a redundant robotic arm according to claim 1, characterized in that, The quadratic optimization scheme in step S3 is expressed as follows: the designed minimum performance index is a quadratic function of the joint angular velocity of the redundant robotic arm, constrained by the velocity layer control formula of the end effector and the joint physical constraints; that is, the minimum performance index is... The constraints are and in, It is a positive definite diagonal matrix; Ψ represents the set of feasible angular velocities of the redundant robotic arm, where Ψ is the performance metric to be optimized.

4. The parameter learning and synchronization control method for a redundant robotic arm according to claim 3, characterized in that, The quadratic optimization scheme described in step S4 is transformed into a quadratic programming problem, specifically by introducing a vector u to replace the original variables. The quadratic optimization scheme is rewritten as follows: Minimize the performance index u. T Ωu / 2+w T u, with constraints Au = c and u - ≤u≤u + ,in, u + and u - These represent the upper and lower limits of the feasible domain of the joint angular velocity of the redundant robotic arm, respectively.

5. The parameter learning and synchronization control method for a redundant robotic arm according to claim 1, characterized in that, Step S6 specifically involves converting the quadratic programming result obtained by the solver into the control signal required for the redundant robotic arm motor drive, thereby driving the redundant robotic arm to achieve the control task.

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