A planar manipulator trajectory tracking control method based on iterative learning

Abstract

The present invention discloses a planar manipulator trajectory tracking control method based on iterative learning. The method first proposes an iterative learning control scheme based on radial basis function based on the manipulator dynamics model established by Lagrange method, uses a reference trajectory modification method to adapt to the alignment condition of the initial state of the system during the iteration process, and constructs a variable learning gain based on a decreasing sequence to suppress the adverse effects of iterative change disturbances. Finally, a controller is designed to make the trajectory tracking error of the planar manipulator converge within a bounded range. Compared with the traditional control algorithm based on the precise mathematical model of the task, the present method is a new control scheme. When the method is applied to repetitive tasks, it effectively improves the control accuracy and has certain engineering application value.

Description

Technical Field

[0001] The present invention relates to a control method for a planar robot arm, and in particular to a planar robot arm trajectory tracking control method based on iterative learning. Background Art

[0002] The robot arm is a complex system with high precision, multiple inputs and multiple outputs, high nonlinearity, and strong coupling. The robot arm is one of the most widely used automated mechanical devices in the field of robotics. The robot arm can replace manual labor in many dangerous and heavy tasks in industries such as assembly, painting, welding, and high-temperature casting and forging. At present, the robot arm has been widely used in industrial assembly, safety and explosion-proof fields due to its unique operational flexibility.

[0003] The design methods applied to the robot control system mainly include PID control, adaptive control and robust control. However, the robot system has uncertainties such as parameter perturbation, external interference and unmodeled dynamics. Model uncertainty affects the realization of robot trajectory tracking, and some control algorithms are limited by certain uncertainties. Therefore, it is necessary to use its empirical knowledge, operation data, etc. to study new control algorithms that combine it with neural networks, learning control and other algorithms. Summary of the invention

[0004] The purpose of the present invention is to propose a planar robot arm trajectory tracking control method based on iterative learning, which can effectively utilize its empirical knowledge and operation data to achieve good control effects when there are uncertainties such as parameter perturbations, external interferences and unmodeled dynamics.

[0005] The specific technical solution of the present invention is as follows: A planar robot arm trajectory tracking control method based on iterative learning comprises the following steps:

[0006] The dynamic model of the robotic arm based on the Lagrange method is as follows:

[0007]

[0008] In the formula, q k , are joint positions, joint positions, joint accelerations, respectively, M is the symmetric positive definite inertia matrix, C is the Coriolis force matrix and is a skew-symmetric matrix, G is the gravity vector, τ k is the torque input, d k is the unmodeled dynamics and other unknown disturbances, t represents time, k represents the iteration batch, T k Indicates the actual iteration duration and satisfies 0<T min ≤T k ≤T;

[0009] Furthermore, considering the continuous operation of the robotic arm system, the initial state of the system in each iteration is the final state of the previous iteration, that is:

[0010]

[0011] Further, the reference trajectory modification method is constructed as follows:

[0012]

[0013] In the formula, q d (t) represents the original reference trajectory of the system, q m，k (t) represents the modified reference trajectory, and is the tracking error, is a second-order differentiable function and satisfies the following requirements:

[0014] ●

[0015] ●

[0016] ●

[0017] ●

[0018] Where T a is the modified length and satisfies 0<T a ≤T k ;

[0019] Furthermore, based on the robot dynamics model, there is an unknown nonlinear function α k (t) satisfies the following formula:

[0020]

[0021] Furthermore, a radial basis function neural network is used to k (t) is estimated as follows:

[0022]

[0023]

[0024] μ(Ψ(t),t)=[μ 1 (Ψ(t), t), ..., μ m (Ψ(t), t)] T

[0025]

[0026] In the formula, For α k The estimated value of (t), Λi , γ i are the center and width of the basis function, η k (t) is the learning gain and satisfies the following formula:

[0027]

[0028] In the formula, η 0 >0 is the initial gain, Δ η >0 is an arbitrarily large constant; ζ 1 (t) = 1,

[0029] Furthermore, based on the composite energy function, an iterative learning control scheme for the planar trajectory tracking of the robot arm involved in the present invention is established as follows:

[0030]

[0031] In the formula, K P , K D is a positive feedback gain matrix; the algorithm can ensure that the tracking error is bounded, and the proof process is as follows:

[0032] C001: Select a composite energy function of the following form

[0033] V k (t) = V 1，k (t)+V 2，k (t)+V 3，k (t)

[0034]

[0035]

[0036]

[0037] C002: In the formula, is an auxiliary scalar;

[0038] C003: Consider the V between the kth and k-1th times k (t) difference ΔV k (t) = ΔV 1，k (t)+ΔV 2，k (t)+ΔV 3，k (t), where:

[0039]

[0040]

[0041]

[0042] C004: δ k =0.2785n∈η k α k , according to C003, we can get the following formula:

[0043]

[0044] C005: Therefore, we can get from C004 There is ΔV k (t)<0;

[0045] C006: Therefore, when V 1 When (t) is bounded, we can get V k (t) has bounded convergence, so we consider as follows:

[0046]

[0047] C007: According to C006, V 1 (t) is bounded, combined with C005, we get V k (t) has bounded convergence, and according to the form of the composite energy function in C001, the tracking error can be obtained and Bounded convergence of . BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0049] Figure 2 A schematic diagram of a mechanical arm according to an embodiment of the present invention;

[0050] Figure 3 This is a position tracking diagram of joint 1 when the method proposed by the present invention is used in the first iteration of the embodiment;

[0051] Figure 4 This is a position tracking diagram of joint 2 when the method proposed by the present invention is used in the first iteration of the embodiment;

[0052] Figure 5 This is a position tracking diagram of joint 1 at the 20th iteration of the method proposed in the embodiment;

[0053] Figure 6 This is a position tracking diagram of joint 2 when the method proposed by the present invention is used in the embodiment at the 20th iteration; DETAILED DESCRIPTION

[0054] The present invention is further explained below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0055] like Figure 1 As shown, a planar robot trajectory tracking control method based on iterative learning includes the following steps:

[0056] Step 1: Set the initial values ​​of various parameters;

[0057] Step 2: Update algorithm parameters

[0058] Step 3: Based on the updated algorithm parameters and Generate control input τ in real time k (t);

[0059] Step 4: According to the control input τ k (t) The tracking error generated and the algorithm parameters are updated synchronously;

[0060] Step 5: Repeat steps 3 and 4 until this iteration ends and enters the next loop.

[0061] An embodiment of the present invention is described below:

[0062] Considering the joint trajectory tracking control problem of a two-degree-of-freedom planar manipulator, the corresponding dynamic model is:

[0063]

[0064] The system parameters are:

[0065]

[0066]

[0067]

[0068] The expected tracking trajectory is: The expected running time of the system is T, which is 1s, and the actual running time is T. k Evenly distributed on 0.7-1 and

[0069] Figure 1 A schematic diagram of a mechanical arm according to an embodiment of the present invention; Figure 2 is a flow chart of a method according to an embodiment of the present invention; applying the proposed method, Figure 3 , 4 The position tracking of joints 1 and 2 at the first iteration are shown respectively. Figure 5 , 6 The position tracking of joints 1 and 2 at the 20th iteration are shown respectively.

[0070] It can be seen from the figure that at the 20th iteration, a satisfactory tracking performance can be obtained.

[0071] References

[0072] [1]T.Bensidhoum, F.Bouakrif.Adaptive P-type iterative learning radialbasis function control for robot manipulators with unknown varyingdisturbances and unknown input dead zone.International Journal of Robust andNonlinear Control, vol 30, pp, 4075-4094, 2020.

[0073] [2]

Claims

1. A planar robot arm trajectory tracking control method based on iterative learning, characterized in that: The following steps are involved: The dynamic model of the robotic arm based on the Lagrange method is as follows: In the formula, are joint positions, joint velocities, and joint accelerations respectively, M is a symmetric positive definite inertia matrix, C is a Coriolis force matrix, and is a skew-symmetric matrix, G is the gravity vector, τ k is the torque input, d k is the unmodeled dynamics and other unknown disturbances, t represents time, k represents the iteration batch, T k Indicates the actual iteration duration and satisfies 0<T min ≤T k ≤T; By modifying the reference trajectory, the tracking error at the beginning of the iteration is consistent with the tracking error at the end of the previous iteration when the iteration duration is not fixed. The specific steps are as follows: In the formula, q d (t) represents the original reference trajectory of the system, q m,k (t) represents the modified reference trajectory, and is the tracking error, is a second-order differentiable function and satisfies the following requirements: Where T a is the modified length and satisfies 0<T a ≤T k ; A radial basis function neural network is used to estimate and compensate for system uncertainty, and an iterative learning-based controller is used to control the robotic arm system. The specific steps are as follows: Based on the dynamics model of the robot arm, there is an unknown nonlinear function α k (t) satisfies the following formula: Furthermore, a radial basis function neural network is used to k (t) is estimated as follows: μ(Ψ(t),t)=[μ1(Ψ(t),t),...,μ m (Ψ(t),t)] T In the formula, For α k The estimated value of (t), Λ i ,γ i are the center and width of the basis function, η k (t) is the learning gain and satisfies the following formula: in, η0>0 is the initial gain, Δ η >0 is an arbitrarily large constant; ζ1(t)=1, Furthermore, a planar robot trajectory tracking control method based on iterative learning is established as follows: In the formula, K P ,K D is a positive definite feedback gain matrix; τ k (t) Ensure that the tracking error is bounded. The proof process is as follows: B001: Select the following composite energy function V k (t)=V 1,k (t)+V 2,k (t)+V 3,k (t) B002: In the formula, is an auxiliary scalar; B003: Consider V k (t) and V k-1 (t) difference ΔV k (t) = ΔV 1,k (t)+ΔV 2,k (t)+ΔV 3,k (t), where: B004: δ k =0.2785n∈η k α k According to B003, the following formula can be obtained: B005: Therefore, we can get from B004 There is ΔV k (t)<0; B006: Therefore, when V1(t) is bounded, we can get V k (t) has bounded convergence, so we consider as follows: B007: According to B006, V1(t) is bounded. Combining B005, we get V k (t) has bounded convergence, and according to the form of the composite energy function in B001, the tracking error can be obtained and Bounded convergence of .

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