A planar manipulator trajectory tracking intermittent control method based on sliding mode iterative learning

Abstract

The present invention discloses an intermittent control method for trajectory tracking of a planar manipulator based on sliding mode iterative learning. The method firstly uses a reference trajectory modification method to adapt to the alignment condition of the initial state of the system in the iterative process based on the dynamic model of the manipulator established by the Lagrange method, and at the same time constructs an intermittent controller of sliding mode iterative learning, and intermittently opens and closes the controller according to the sliding mode function. 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 invention relates to a control method for a planar robot arm, and in particular to a planar robot arm trajectory tracking intermittent control method based on sliding mode 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. In the field of robotics, the robot arm is one of the most widely used automated mechanical devices. It can replace manual labor to complete many dangerous and heavy tasks in industry, such as assembly, painting, welding and high-temperature casting and forging. At present, the robot arm is 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 an intermittent control method for planar robot trajectory tracking based on sliding mode 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 intermittent control method based on sliding mode 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, 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, by modifying the reference trajectory, the tracking error at the beginning of the iteration is made 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:

[0010]

[0011] 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:

[0012] ·

[0013] ·

[0014] ·

[0015] ·

[0016] Where T a is the modified length and satisfies 0<T a ≤T k ;

[0017] Furthermore, based on the dynamics model of the robot arm, a sliding mode function is constructed When ||S k (t)||>P O The controller is turned on when ||S k (t)||<P C Controller off;

[0018] 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:

[0019]

[0020]

[0021]

[0022] Where k1, k2, k3, k4, k5 are positive scalars; the algorithm can ensure the convergence of the tracking error, and the proof process is as follows:

[0023] C001: Select a composite energy function of the following form

[0024] V k (t) = V 1，k (t)+V2，k (t)+V 3，k (t)+V 4，k (t)+V 5，k (t)

[0025]

[0026]

[0027]

[0028]

[0029] C002: In the formula, s is an auxiliary scalar;

[0030] C003: Consider the V between the kth and k-1th times k (t) difference ΔV k (t), where:

[0031]

[0032]

[0033]

[0034]

[0035] C004: Therefore, according to C003, the following formula can be obtained:

[0036]

[0037] C005: Therefore, it can be obtained from C004 that when k2 and k4 are properly selected, ΔV can be guaranteed. k (t)<0;

[0038] C006: Therefore, according to the composite energy function V in C001 k (t) can be obtained in the form of S k (t) and according to the sliding mode function S k (t) can be used to obtain the convergence of the tracking error. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0040] Figure 2 A schematic diagram of a mechanical arm according to an embodiment of the present invention;

[0041] Figure 3This 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;

[0042] 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;

[0043] Figure 5 This is a position tracking diagram of joint 1 when the method proposed in the present invention is used in the embodiment at the 10th iteration;

[0044] Figure 6 This is a position tracking diagram of joint 2 when the method proposed in the present invention is used in the embodiment at the 10th iteration; DETAILED DESCRIPTION

[0045] 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.

[0046] like Figure 1 As shown, a planar robot trajectory tracking control method based on iterative learning includes the following steps:

[0047] Step 1: Set the initial values ​​of various parameters;

[0048] Step 2: Update algorithm parameters;

[0049] Step 3: Generate control input τ in real time based on updated algorithm parameters k (t);

[0050] Step 4: According to the control input τ k (t) The tracking error generated is used to update the algorithm parameters synchronously;

[0051] Step 5: Repeat steps 3 and 4 until this iteration ends and enters the next loop.

[0052] An embodiment of the present invention is described below:

[0053] Considering the joint trajectory tracking control problem of a two-degree-of-freedom planar manipulator, the corresponding dynamic model is:

[0054]

[0055] The system parameters are:

[0056]

[0057]

[0058]

[0059] 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 0.7-1s and

[0060] Figure 1 is a flow chart of a method according to an embodiment of the present invention; Figure 2 is a schematic diagram of a mechanical arm 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 10th iteration are shown respectively.

[0061] It can be seen from the figure that at the 10th iteration, a satisfactory tracking performance can be obtained.

[0062] References

[0063] [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.

[0064] [2]

Claims

1. A planar robot trajectory tracking intermittent control method based on sliding mode iterative learning, characterized in that: The following steps are involved: Establish the dynamic model of the robot arm based on the Lagrange method; 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; A controller based on sliding mode iterative learning is used to control the robotic arm system. The norm of the sliding mode function is used to determine the intermittent opening and closing of the controller. The specific steps are as follows: Based on the dynamics model of the robot arm, a sliding mode function is constructed When ||S k (t)||>P O The controller is turned on when ||S k (t)||<P C Controller off; Furthermore, an iterative learning control scheme for the manipulator’s planar trajectory tracking is established as follows: In the formula, τ k (t) is the torque input, T k represents the actual iteration time, k1, k2, k3, k4, k5 are positive scalars; it can ensure the convergence of tracking error, and 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)+V 4,k (t)+V 5,k (t) B002: In the formula, q k (t) is the joint position, s is an auxiliary scalar; B003: Consider the V between the kth and k-1th times k (t) difference ΔV k (t), where: B004: Therefore, according to B003, the following formula can be obtained: B005: Therefore, it can be concluded from B004 that when k2 and k4 are properly selected, ΔV can be guaranteed. k (t)<0; B006: Therefore, according to the composite energy function V in B001 k (t) can be obtained in the form of S k (t) and according to the sliding mode function S k (t) can be used to obtain the convergence of the tracking error.

2. According to claim 1, a planar robot arm trajectory tracking intermittent control method based on sliding mode iterative learning is characterized in that: The expression of the mechanical arm dynamics model based on the Lagrange method is as follows: In the formula, 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, t represents time, k represents the iteration batch, T k Indicates the actual iteration duration and satisfies 0<T min ≤T k ≤T.

3. The intermittent control method for trajectory tracking of a planar manipulator based on sliding mode iterative learning according to claim 2, characterized in that: 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 .

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