A planar robot trajectory tracking method based on intermittent iterative learning control

Abstract

The present invention discloses a planar manipulator trajectory tracking method based on intermittent iterative learning control. The method first proposes a proportional differential feedback controller in the case of random packet loss based on the manipulator dynamics model established by the Lagrange method, and constructs an iterative estimator based on interpolation data. A reference trajectory modification method is used to construct a feedforward input in the case of input intermittent. Finally, feedback and feedforward are combined to design a controller that makes the trajectory tracking error of the planar manipulator always bounded in mathematical expectation. Compared with the traditional control algorithm based on the precise mathematical model of the task, this 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 method based on intermittent iterative learning control. 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 combined with 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 method based on intermittent iterative learning control, 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 method based on intermittent iterative learning control 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 i , 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 i is the torque input, d i is the unmodeled dynamics and other unknown disturbances, t represents time, i represents the iteration batch, and the system running time for each iteration is T, and the system reference trajectory is q d , the system tracking error is

[0009] Furthermore, considering the packet loss during the transmission of the position sensor and speed sensor signals of the robotic arm system, the packet loss process is described as a Bernoulli distribution function γ, where γ = 0 when packet loss occurs and γ = 1 otherwise, and its mathematical expectation is recorded as

[0010] Further, construct feedback input Where:

[0011]

[0012] Furthermore, the system operation interval is divided into [T l , T l+1 ), (l = 0, 1, ...), considering that the input of the robot system is intermittent, only in [T 2l , T 2l+1 ) has input;

[0013] Furthermore, the iterative state estimator is constructed based on the robot dynamics model as follows:

[0014]

[0015] Where q int，i is the interpolation state obtained by interpolating the sensor transmission information qi, is the estimator state, Ψ is the known regression matrix, j represents the estimator iteration batch, The update law is as follows:

[0016]

[0017] Where λ1, λ2, λ3 are positive scalars, This estimator can ensure the convergence of the estimation error. The proof process is as follows:

[0018] C001: Select the composite energy function as follows:

[0019]

[0020] C002: Consider the E between the jth and j-1th i，j (t) difference ΔE i，j =ΔV 1，i，j +ΔV 2，i，j +ΔV 3，i，j +ΔV 4，i，j ,in:

[0021]

[0022]

[0023]

[0024] C003: Based on C002, we can get ΔE i，j (t)≤0, then we can get E i，j (t) If the convergence of the extended iteration is good, then the convergence of the estimated error is proved;

[0025] Furthermore, according to the input interval, the modified trajectory is constructed as follows:

[0026]

[0027] In the formula, q m，i (t) represents the modified reference trajectory, is a second-order differentiable function and satisfies the following requirements:

[0028] ●

[0029] ●

[0030] ●

[0031] ●

[0032] Where T a To modify the length;

[0033] Further, construct the feedforward input

[0034] Further, construct the torque input as τ i =τ fb，i +τ ff，i , the torque input can ensure that the tracking error is always bounded in mathematical expectation. The proof process is as follows:

[0035] C004: Select the energy function as follows:

[0036]

[0037] C005: k1 is a positive scalar, P is a symmetric positive definite matrix;

[0038] C006: Consider The mathematical expectation of as follows:

[0039]

[0040] C007: According to C006, when input working time t∈[T 2l , T 2l+1 ),have as follows:

[0041]

[0042] C008: According to C006, during the input intermittent time t∈[T 2l+1 , T 2l+2 ),have as follows:

[0043]

[0044] C009: According to C007 and C008, W i The mathematical expectation is ultimately always bounded, so it is proved that the tracking error is ultimately always bounded in terms of mathematical expectation. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0046] Figure 2 A schematic diagram of a mechanical arm according to an embodiment of the present invention;

[0047] 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;

[0048] 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;

[0049] 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;

[0050] 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

[0051] 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.

[0052] like Figure 1 As shown, a planar robot trajectory tracking method based on intermittent iterative learning control includes the following steps:

[0053] Step 1: Set the initial values ​​of various parameters;

[0054] Step 2: Run the system to record sensor sampling data q i ,

[0055] Step 3: Iterate and estimate the feedforward input τ based on the sampled data ff，i ;

[0056] Step 4: According to the feedforward input τ ff，i and feedback input τ fb，i The torque input τ generated i ;

[0057] Step 5: Repeat steps 2, 3, and 4 until this iteration ends and enters the next loop.

[0058] An embodiment of the present invention is described below:

[0059] Considering the joint trajectory tracking control problem of a two-degree-of-freedom planar manipulator, the corresponding dynamic model is:

[0060]

[0061] The system parameters are:

[0062]

[0063]

[0064]

[0065] The expected tracking trajectory is: The expected running time T of the system is 5s, the probability of sensor packet loss is 50%, and the intermittent input is 0.9s of work and 0.1s of stop.

[0066] 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.

[0067] It can be seen from the figure that at the 10th iteration, a satisfactory tracking performance can be obtained.

[0068] References

[0069] [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.

[0070] [2]X.Jin.Iterative learning control for non-repetitive trajectorytracking of robot manipulators with joint position constraints and actuatorfaults.International Journal ofAdaptive Control and Signal Processing,vol.31,pp.859-875,2017。

Claims

1. A planar robot trajectory tracking method based on intermittent iterative learning control, characterized in that: The following steps are involved: Establish the dynamic model of the robot arm based on the Lagrange method; Consider the packet loss during the transmission of the position sensor and speed sensor signals of the robot system and construct feedback control input; Interpolation method is used to complete the packet loss sampling data and an iterative estimator is constructed to estimate the system uncertainty; By modifying the reference trajectory and constructing the feedforward input based on the iterative estimator; Combining feedback and feedforward to achieve trajectory tracking of the robotic arm system; Among them, the expression of the mechanical arm dynamics model based on the Lagrange method is as follows: In the formula, q i , 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 i is the torque input, d i is the unmodeled dynamics and other unknown disturbances, t represents time, i represents the iteration batch, and the system running time for each iteration is T, and the system reference trajectory is q d , the system tracking error is When there is packet loss during the transmission of position sensor and speed sensor signals, the packet loss process is described as a Bernoulli distribution function γ, where γ = 0 when packet loss occurs and γ = 1 otherwise, and its mathematical expectation is recorded as Further, construct feedback input Where: The system operation interval is divided into [T l ,T l+1 ), (l=0,1,...), considering that the input of the robot system is intermittent, only in [T 2l ,T 2l+1 ) has input, and constructs an iterative state estimator based on the robot arm dynamics model as follows: Where q int,i To transmit information to the sensor i The interpolation state obtained by interpolation method, is the estimator state, Ψ is the known regression matrix, j represents the estimator iteration batch, The update law is as follows: Where λ1, λ2, λ3 are positive scalars, According to the input interval, the modified trajectory is constructed as follows: In the formula, q m,i (t) represents the modified reference trajectory, is a second-order differentiable function and satisfies the following requirements: · · · · Where T a To modify the length, further, construct the feedforward input And construct the torque input as τ i =τ fb,i +τ ff,i .

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