Rope-driven multi-joint mechanical arm motion control method and system considering time delay, medium and product

Abstract

The invention belongs to the technical field of robot system control, and particularly discloses a rope-driven multi-joint mechanical arm motion control method and system considering time delay, a medium and a product, and the method comprises the steps that when time delay estimation is carried out, a time delay estimation item is designed based on a multi-time-delay sample, and time delay estimation is adjusted through self-adaptive gain; a multi-sample delay signal is considered, a gradient with adaptive gain is also considered, time delay estimation with adaptive gain can compensate a dynamic model and provide stable torque input, a non-singular terminal sliding mode surface is designed to accelerate convergence speed, and under the condition that instantaneous interference exists, time delay estimation with adaptive gain can compensate the dynamic model and provide stable torque input. Accurate control can also be achieved under the conditions of friction, effective load or track change and the like. According to the control method based on time delay estimation, an accurate model is not needed, the precision is high, the robustness is good, and the trajectory tracking effect and the operation performance of the rope-driven multi-joint mechanical arm are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot system control, and more specifically, relates to a rope-driven multi-joint robot arm motion control method, system, medium and product taking time delay into consideration. Background Art

[0002] The rope-driven multi-joint manipulator is composed of a series of rigid connecting rods, and uses rope transmission to simulate the driving effect of biological tendons. It has a large driving force, multiple degrees of freedom, and high reliability. It can achieve telescopic, sideways, ups and downs, linear motion, lateral motion, etc. It is flexible in movement, has a large working space, and can carry equipment to perform operational tasks in narrow and confined environments. It has great application potential and has therefore received widespread attention.

[0003] However, its rope-driven super-redundant structure makes motion control very complicated. In the field of robot dynamics control, nonlinear terms of gravity, Coriolis, friction and other disturbances pose great challenges to the motion control of manipulators. Model-based controllers have been studied for decades and their performance has been well demonstrated. However, the identification of manipulator dynamic parameters is a very complex and difficult task, and the complexity of the robot model increases significantly with the number of estimated model parameters, which is particularly prominent in rope-driven multi-joint manipulators.

[0004] Control schemes based on time delay estimation (TDE) are well-known for effectively handling highly nonlinear and complex systems with external disturbances and model uncertainties. Due to its simplicity, efficiency, and robustness, it is widely used in the field of robotics. Practical applications have shown that the more complex and uncertain the system is, the more obvious the actual effect of TDE technology is. However, the performance of traditional TDE is limited by the system delay samples. When intermittent disturbances or uncertainties exist, it is difficult to find a suitable delay estimation gain, resulting in an increase in the error of the delay estimation. Therefore, a reliable and easy-to-implement method is needed to solve the problem in this TDE application, so as to achieve stable motion control of the robot arm under transient disturbances while having a faster convergence speed. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides a rope-driven multi-joint robotic arm motion control method, system, medium and product taking into account time delay, the purpose of which is to achieve stable motion control of the robotic arm under instantaneous disturbance and improve the motion control effect of the rope-driven multi-joint robotic arm.

[0006] To achieve the above object, according to a first aspect of the present invention, a rope-driven multi-joint robot arm motion control method considering time delay is proposed, comprising the following steps:

[0007] The motion control of the rope-driven multi-joint robot is performed based on the following control law:

[0008]

[0009] in, is τ k The estimated value of τ k represents the joint torque vector at time k, u k is the control input, is a constant diagonal matrix, n is the degree of freedom of the robot;

[0010] is the delay estimate calculated using the adaptive gain:

[0011]

[0012] Among them, δ k is a diagonal matrix used to adaptively adjust the gradient effect, N k-1 N k The value at the previous moment, N k-2 N k-1 The value at the previous moment, N k-3 N k-2 The value at the previous moment; N k is the disturbance term of the dynamic model, and the calculation formula is is the acceleration of the robot joint.

[0013] As a further preferred embodiment, the control input u is determined based on the non-singular terminal sliding surface k .

[0014] As a further preferred embodiment, the non-singular terminal sliding surface is designed as follows:

[0015]

[0016] Among them, s k is the sliding mode variable, e k is the robot joint position tracking error vector, is the robot joint velocity tracking error vector, β is a positive diagonal matrix, p and q are positive odd diagonal matrices, and the mth element p in p m,k and the mth element q in q m,k Satisfying 1<p m,k / q m,k <2, m = 1, 2…n;

[0017] Sliding mode reaching law The design is as follows:

[0018]

[0019] Where k and ε are positive constant switching gain matrices, and sgn is the sign function.

[0020] As a further preferred embodiment, the control input u k The calculation formula is as follows:

[0021]

[0022] in, is the expected angular acceleration vector of the robot joint, and I is the unit matrix.

[0023] As a further preferred embodiment, the control law of the rope-driven multi-joint robotic arm is as follows:

[0024]

[0025]

[0026] in, is an equivalent control item, Toggle control.

[0027] As a further preferred embodiment, the diagonal matrix δ k Through the sliding mode variable s k The calculation results are:

[0028]

[0029] Among them, δ m,k is the diagonal matrix δ k The mth element of s m,k is the sliding mode variable s k The mth element of For m,k The derivative of m With γ m is the positive gain constant, is a non-negative constant.

[0030] As a further preference, the constant diagonal matrix The following stability conditions are met:

[0031]

[0032] Among them, M(q k ) is the inertia matrix of the robot, qk is the position of the robot joint, ∥·∥ represents the norm, and I is the unit matrix.

[0033] According to a second aspect of the present invention, a rope-driven multi-joint robotic arm motion control system considering time delay is provided, comprising a processor, wherein the processor is used to execute the rope-driven multi-joint robotic arm motion control method considering time delay.

[0034] According to a third aspect of the present invention, there is provided a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the motion control method of a rope-driven multi-joint robot arm taking into account the delay is implemented.

[0035] According to a fourth aspect of the present invention, there is provided a computer program product, which includes a computer program, and when the computer program is executed by a processor, the above-mentioned rope-driven multi-joint robot arm motion control method considering time delay is implemented.

[0036] In general, the above technical solution conceived by the present invention has the following technical advantages compared with the prior art:

[0037] 1. Compared with traditional delay estimation control, the present invention uses multiple delay samples for delay estimation to reduce the estimation mutation caused by instantaneous disturbance, and uses adaptive gain to calculate the delay estimation, thereby obtaining a more accurate and stable estimation effect. The control method based on delay estimation of the present invention does not require an accurate model, has high accuracy and good robustness, thereby further improving the trajectory tracking effect and operating performance of the rope-driven multi-joint manipulator, can meet the needs of joint motion control of the rope-driven multi-joint manipulator, and is suitable for implementation in practical engineering applications.

[0038] 2. The present invention adopts non-singular terminal sliding mode control, which improves the convergence speed while ensuring good tracking ability and control stability, and can be easily transplanted into the existing delay estimation control. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a schematic diagram of the structure of a rope-driven multi-joint mechanical arm according to an embodiment of the present invention;

[0040] Figure 2 The figure is a schematic diagram of the control algorithm flow of the rope-driven multi-joint robotic arm according to an embodiment of the present invention. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0042] An embodiment of the present invention provides a rope-driven multi-joint mechanical arm motion control method considering time delay, comprising the following steps:

[0043] (1) The structure of the rope-driven multi-joint robotic arm is as follows: Figure 1 As shown, dynamic modeling and analysis are performed;

[0044] The dynamic model of the n-DOF rope-driven multi-joint manipulator is established as follows:

[0045]

[0046] Where M(q k )∈R n×n represents the inertia matrix of the robot arm, represents the Coriolis force term and the centrifugal force term, G(q k )∈R n×1 represents the gravity term, Represents system uncertainty and disturbance terms such as friction, coupling, etc.; q k ∈R n , and Represents the position, velocity and acceleration of the robot arm joints.

[0047] The Coriolis force, centrifugal force, gravity, system uncertainty and disturbance terms are considered as system model uncertainty terms. It is expressed as follows:

[0048]

[0049] The system dynamics model is reformulated as follows:

[0050]

[0051] In the formula is a constant diagonal matrix, which is used to replace M(q k ), N k Represents the disturbance term of the unknown dynamic model of the lumped system.

[0052] (2) In order to eliminate the disturbance term N of the unknown dynamic model of the lumped system k In order to reduce the influence of delay estimation mutation caused by instantaneous disturbance, a delay estimation method based on multiple delay samples is designed, and the system dynamics model is modified as follows:

[0053]

[0054] Where u k represents the control input, Represents the delay estimation item.

[0055] Use TDE technique to approximate N k , Design delay estimation based on multiple delay samples, design delay estimation items The details are as follows:

[0056]

[0057] Where Nk-1 N k The value at the previous moment, N k-2 N k-1 The value at the previous moment, N k-3 N k-2 The value at the previous moment, μ1, μ2, μ3 are the corresponding coefficient vectors.

[0058] Through the above design, the delay estimation term is represented as a linear combination of the delay samples at multiple previous moments, and the calculation of the coefficient vector is further determined in combination with the adaptive gain.

[0059] In order to obtain a more accurate and stable delay estimation, the delay estimation is adjusted using adaptive gain based on multi-sample delay estimation. The calculation is as follows:

[0060]

[0061] Where δ k =diag(δ 1,k ,δ 2,k ,…,δ n,k )∈R n×n Is a diagonal matrix used to adaptively adjust the gradient effect. Any element δ in this matrix m,k Through the sliding mode variable s k The calculation is as follows:

[0062]

[0063] Where δ m,k is the adaptive diagonal matrix δ k The mth element of s m,k is the mth element of the sliding mode variable, α m With γ m is a positive gain constant. In order to ensure the stability of the adaptive delay estimation, Designed to be a non-negative constant.

[0064] (3) Design a non-singular terminal sliding surface to compensate for the delay control error.

[0065] Design the non-singular terminal sliding surface as follows:

[0066]

[0067] Where p = diag (p1, p2, ..., p n )∈R n×n and q=diag(q1,q2,…,q n )∈R n×n is a positive odd diagonal matrix, and for any element m, 1<p m,k / q m,k <2; β = diag(β 1,k ,β 2,k ,…,β n,k )∈R n×n is a positive diagonal matrix.

[0068] The designed sliding mode reaching law is as follows:

[0069]

[0070] Where k = diag(k 1,k ,k 2,k ,…,k n,k )∈R n×n and ε=diag(ε 1,k ,ε 2,k ,…,ε n,k )∈R n×n is a positive constant switching gain matrix, and sgn is a sign function.

[0071] (4) According to the sliding mode reaching law and adaptive delay estimation, the control law is designed as follows:

[0072]

[0073] In the formula represents the equivalent control term, Represents a toggle control.

[0074] According to the control law and system model, the system error dynamics is obtained as follows:

[0075]

[0076] In the formula is the adaptive delay estimation error.

[0077] In order for the tracking error to converge, the TDE error should satisfy Γ * is a constant diagonal matrix, for which the following stability conditions must be satisfied:

[0078] In summary, the delay estimation with adaptive gain of the present invention can compensate the dynamic model and provide a stable torque input, while the non-singular terminal sliding mode is used to accelerate the convergence speed, and accurate control can be achieved in the presence of transient disturbances, such as friction, payload or trajectory changes. Different from the traditional controller based on delay estimation that directly uses a single sample delayed signal to estimate the unmodeled dynamics and uncertainties, the present invention not only considers multi-sample delayed signals, but also considers the gradient with adaptive gain, which can obtain better tracking performance.

[0079] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A rope-driven multi-joint robotic arm motion control method considering time delay, characterized in that: The steps include: The motion control of the rope-driven multi-joint robot is performed based on the following control law: in, is τ k The estimated value of τ k represents the joint torque vector at time k, u k is the control input, is a constant diagonal matrix, n is the degree of freedom of the robot; is the delay estimate calculated using the adaptive gain: Among them, δ k is a diagonal matrix used to adaptively adjust the gradient effect, N k-1 N k The value at the previous moment, N k-2 N k-1 The value at the previous moment, N k-3 N k-2 The value at the previous moment; N k is the disturbance term of the dynamic model, and the calculation formula is is the acceleration of the robot joint.

2. The method for controlling the motion of a rope-driven multi-joint manipulator considering time delay as claimed in claim 1, characterized in that: Determine the control input u based on the non-singular terminal sliding surface k .

3. The motion control method of a rope-driven multi-joint manipulator considering time delay as claimed in claim 2, characterized in that: The non-singular terminal sliding surface is designed as follows: Among them, s k is the sliding mode variable, e k is the robot joint position tracking error vector, is the robot joint velocity tracking error vector, β is a positive diagonal matrix, p and q are positive odd diagonal matrices, and the mth element p in p m,k and the mth element q in q m,k Satisfying 1<p m,k / q m,k <2, m = 1, 2…n; Sliding mode reaching law The design is as follows: Where k and ε are positive constant switching gain matrices, and sgn is the sign function.

4. The method for controlling the motion of a rope-driven multi-joint manipulator considering time delay as claimed in claim 3, characterized in that: Control input u k The calculation formula is as follows: in, is the expected angular acceleration vector of the robot joint, and I is the unit matrix.

5. The motion control method of a rope-driven multi-joint manipulator considering time delay as claimed in claim 4, characterized in that: The control law of the rope-driven multi-joint manipulator is as follows: in, is an equivalent control item, Toggle control.

6. The method for controlling the motion of a rope-driven multi-joint manipulator considering time delay as claimed in claim 3, characterized in that: Diagonal matrix δ k Through the sliding mode variable s k The calculation results are: Among them, δ m,k is the diagonal matrix δ k The mth element of s m,k is the sliding mode variable s k The mth element of For m,k The derivative of m With γ m is the positive gain constant, is a non-negative constant.

7. The method for controlling the motion of a rope-driven multi-joint manipulator considering time delay according to any one of claims 1 to 6, characterized in that: Constant diagonal matrix The following stability conditions are met: Among them, M(q k ) is the inertia matrix of the robot, qk is the position of the robot joint, ∥·∥ represents the norm, and I is the unit matrix.

8. A rope-driven multi-joint robotic arm motion control system considering time delay, characterized in that: It comprises a processor, wherein the processor is used to execute the rope-driven multi-joint robot arm motion control method considering time delay as described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the rope-driven multi-joint robotic arm motion control method considering delay as described in any one of claims 1 to 7 is implemented.

10. A computer program product, characterized in that It comprises a computer program, which, when executed by a processor, implements the rope-driven multi-joint robotic arm motion control method considering delay as described in any one of claims 1 to 7.

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