A rope-driven multi-joint robotic arm motion control method, system, medium and product considering time delay

Abstract

The present invention belongs to the field of robotic system control technology and specifically discloses a method, system, medium, and product for motion control of a rope-driven multi-joint manipulator that takes time delay into account. The method includes: when performing time delay estimation, designing a time delay estimation term based on multiple time delay samples, and adjusting the time delay estimation through adaptive gain; that is, not only considering the multi-sample delayed signal, but also considering the gradient with adaptive gain. The time delay estimation with adaptive gain can compensate for the dynamic model and provide a stable torque input. At the same time, a non-singular terminal sliding surface is designed to accelerate the convergence speed. In the presence of transient interference, such as friction, payload, or trajectory changes, precise control can also be achieved. The control method based on time delay estimation proposed by the present invention does not require a precise model, has high accuracy, and good robustness, and improves the trajectory tracking effect and operating performance of the rope-driven multi-joint manipulator.

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 considering time delay. Background Art

[0002] Rope-driven multi-jointed robotic arms are composed of a series of rigid links, using rope transmission to simulate the actuation effects of biological tendons. They offer high driving force, multiple degrees of freedom, and high reliability, enabling telescoping, swaying, heaving, linear, and lateral movements. Their flexible movements and large workspace allow them to carry equipment and perform tasks deep within confined environments. Their enormous potential has garnered widespread attention.

[0003] However, its rope-driven, hyper-redundant structure complicates motion control. In the field of robot dynamics control, nonlinear terms such as gravity, Coriolis, friction, and other disturbances pose significant challenges to manipulator motion control. Model-based controllers have been studied for decades, and their performance has been well-proven. However, identifying the manipulator's dynamic parameters is a complex and difficult task, and the complexity of the robot model increases significantly with the number of estimated model parameters, a particular problem for rope-driven multi-joint manipulators.

[0004] Control schemes based on time delay estimation (TDE) are known for their ability to effectively handle highly nonlinear and complex systems with external disturbances and model uncertainties. Due to their simplicity, efficiency, and robustness, they are widely used in the field of robotics. Practical applications have shown that the more complex and uncertain the system, the more pronounced the practical effects of TDE technology. However, the performance of traditional TDE is limited by the system's time delay samples. When intermittent disturbances or uncertainties exist, it is difficult to find a suitable time delay estimation gain, resulting in increased error in the time delay estimation. Therefore, a reliable and easy-to-implement method is needed to solve the problems in TDE applications and achieve stable motion control of the robotic arm under transient disturbances while also achieving a fast convergence speed. Summary of the Invention

[0005] In response to the above-mentioned 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 that take time delay into consideration, with the aim of achieving stable motion control of the robotic arm under transient disturbances and improving 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 motion control method for a rope-driven multi-joint manipulator taking time delay into consideration is proposed, comprising the following steps:

[0007] The motion control of the rope-driven multi-joint manipulator 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 manipulator;

[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 Indicates N k The value at the previous moment, N k-2 Indicates N k-1 The value at the previous moment, N k-3 Indicates 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 mode 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 arm 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 desired 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 option, the diagonal matrix δ k Through the sliding mode variable s k Calculation yields:

[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 s m,k The derivative of α 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 arm, qk is the position of the robot arm 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 configured 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, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the method for controlling the motion of a rope-driven multi-joint robotic arm taking into account the time delay is implemented.

[0035] According to a fourth aspect of the present invention, a computer program product is provided, comprising a computer program, wherein when the computer program is executed by a processor, the computer program implements the above-mentioned delay-considered rope-driven multi-joint robotic arm motion control method.

[0036] In general, the above technical solutions conceived by the present invention have the following technical advantages compared with the existing technology:

[0037] Compared to traditional delay estimation control, this invention uses multiple delay samples for delay estimation to reduce sudden changes in the estimation caused by transient disturbances. It also employs adaptive gain calculations for delay estimation, resulting in more accurate and stable estimation results. This delay estimation-based control method, which does not require a precise model and offers high accuracy and robustness, further improves the trajectory tracking and operational performance of rope-driven multi-joint manipulators. It meets the requirements for joint motion control of rope-driven multi-joint manipulators 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 structural diagram of a rope-driven multi-joint robotic arm according to an embodiment of the present invention;

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

[0041] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining 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 may be combined with each other as long as they do not conflict with each other.

[0042] An embodiment of the present invention provides a method for controlling motion of a rope-driven multi-joint robotic arm taking into account 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 carried out;

[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 robotic 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 term, centrifugal force term, gravity term, system uncertainty and disturbance term are regarded 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, 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 unknown dynamic model disturbance term N 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 Indicates N k The value at the previous moment, N k-2 Indicates N k-1 The value at the previous moment, N k-3 Indicates 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 expressed as a linear combination of delay samples at multiple previous moments. The calculation of the coefficient vector is further combined with the adaptive gain.

[0059] In order to obtain more accurate and stable delay estimation, adaptive gain is used to adjust the delay estimation 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 It is a diagonal matrix used to adaptively adjust the gradient effect. Any element in this matrix is 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] The non-singular terminal sliding surface is designed 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 the positive constant switching gain matrix, and sgn is the sign function.

[0071] (4) Based on the sliding mode reaching law and adaptive time 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 to make the tracking error converge, the TDE error should satisfy Γ * is a constant diagonal matrix, and the following stability conditions must be met:

[0078] In summary, the delay estimation with adaptive gain in the present invention compensates for the dynamic model and provides stable torque input. Meanwhile, a non-singular terminal sliding mode is used to accelerate convergence, enabling precise control in the presence of transient disturbances such as friction, payload, or trajectory changes. Unlike traditional delay estimation-based controllers that directly use a single-sample delayed signal to estimate unmodeled dynamics and uncertainties, the present invention not only considers multiple-sample delayed signals but also gradients with adaptive gain, resulting in better tracking performance.

[0079] It will be easily understood by those skilled in the art that the above description is merely 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 scope of protection of the present invention.

Claims

1. A motion control method for a rope-driven multi-joint manipulator considering time delay, characterized in that: The steps include: The motion control of the rope-driven multi-joint manipulator 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 manipulator; 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 Indicates N k The value at the previous moment, N k-2 Indicates N k-1 The value at the previous moment, N k-3 Indicates 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 according to claim 1, wherein: Determine the control input u based on the non-singular terminal sliding surface k .

3. The delay-considered rope-driven multi-joint robotic arm motion control method according to 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 arm 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 according to claim 3, wherein: Control input u k The calculation formula is as follows: in, is the desired angular acceleration vector of the robot joint, and I is the unit matrix.

5. The method for controlling the motion of a rope-driven multi-joint manipulator considering time delay according to claim 4, wherein: 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 according to claim 3, wherein: Diagonal matrix δ k Through the sliding mode variable s k Calculation yields: 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 s m,k The derivative of α m with γ m is the positive gain constant, is a non-negative constant.

7. The motion control method 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 arm, qk is the position of the robot arm 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: The method comprises a processor configured to execute the delay-considered rope-driven multi-joint robotic arm motion control method according to any one of claims 1 to 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 delay-considered rope-driven multi-joint robotic arm motion control method according to any one of claims 1 to 7 is implemented.

10. A computer program product, characterized in that The invention comprises a computer program, which, when executed by a processor, implements the motion control method of a rope-driven multi-joint robotic arm taking into account the time delay as claimed in any one of claims 1 to 7.

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