A method and system for hierarchical solution of a snake-like robot based on model predictive control

Abstract

The application provides a model predictive control-based layered solving method and system for a snake-shaped mechanical arm, relates to the field of rope-driven snake-shaped mechanical arms, and comprises the following steps: decomposing a snake-shaped mechanical arm in structure by using a Bezier curve, dividing a preset number of low-redundancy snake-shaped mechanical arms, constructing a model predictive control method, determining an inverse kinematics problem of the low-redundancy snake-shaped mechanical arm, designing a finite-time dual neural network model, solving the inverse kinematics problem through the finite-time dual neural network model, and controlling the joint angles of the low-redundancy snake-shaped mechanical arm according to a solving result. The snake-shaped mechanical arm is decomposed in structure by using the Bezier curve, a low-complexity segmented mechanical arm is obtained, and the calculation complexity is reduced. A model predictive control scheme is designed, and an optimization problem is converted into a QP problem; a finite-time dual neural network model is designed for solving, and the solving speed is accelerated.

Description

Technical Field

[0001] This application relates to the field of rope-driven snake-like robotic arms, and in particular to a hierarchical solution method and system for snake-like robotic arms based on model predictive control. Background Technology

[0002] Snake-like robotic arms are crucial tools for automating industrial production, and various industrial and special-purpose robots are already playing a significant role in fields such as automotive, shipbuilding, and petrochemicals. However, with the rapid development of science and technology, leading technological nations are investing heavily in high-tech industries such as aerospace, aviation, and nuclear power. In this era of rapid technological advancement, regular monitoring and maintenance are essential for ensuring the safe operation of equipment such as spacecraft, large aircraft, and nuclear facilities. However, the complex structures of these devices often limit the space available for monitoring and maintenance. Therefore, to achieve the monitoring and maintenance of such equipment, countries are actively exploring technologies for robots to perform equipment monitoring and maintenance in confined spaces. To successfully complete monitoring and maintenance in confined spaces, robots need the ability to traverse narrow environments, avoid obstacles, overcome joint oddities and exceeding limits, and possess a sufficiently large maneuvering space. Traditional 6- or 7-DOF robots struggle to achieve these goals simultaneously. However, snake-like robotic arms not only possess excellent environmental adaptability and high obstacle avoidance capabilities but can also operate in unstructured environments and multi-device environments with non-cooperative targets using methods such as circling.

[0003] Snake-like robotic arms (also known as hyper-redundant snake-like robotic arms) are a new type of special-purpose robot. They have a large number of joints and high degrees of freedom. The arm body does not contain power components; instead, it is driven by a motor at the bottom that drives multiple ropes via a ball screw. This design makes snake-like robotic arms flexible in movement and have a large working range. They can work in special and harsh environments such as narrow and confined spaces, high temperatures and pressures, and extreme cold and vacuum. They have broad application prospects in fields such as aircraft manufacturing, space station maintenance, nuclear power plant repair, and seabed exploration.

[0004] Rope-driven serpentine robotic arms have a large number of degrees of freedom and actuators, posing challenges to motion modeling and control while ensuring the flexibility of the mechanism. Traditional industrial robots use independent actuator modules for each degree of freedom, naturally decoupling joint motion from actuator signals. However, in rope-driven serpentine robotic arms, the actuator ropes are distributed in parallel, and the rope length is affected by the motion of all joints, resulting in a complex nonlinear function mapping. Furthermore, the actuator ropes can only bear tension, not compression; therefore, the number of ropes in the serpentine robotic arm must exceed the number of degrees of freedom to maintain motion posture and stiffness through the "antagonistic" forces between the ropes. The serpentine robotic arm possesses redundant degrees of freedom and redundant actuators, with the task space motion corresponding to various joint motions and rope force distributions. Solving for joint motions and rope tension requires the addition of corresponding zero-space optimization constraints. The large number of moving and actuator components increases the uncertainty of the control model. To ensure good maneuverability of the serpentine robotic arm, its controller needs to have strong robustness while maintaining motion accuracy. Therefore, in order for the rope-driven serpentine robotic arm to perform its tasks smoothly, it is necessary to analyze the motion and forces of its rope, joints, and task space using kinematic and dynamic models, and design a stable and reliable motion controller based on this analysis.

[0005] In end-effector control, the main challenge lies in solving the inverse kinematics problem. The inverse kinematics of a serpentine robot is defined as solving the joint angles based on the pose of the end-effector, and is generally solved using numerical and analytical methods. In general or low-redundancy serpentine robots, some mature research results based on these two methods have been achieved. Geometric methods offer a simple and intuitive approach to handling inverse kinematics. Some scholars have proposed an improved mode function method to solve the inverse kinematics of tethered serpentine robots, or a method based on piecewise geometry to solve the inverse kinematics. However, for tethered serpentine robots, their structure does not satisfy the conditions for obtaining a closed-form solution, making it impossible to obtain an accurate analytical solution using only geometric methods. Furthermore, geometric methods cannot achieve constrained motion control, further weakening their advantages.

[0006] Numerical methods are more direct and generally applicable to solving inverse kinematic problems. Some studies are based on the Jacobian matrix. The augmented Jacobian matrix method introduces task constraints into the velocity Jacobian matrix by expanding the row vectors of the Jacobian matrix. In this case, the velocity Jacobian matrix of the redundant manipulator becomes invertible, allowing unique joint velocities to be obtained from the task velocity. Some scholars have proposed two redundancy utilization strategies based on different evaluation metrics and implemented planar motion optimization of the manipulator using the velocity gradient method. In recent years, intelligent algorithms have been increasingly widely used in robotics. One paper proposed establishing a kinematic model of a cable-driven continuous snake-like manipulator based on artificial neural networks. However, as the degrees of freedom increase, the Jacobian matrix of the snake-like manipulator becomes increasingly complex, leading to a significant increase in the computational cost and complexity of the optimization problem, thus slowing down the solution process.

[0007] The above analysis shows that current inverse kinematics solutions for snake-like robotic arms are not yet mature enough. For example, geometric constraint-based methods have high efficiency and stability, but the introduction of numerous constraints affects the snake-like robotic arm's ability to optimize the objective. Algebraic methods, on the other hand, involve too many equations and are difficult to solve. Summary of the Invention

[0008] The purpose of this invention is to provide a hierarchical solution method and system for snake-like robotic arms based on model predictive control, in order to solve the problem of the complex solution process of existing inverse kinematics solution methods for snake-like robotic arms.

[0009] The above-mentioned objective of this application is achieved through the following technical solution:

[0010] S1: Utilize Bézier curves to structurally decompose the snake-shaped robotic arm and divide it into a preset number of low-redundancy snake-shaped robotic arms.

[0011] S2: Construct a model predictive control method to determine the inverse kinematics problem of a low-redundancy snake-like robotic arm;

[0012] S3: Design a finite-time dual neural network model; solve the inverse kinematics problem using the finite-time dual neural network model;

[0013] S4: Based on the solution results, control the angles of each joint of the low-redundancy snake-shaped robotic arm.

[0014] Optionally, step S1 includes:

[0015] The coordinates of the snake-like robotic arm in Cartesian space were fitted using a third-order Bézier curve, and key joints were selected.

[0016] The Bézier curve is fitted to multiple segments using a polynomial, as shown in the following expression:

[0017]

[0018] In the formula The parameter variables representing the Bézier curve; To control the number of points; These are the coordinates of a point on the Bézier curve, and correspondingly... It is the first The coordinates of the control points; These are basis functions of the Bézier curve, expressed as: ;

[0019] The starting point is set as the origin of the base coordinate system of the snake-like robotic arm, that is... The orientation of the snake-shaped robotic arm at zero position is along positive axis direction, define direction vector , about the base coordinate system Shaft rotation angle Then, around the base coordinate system Shaft rotation angle ,get:

[0020]

[0021] Therefore, we get:

[0022]

[0023] The coordinates of the end point are , direction is ,Depend on Decision, therefore obtained

[0024]

[0025] in Control points and control points The distance between them;

[0026] Set the starting direction of the Bézier curve and The included angle of the shaft does not exceed ,Right now Define optimization parameters The obtained optimization objective function as follows:

[0027]

[0028] in Let be the length of the Bézier curve. For the first snake-shaped robotic arm Linkage length, This refers to the number of universal joints;

[0029] Bézier curves with respect to parameters The differential is:

[0030]

[0031] The length of a Bézier curve is expressed as an integral:

[0032]

[0033] in Represents the L2 norm;

[0034] Using the 3 / 8 Simpson rule, combined with control points The analytical expression for the length of the Bézier curve is obtained as follows:

[0035]

[0036] Select a preset number of universal joints as key joints: the center of each key joint lies on a Bézier curve. Assume the ratio of the center positions of the preset number of universal joints on the Bézier curve to their ratios on the robotic arm's lever. That is, if the first... The universal joint is a key joint, for those with For a serpentine robotic arm with a universal joint, there are

[0037]

[0038] Numerical solution method is used to obtain , This refers to the positional parameters of the center of the key joint;

[0039] Based on the position parameters of the key joint centers, the snake-like robotic arm is divided into a preset number of low-redundancy snake-like robotic arms to complete the degree of freedom reconstruction.

[0040] Optionally, step S2 includes:

[0041] The end effector pose of the snake-like robotic arm is represented as follows:

[0042]

[0043] in It is the pose vector of the end effector of the snake-shaped robotic arm, and the end attitude is represented by Euler angles; For joint angle vectors, The number of degrees of freedom; Let q(t) represent the joint angle and x(t) be the positive kinematic mapping of the end pose.

[0044] The instantaneous kinematics of the snake-like robotic arm is described as follows:

[0045]

[0046] in The Jacobian matrix for the snake-like robotic arm; For the terminal velocity, Joint velocity;

[0047] The joint velocity can be represented in a discretized form, such as:

[0048]

[0049] in For time intervals; For the first The joint velocity obtained from the second sampling. and They are the first Second and third The joint angle obtained from the second sampling;

[0050] The back-bearing Euler representation of joint acceleration is obtained as follows:

[0051]

[0052] in For the first The joint acceleration obtained from the second sampling For the first The joint velocity obtained from the previous sample will be used for the next sample. Record ,get:

[0053]

[0054] in To control the time domain; For the first The joint velocity obtained from the second sampling; Used to describe joint acceleration;

[0055] Obtain joint angle :

[0056]

[0057] in To predict the time domain, For the first The joint angle obtained from the second sampling; when hour ;right Using a first-order Taylor expansion, we obtain

[0058]

[0059] in Indicates the first The end position obtained from the second sampling Indicates joint angle The corresponding Jacobian matrix is ​​used to define the end-tracking error. ,in Indicates the first One expected end position;

[0060] The design model predictive control method is given by the following formula:

[0061]

[0062] in , , Both are weight matrices. These represent the upper and lower bounds of the joint angle constraint, respectively. These represent the upper and lower bounds of the joint velocity constraint, respectively. These represent the upper and lower bounds of the joint acceleration constraint, respectively. To predict the time domain, To control the time domain.

[0063] Optionally, step S2 may further include:

[0064] The formulas for model predictive control methods, after being rearranged and rewritten, are as follows:

[0065]

[0066] in This indicates that the matrix is ​​vectorized. and It is a constraint matrix. and These are all matrices obtained by simplification using model predictive control methods; denoted as the optimal joint angular acceleration; W represents the matrix obtained by simplifying the constraints of the model predictive control method.

[0067] The inverse kinematics problem specifically involves finding the optimal joint angular acceleration. The first item The joint velocities of the low-redundancy snake-like robotic arm are obtained. .

[0068] Optionally, step S3 includes:

[0069] The problem of solving the model predictive control method is simplified into a QP problem, as follows:

[0070]

[0071] in , , ;

[0072] According to the KKT conditions, the optimal solution to the QP problem should satisfy the following conditions:

[0073]

[0074] in These are the dual variables of the inequality constraints;

[0075] Define a projection function as follows:

[0076]

[0077] in

[0078]

[0079] Represents each element Z i From the processing function, we can obtain:

[0080]

[0081] .

[0082] Optionally, step S3 may also include:

[0083] A finite-time dual neural network model was designed, and the optimal joint angular acceleration was obtained. ,as follows:

[0084]

[0085] in dual variables The derivative of the network parameters and , The activation function is specifically defined as follows: ;

[0086] This represents the processing function for each element, and... Having the same attributes in and , It is a symbolic function, because It is a constant matrix, so we get ,in for The false rebellion.

[0087] A hierarchical solution system for a snake-like robotic arm based on model predictive control, the system comprising: a computer, a snake-like robotic arm, and a display screen;

[0088] The computer is used to acquire data parameters of the snake-like robotic arm;

[0089] The computer is also used to decompose the snake-shaped robotic arm structurally using Bézier curves and data parameters, and to divide it into a preset number of low-redundancy snake-shaped robotic arms.

[0090] The computer is also used to construct model predictive control methods to determine the inverse kinematics problem of a low-redundancy snake-like robotic arm.

[0091] The computer is also used to design finite-time dual neural network models; and to solve inverse kinematics problems using finite-time dual neural network models.

[0092] The computer is also used to control the angles of each joint of the low-redundancy snake-like robotic arm based on the solution results.

[0093] The display screen is used to visualize the three-dimensional motion state of the snake-shaped robotic arm in real time.

[0094] A computer-readable storage medium storing instructions that, when executed, perform a hierarchical solution method for a snake-like robotic arm based on model predictive control.

[0095] The beneficial effects of the technical solution provided in this application are:

[0096] The kinematics of a rope-driven serpentine robot arm are analyzed, and a novel two-stage motion optimization method is proposed to solve the inverse kinematic problem of the serpentine robot arm. In the first layer, Bézier curves are used to structurally decompose the serpentine robot arm, dividing it into several low-redundancy serpentine robot arms, thus solving the problem of high degrees of freedom.

[0097] In the second layer, a model predictive control (MMC) approach was used to establish the inverse kinematics problem of a low-redundancy snake-like robotic arm, and a finite-time dual neural network model was designed to solve it. This method reduces the degrees of freedom through structural decomposition, simplifies the problem-solving process through MMC, and finally uses a finite-time solution to obtain the joint angles. This not only reduces computational complexity and speeds up the solution process but also improves the accuracy, providing a foundation for further control. Attached Figure Description

[0098] The present application will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0099] Figure 1This is a flowchart illustrating the hierarchical solution method for a snake-like robotic arm based on model predictive control in this application embodiment;

[0100] Figure 2 This is the end effector trajectory diagram of the first segment of the low-redundancy robotic arm in the hierarchical solution method for the snake-like robotic arm based on model predictive control in the embodiments of this application.

[0101] Figure 3 This is the end effector motion error diagram of the first segment of the low-redundancy robotic arm in the hierarchical solution method for the snake-like robotic arm based on model predictive control in the embodiments of this application.

[0102] Figure 4 This is the joint angle diagram obtained by solving the first segment of the low-redundancy robotic arm in the hierarchical solution method of the snake-like robotic arm based on model predictive control in the embodiments of this application;

[0103] Figure 5 This is the joint velocity diagram obtained from solving the first segment of the low-redundancy robotic arm in the hierarchical solution method for the snake-like robotic arm based on model predictive control in the embodiments of this application.

[0104] Figure 6 This is the end effector trajectory diagram of the second segment of the low-redundancy robotic arm in the hierarchical solution method for snake-like robotic arms based on model predictive control in the embodiments of this application.

[0105] Figure 7 This is the end effector motion error diagram of the second segment of the low-redundancy robotic arm in the hierarchical solution method for snake-like robotic arms based on model predictive control in the embodiments of this application.

[0106] Figure 8 This is the joint angle diagram obtained from solving the second low-redundancy robotic arm in the hierarchical solution method for the snake-like robotic arm based on model predictive control in the embodiments of this application;

[0107] Figure 9 This is the joint velocity diagram obtained from solving the second segment of the low-redundancy robotic arm using the hierarchical solution method for the snake-like robotic arm based on model predictive control in this embodiment of the application. Detailed Implementation

[0108] To provide a clearer understanding of the technical features, objectives, and effects of this application, the specific embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0109] The embodiments of this application provide a hierarchical solution method for a snake-like robotic arm based on model predictive control.

[0110] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating the steps of a hierarchical solution method for a snake-like robotic arm based on model predictive control, as described in an embodiment of this application, including:

[0111] S1: Utilize Bézier curves to structurally decompose the snake-shaped robotic arm and divide it into a preset number of low-redundancy snake-shaped robotic arms.

[0112] Step S1 includes:

[0113] The coordinates of the snake-like robotic arm in Cartesian space were fitted using a third-order Bézier curve, and key joints were selected.

[0114] The Bézier curve is fitted to multiple segments using a polynomial, as shown in the following expression:

[0115]

[0116] In the formula The parameter variables representing the Bézier curve; To control the number of points; These are the coordinates of a point on the Bézier curve, and correspondingly... It is the first The coordinates of the control points; These are basis functions of the Bézier curve, expressed as: ;

[0117] Specifically, the shape of the snake-like robotic arm is fitted using a third-order Bézier curve.

[0118] The starting point is set as the origin of the base coordinate system of the snake-like robotic arm, that is... The orientation of the snake-shaped robotic arm at zero position is along positive axis direction, define direction vector , about the base coordinate system Shaft rotation angle Then, around the base coordinate system Shaft rotation angle ,get:

[0119]

[0120] Therefore, we get:

[0121]

[0122] The coordinates of the end point are , direction is ,Depend on Decision, therefore obtained

[0123]

[0124] in Control points and control points The distance between them;

[0125] Specifically, in order to ensure that the key joints can fall on the curve of the arm, the difference between the curve length and the actual length of the arm is taken as the optimization target. Since the joint angle of the snake-shaped robotic arm is limited, an optimization objective function is defined for safety.

[0126] Set the starting direction of the Bézier curve and The included angle of the shaft does not exceed ,Right now Define optimization parameters The obtained optimization objective function as follows:

[0127]

[0128] in Let be the length of the Bézier curve. For the first snake-shaped robotic arm Linkage length, This refers to the number of universal joints;

[0129] Bézier curves with respect to parameters The differential is:

[0130]

[0131] The length of a Bézier curve is expressed as an integral:

[0132]

[0133] in Represents the L2 norm;

[0134] Using the 3 / 8 Simpson rule, combined with control points The analytical expression for the length of the Bézier curve is obtained as follows:

[0135]

[0136] Select a preset number of universal joints as key joints: the center of each key joint lies on a Bézier curve. Assume the ratio of the center positions of the preset number of universal joints on the Bézier curve to their ratios on the robotic arm's lever. That is, if the first... The universal joint is a key joint, for those with For a serpentine robotic arm with a universal joint, there are

[0137]

[0138] Numerical solution method is used to obtain , This refers to the positional parameters of the center of the key joint;

[0139] Based on the position parameters of the key joint centers, the snake-like robotic arm is divided into a preset number of low-redundancy snake-like robotic arms to complete the degree of freedom reconstruction.

[0140] S2: Construct a model predictive control method to determine the inverse kinematics problem of a low-redundancy snake-like robotic arm;

[0141] Step S2 includes:

[0142] The end effector pose of the snake-like robotic arm is represented as follows:

[0143]

[0144] in It is the pose vector of the end effector of the snake-shaped robotic arm, and the end attitude is represented by Euler angles; For joint angle vectors, The number of degrees of freedom; Let q(t) represent the joint angle and x(t) be the positive kinematic mapping of the end pose.

[0145] The instantaneous kinematics of the snake-like robotic arm is described as follows:

[0146]

[0147] in The Jacobian matrix for the snake-like robotic arm; For the terminal velocity, Joint velocity;

[0148] The joint velocity can be represented in a discretized form, such as:

[0149]

[0150] in For time intervals; For the first The joint velocity obtained from the second sampling. and They are the first Second and third The joint angle obtained from the second sampling;

[0151] The back-bearing Euler representation of joint acceleration is obtained as follows:

[0152]

[0153] in For the first The joint acceleration obtained from the second sampling For the first The joint velocity obtained from the previous sample will be used for the next sample. Record ,get:

[0154]

[0155] in To control the time domain; For the first The joint velocity obtained from the second sampling; Used to describe joint acceleration;

[0156] Obtain joint angle :

[0157]

[0158] in To predict the time domain, For the first The joint angle obtained from the second sampling; when hour ;right Using a first-order Taylor expansion, we obtain

[0159]

[0160] in Indicates the first The end position obtained from the second sampling Indicates joint angle The corresponding Jacobian matrix is ​​used to define the end-tracking error. ,in Indicates the first One expected end position;

[0161] The design model predictive control method is given by the following formula:

[0162]

[0163] in , , Both are weight matrices. These represent the upper and lower bounds of the joint angle constraint, respectively. These represent the upper and lower bounds of the joint velocity constraint, respectively. These represent the upper and lower bounds of the joint acceleration constraint, respectively. To predict the time domain, To control the time domain.

[0164] Step S2 also includes:

[0165] The formulas for model predictive control methods, after being rearranged and rewritten, are as follows:

[0166]

[0167] in This indicates that the matrix is ​​vectorized. and It is a constraint matrix. and These are all matrices obtained by simplification using model predictive control methods; denoted as the optimal joint angular acceleration; W represents the matrix obtained by simplifying the constraints of the model predictive control method.

[0168] The inverse kinematics problem specifically involves finding the optimal joint angular acceleration. The first item The joint velocities of the low-redundancy snake-like robotic arm are obtained. .

[0169] S3: Design a finite-time dual neural network model; solve the inverse kinematics problem using the finite-time dual neural network model;

[0170] Step S3 includes:

[0171] The problem of solving the model predictive control method is simplified into a QP problem, as follows:

[0172]

[0173] in , , ;

[0174] According to the KKT conditions, the optimal solution to the QP problem should satisfy the following conditions:

[0175]

[0176] in These are the dual variables of the inequality constraints;

[0177] Specifically, the KKT (Karush-Kuhn-Tucker Conditions) conditions; the QP problem is a quadratic programming problem.

[0178] Define a projection function as follows:

[0179]

[0180] in

[0181]

[0182] Represents each element Z i From the processing function, we can obtain:

[0183]

[0184] .

[0185] Step S3 also includes:

[0186] A finite-time dual neural network model was designed, and the optimal joint angular acceleration was obtained. ,as follows:

[0187]

[0188] in dual variables The derivative of the network parameters and , The activation function is specifically defined as follows: ;

[0189] This represents the processing function for each element, and... Having the same attributes in and , It is a symbolic function, because It is a constant matrix, so we get ,in for The false rebellion.

[0190] S4: Based on the solution results, control the angles of each joint of the low-redundancy snake-shaped robotic arm.

[0191] A hierarchical solution system for a snake-like robotic arm based on model predictive control, the system comprising: a computer, a snake-like robotic arm, and a display screen;

[0192] The computer is used to acquire data parameters of the snake-like robotic arm;

[0193] The computer is also used to decompose the snake-shaped robotic arm structurally using Bézier curves and data parameters, and to divide it into a preset number of low-redundancy snake-shaped robotic arms.

[0194] The computer is also used to construct model predictive control methods to determine the inverse kinematics problem of a low-redundancy snake-like robotic arm.

[0195] The computer is also used to design finite-time dual neural network models; and to solve inverse kinematics problems using finite-time dual neural network models.

[0196] The computer is also used to control the angles of each joint of the low-redundancy snake-like robotic arm based on the solution results.

[0197] The display screen is used to visualize the three-dimensional motion state of the snake-shaped robotic arm in real time.

[0198] This application also discloses a computer-readable storage medium storing multiple instructions adapted for loading by a processor to execute the above-described hierarchical solution method for a snake-like robotic arm based on model predictive control.

[0199] Figure 2 This is the end effector trajectory diagram of the first low-redundancy robotic arm; Figure 3 This is the end-effector motion error diagram of the first low-redundancy robotic arm; Figure 4 This is the joint angle diagram obtained from the solution of the first low-redundancy robotic arm; Figure 5 This is the joint velocity diagram obtained from solving the first segment of the low-redundancy robotic arm; Figure 6 This is the end effector trajectory diagram of the second low-redundancy robotic arm; Figure 7 This is the end effector motion error diagram of the second low-redundancy robotic arm; Figure 8 This is the joint angle diagram obtained from solving the second segment of the low-redundancy robotic arm; Figure 9 This is the joint velocity diagram obtained from solving the second segment of the low-redundancy robotic arm.

[0200] Simulation verification was performed on MATLAB 2022a, and a 14-DOF robotic arm model was designed. The simulation results are as follows. Figures 2-9 As shown, by providing a virtual path, the joint angles at the desired end points are obtained. It can be seen that the end-point error is small, and both the joint angles and angular velocities are within the constraints.

[0201] The above are merely exemplary embodiments of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure. Other embodiments of this disclosure will readily conceive of those skilled in the art upon consideration of the specification and the disclosure of practical truths.

[0202] This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure. The specification and embodiments are to be considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

Claims

1. A hierarchical solution method for a snake-like robotic arm based on model predictive control, characterized in that, The method includes the following steps: S1: Utilize Bézier curves to structurally decompose the snake-shaped robotic arm and divide it into a preset number of low-redundancy snake-shaped robotic arms. Step S1 includes: The coordinates of the snake-like robotic arm in Cartesian space were fitted using a third-order Bézier curve, and key joints were selected. The Bézier curve is fitted to multiple segments using a polynomial, as shown in the following expression: In the formula The parameter variables representing the Bézier curve; To control the number of points; These are the coordinates of a point on the Bézier curve, and correspondingly... It is the first The coordinates of the control points; These are basis functions of the Bézier curve, expressed as: ; The starting point is set as the origin of the base coordinate system of the snake-like robotic arm, that is... The orientation of the snake-shaped robotic arm at zero position is along positive axis direction, define direction vector , about the base coordinate system Shaft rotation angle Then, around the base coordinate system Shaft rotation angle ,get: Therefore, we get: The coordinates of the end point are , direction is ,Depend on Decision, therefore obtained in Control points and control points The distance between them; Set the starting direction of the Bézier curve and The included angle of the shaft does not exceed ,Right now Define optimization parameters The obtained optimization objective function as follows: in Let be the length of the Bézier curve. For the first snake-shaped robotic arm Linkage length, This refers to the number of universal joints; Bézier curves with respect to parameters The differential is: The length of a Bézier curve is expressed as an integral: in Represents the L2 norm; Using the 3 / 8 Simpson rule, combined with control points The analytical expression for the length of the Bézier curve is obtained as follows: Select a preset number of universal joints as key joints: the center of each key joint lies on a Bézier curve. Assume the ratio of the center positions of the preset number of universal joints on the Bézier curve to their ratios on the robotic arm's lever. That is, if the first... The universal joint is a key joint, for those with For a serpentine robotic arm with a universal joint, there are Numerical solution method is used to obtain , This refers to the positional parameters of the center of the key joint; Based on the position parameters of the key joint centers, the snake-shaped robotic arm is divided into a preset number of low-redundancy snake-shaped robotic arms to complete the degree of freedom reconstruction; S2: Construct a model predictive control method to determine the inverse kinematics problem of a low-redundancy snake-like robotic arm; Step S2 includes: The end effector pose of the snake-like robotic arm is represented as follows: in It is the pose vector of the end effector of the snake-shaped robotic arm, and the end attitude is represented by Euler angles; For joint angle vectors, The number of degrees of freedom; Let q(t) represent the joint angle and x(t) be the positive kinematic mapping of the end pose. The instantaneous kinematics of the snake-like robotic arm is described as follows: in The Jacobian matrix for the snake-like robotic arm; For the terminal velocity, Joint velocity; The joint velocity can be represented in a discretized form, such as: in For time intervals; For the first The joint velocity obtained from the second sampling. and They are the first Second and third The joint angle obtained from the second sampling; The back-bearing Euler representation of joint acceleration is obtained as follows: in For the first The joint acceleration obtained from the second sampling For the first The joint velocity obtained from the previous sample will be used for the next sample. Record ,get: in To control the time domain; For the first The joint velocity obtained from the second sampling; Used to describe joint acceleration; Obtain joint angle : in To predict the time domain, For the first The joint angle obtained from the second sampling; when hour ;right Using a first-order Taylor expansion, we obtain in Indicates the first The end position obtained from the second sampling Indicates joint angle The corresponding Jacobian matrix is ​​used to define the end-tracking error. ,in Indicates the first One expected end position; The design model predictive control method is given by the following formula: in , , Both are weight matrices. These represent the upper and lower bounds of the joint angle constraint, respectively. These represent the upper and lower bounds of the joint velocity constraint, respectively. These represent the upper and lower bounds of the joint acceleration constraint, respectively. To predict the time domain, To control the time domain; Step S2 also includes: The formulas for model predictive control methods, after being rearranged and rewritten, are as follows: in This indicates that the matrix is ​​vectorized. and It is a constraint matrix. and These are all matrices obtained by simplification using model predictive control methods; denoted as the optimal joint angular acceleration; W represents the matrix obtained by simplifying the constraints of the model predictive control method. The inverse kinematics problem specifically involves finding the optimal joint angular acceleration. The first item The joint velocities of the low-redundancy snake-like robotic arm are obtained. ; S3: Design a finite-time dual neural network model; solve the inverse kinematics problem using the finite-time dual neural network model; Step S3 includes: The problem of solving the model predictive control method is simplified into a QP problem, as follows: in , , ; According to the KKT conditions, the optimal solution to the QP problem should satisfy the following conditions: in These are the dual variables of the inequality constraints; Define a projection function as follows: in Represents each element Z i From the processing function, we can obtain: S4: Based on the solution results, control the angles of each joint of the low-redundancy snake-shaped robotic arm.

2. The hierarchical solution method for a snake-like robotic arm based on model predictive control as described in claim 1, characterized in that, Step S3 also includes: A finite-time dual neural network model was designed, and the optimal joint angular acceleration was obtained. ,as follows: in dual variables The derivative of the network parameters and , The activation function is specifically defined as follows: ; This represents the processing function for each element, and... Having the same attributes in and , It is a symbolic function, because It is a constant matrix, so we get ,in for The false rebellion.

3. A hierarchical solution system for a snake-like robotic arm based on model predictive control, used to implement the hierarchical solution method for a snake-like robotic arm based on model predictive control as described in any one of claims 1-2, characterized in that, The system includes: a computer, a snake-like robotic arm, and a display screen; The computer is used to acquire data parameters of the snake-like robotic arm; The computer is also used to decompose the snake-shaped robotic arm structurally using Bézier curves and data parameters, and to divide it into a preset number of low-redundancy snake-shaped robotic arms. The computer is also used to construct model predictive control methods to determine the inverse kinematics problem of a low-redundancy snake-like robotic arm. The computer is also used to design finite-time dual neural network models; and to solve inverse kinematics problems using finite-time dual neural network models. The computer is also used to control the angles of each joint of the low-redundancy snake-like robotic arm based on the solution results. The display screen is used to visualize the three-dimensional motion state of the snake-shaped robotic arm in real time.

4. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores instructions that, when executed by a computer, perform the method as described in any one of claims 1-2.

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