Pneumatic flexible mechanical arm trajectory planning and control method based on RBF neural network

Abstract

The invention discloses a pneumatic flexible mechanical arm trajectory planning and RBF neural network-based control method. The method comprises the following steps: S1, establishing kinematics and dynamics models of a pneumatic flexible mechanical arm; s2, according to the grabbing and carrying tasks, joint space trajectory planning is conducted on the pneumatic flexible mechanical arm; s3, designing an adaptive RBF neural network, and estimating load disturbance in real time; s4, designing a backstepping integral sliding mode controller to realize disturbance compensation and robust motion control based on the adaptive RBF neural network and a backstepping technical idea; s5, using a Lyapunov method to carry out convergence test on the estimated value of the RBF neural network and the backstepping integral sliding mode controller; the joint space trajectory planning method based on cubic spline interpolation and particle swarm optimization is provided for a multi-degree-of-freedom pneumatic flexible mechanical arm, singular configuration is effectively avoided, a backstepping integral sliding mode controller is designed based on a self-adaptive RBF neural network, online disturbance compensation is achieved, the control performance is improved, and the joint space trajectory planning method is suitable for the multi-degree-of-freedom pneumatic flexible mechanical arm. And grabbing and carrying tasks can be efficiently completed.

Description

Technical Field:

[0001] The present invention belongs to the technical field of industrial intelligent manufacturing and robotic arm servo control, and particularly relates to the trajectory planning of a pneumatic flexible robotic arm and a control method based on an RBF neural network. Background Art:

[0002] Intelligent manufacturing aims to achieve the high efficiency, flexibility, and intelligence of the production process by integrating information technology, automation control technology, and artificial intelligence technology. As one of the indispensable devices in an automated production line, robotic arms are widely used in various tasks such as assembly and handling. To provide higher adaptability and compliance when dealing with complex or irregular objects, a multi-degree-of-freedom pneumatic flexible robotic arm driven by pneumatic artificial muscles is designed. Due to the multi-degree-of-freedom characteristics, when the end effector or joints of the robotic arm are in certain specific configurations, the pneumatic flexible robotic arm may exhibit singular configurations. When some joints are close to or coincide with each other, the determinant of the Jacobian matrix of the robotic arm may be zero, resulting in singularity phenomena. This singularity makes it impossible for the speed or mechanical output of the robotic arm in this configuration to directly correspond to the control input, making the control of the robotic arm more difficult. Joint space trajectory planning can avoid singular configurations through simple calculations, thus showing unique advantages in the trajectory control of pneumatic flexible robotic arms.

[0003] The driving principle of the pneumatic system and the gas compression characteristics make the dynamic and kinematic models of the pneumatic flexible robotic arm highly nonlinear, which makes it difficult for traditional control methods to handle efficiently. Therefore, in recent years, control methods based on artificial intelligence, especially neural network control methods, have become a research hotspot. Among them, the radial basis function (RBF) neural network has been widely used in robotic arm control due to its strong nonlinear fitting ability and good approximation performance. In the presence of external disturbances and modeling errors, sliding mode control can effectively eliminate these uncertainties and improve the robustness and adaptability of the system. Combining the RBF neural network with sliding mode control can achieve more efficient and stable control of the pneumatic flexible robotic arm. By estimating the load disturbance of the pneumatic flexible robotic arm through the RBF neural network and combining the robustness of sliding mode control, a new hybrid control strategy is formed, which can still maintain high-precision and high-robustness control effects when facing complex working environments and uncertain factors. Summary of the Invention:

[0004] The objective of the present invention is to achieve trajectory planning of a pneumatic flexible robotic arm and motion control based on an RBF neural network, and complete the tasks of grasping and transporting a load. First, to plan the joint space trajectory of the pneumatic flexible robotic arm, a cubic spline interpolation method is used to generate a smooth joint motion curve, and the particle swarm optimization algorithm is combined to optimize the trajectory, ensuring that the robotic arm avoids singular configurations during motion and improving motion stability and efficiency. Second, aiming at the load disturbance problem faced by the pneumatic flexible robotic arm during grasping and transporting tasks, an adaptive RBF neural network is designed, which can estimate and compensate the load disturbance of the robotic arm in real time, effectively improving the robustness and control accuracy of the system. Finally, a backstepping integral sliding mode controller is designed, which combines the disturbance compensation ability of the adaptive RBF neural network to achieve high-precision trajectory tracking and stable control of the pneumatic flexible robotic arm, ensuring its reliability and performance in complex tasks.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A trajectory planning and RBF neural network-based control method for a pneumatic flexible robotic arm, comprising the following steps:

[0007] S1. Establish the kinematic and dynamic models of the pneumatic flexible robotic arm;

[0008] S2. According to the grasping and transporting tasks, perform joint space trajectory planning for the pneumatic flexible robotic arm;

[0009] S3. Design an adaptive RBF neural network to estimate the load disturbance in real time;

[0010] S4. Based on the adaptive RBF neural network and the backstepping technique idea, design a backstepping integral sliding mode controller to achieve disturbance compensation and robust motion control;

[0011] S5. Use the Lyapunov method to conduct a convergence test on the estimated value of the RBF neural network and the backstepping integral sliding mode controller.

[0012] Further, the specific steps of step S1 include:

[0013] S1.1. Use the D-H method to conduct kinematic analysis on the multi-degree-of-freedom pneumatic flexible robotic arm, and obtain the kinematic model of the robotic arm as follows:

[0014]

[0015] Among them, is the pose matrix, p x (t), p y (t), p z (t) are the position coordinates of the pneumatic flexible robotic arm respectively;

[0016] S1.2. Based on the above kinematic model, the Euler-Lagrange method is further used to establish the dynamic model of the pneumatic flexible manipulator:

[0017]

[0018] Among them, \(H(t)\) is the inertia matrix, \(C(t)\) is the Coriolis matrix, \(G(t)\) represents the gravity matrix, \(D(t)\) represents the damping matrix, \(E(t)\) refers to the preloading matrix, and \(U\) c (t) is the control matrix, and \(x\) 1 (t) is the deflection angle matrix;

[0019] The dynamic model is rewritten in the form of a second-order mathematical model:

[0020]

[0021] In the formula: \(\tau\) u (t)=H -1 (t)D(t)U C (t)=BU C (t) represents the control input, and \(f(t)=H\) -1 (t)(E(t)-G(t)-C(t)x 1 (t)) represents the load disturbance.

[0022] Furthermore, the specific steps of step S2 include:

[0023] S2.1. Use the Monte Carlo method to traverse the six joint angles \(\theta\) in the working range [-20°, 20°] i to obtain the point cloud map of the working space at the end of the manipulator, and store the end position of the pneumatic flexible manipulator in the working space and the corresponding angle data in the dataset;

[0024] S2.2. Intercept the plane cross-section parallel to the Z-axis and passing through two target points, and use the bisection method to equally sample the working points between the two target points as reference points on this cross-section; then retrieve the joint angle values corresponding to the two target points and the reference points between them from the dataset as known angles;

[0025] S2.3. Interpolate between the known angles based on the cubic spline interpolation method: use the known angles as the interpolation nodes of the cubic spline interpolation method, and set the angular accelerations at the starting point and the ending point to zero as boundary conditions; use the joint angle values corresponding to the target points, interpolation points, and reference points to draw the angular trajectory of the cubic polynomial; based on considering the motion characteristics and task requirements of the pneumatic flexible manipulator, perform time planning to generate a continuous and smooth cubic spline interpolation trajectory;

[0026] S2.4. Optimize the values of the interpolation points using the particle swarm optimization algorithm: Take the minimum value of the integral of the joint angle trajectory as the optimization objective, and obtain a smooth and energy-optimal joint angle trajectory by optimizing the values of the interpolation points through the particle swarm optimization algorithm.

[0027] Further, the step S3 specifically includes:

[0028] S3.1. Estimate the load disturbance f(t) of the pneumatic flexible manipulator using an RBF neural network as shown in the following formula:

[0029]

[0030] where is the estimate of the load disturbance f(t), is the estimation weight, and h j (t) is a Gaussian basis function:

[0031]

[0032] In the formula, b j is the width of the j-th neuron, c j = [c 1j , c 2j is the center vector, is the input value, where e(t) is the tracking error, is the auxiliary variable obtained by the controller;

[0033] The adaptive law of the estimation weight is:

[0034]

[0035] where Γ is a positive diagonal constant matrix, and k p is a positive adjustable parameter in the backstepping integral sliding mode control; Through the above iteration, the load disturbance f(t) is estimated in real time using the RBF neural network.

[0036] Further, the step S4 specifically includes:

[0037] S4.1. Design the integral sliding mode surface in the backstepping integral sliding mode controller as:

[0038] s 1 (t) = k p e(t) + k i ∫ρ(t)dt

[0039] where e(t) = x 1 (t) - y 1 (t) is the tracking error, k i is a positive adjustable parameter, and in the formula

[0040] ρ(t) = |e(t)| δ sign(e(t))

[0041] ρ(t) is a bounded differentiable function, where 0 < δ < 1, and satisfies:

[0042]

[0043] S4.2. Combine the integral sliding mode surface and the second-order mathematical model to obtain the following spatial model:

[0044]

[0045] Based on the idea of adaptive RBF neural network and backstepping technique, design a backstepping integral sliding mode controller to achieve disturbance compensation and robust motion control. The backstepping integral sliding mode controller is designed as:

[0046]

[0047] where

[0048]

[0049] α 1 (t) = ξ|s 1 (t)| r sign(s 1 (t))

[0050] where ξ and r are positive adjustable parameters, is an auxiliary variable, Δ 1 (t) is a virtual variable.

[0051] Furthermore, the specific steps of step S5 include:

[0052] S5.1. Design the first Lyapunov function as:

[0053]

[0054] Differentiate V 1 (t) to obtain:

[0055]

[0056] Since ξ > 0, then when is close to 0, is negative definite, that is, the integral sliding mode surface s 1 (t) converges to zero;

[0057] S5.2. Design the second Lyapunov function as:

[0058]

[0059] Deriving the derivative of V 2 (t) gives:

[0060]

[0061] where ξ and k 1 are two positive parameters; if the weight error is bounded, then holds, that is to say, the auxiliary variable can converge to zero;

[0062] S5.3, design the third Lyapunov function as:

[0063]

[0064] Deriving the derivative of V 3 (t) gives:

[0065]

[0066] Therefore, the weight error is bounded and convergent, that is, the estimated value of the RBF neural network can effectively estimate the load disturbance f(t), and the integral sliding mode surface modal surface s 1 (t) converges to zero;

[0067] S5.4, design the fourth Lyapunov function as:

[0068]

[0069] Deriving the derivative of V 4 (t) gives:

[0070]

[0071] Therefore, the tracking error e(t) converges to zero, and the second-order mathematical model composed of the backstepping integral sliding mode controller is stable.

[0072] The beneficial effects of the present invention are as follows:

[0073] 1. In view of the possible singular configuration problems that may occur during the movement of a multi-degree-of-freedom pneumatic flexible manipulator, the present invention proposes a joint space trajectory planning method based on cubic spline interpolation and particle swarm optimization, effectively avoiding the occurrence of singular configurations; cubic spline interpolation ensures the smoothness of the joint trajectory, while the particle swarm optimization algorithm optimizes the trajectory parameters through its global search ability to ensure that the manipulator always stays away from the singular region during movement; this method not only solves the difficult problem of inverse kinematics solution, but also improves the movement efficiency and stability of the manipulator.

[0074] 2. The present invention has made a breakthrough in the non-linear dynamics identification and load disturbance compensation of pneumatic flexible manipulators, and proposes an efficient adaptive RBF neural network method; the adaptive RBF neural network of the present invention can accurately identify the non-linear dynamics characteristics of the manipulator in real time and dynamically estimate and compensate for load disturbances through its powerful non-linear mapping ability and adaptive learning mechanism; this technology not only significantly improves the control accuracy of the manipulator, but also enhances the adaptability of the system to complex working conditions.

[0075] 3. The present invention designs a backstepping integral sliding mode controller based on an adaptive RBF neural network to achieve the grasping and handling tasks of a pneumatic flexible manipulator; the effectiveness of the designed adaptive RBF neural network and backstepping integral sliding mode controller is verified by using multiple Lyapunov functions, while ensuring stable, accurate and fast control performance. Description of the Drawings:

[0076] Figure 1 It is a schematic diagram of the joint space trajectory planning process of the present invention.

[0077] Figure 2 It is a schematic diagram of the structure of the RBF neural network of the present invention.

[0078] Figure 3 It is a control block diagram of the pneumatic flexible manipulator proposed by the present invention.

[0079] Figure 4 It is the joint space trajectory planned according to the actual task in the embodiment of the present invention.

[0080] Figure 5 It is an experimental error diagram of the end position of the pneumatic flexible manipulator in the embodiment of the present invention. Detailed Embodiment:

[0081] To make the purpose of the present invention clearer and the technical solution clearer, the present invention will be described in detail in combination with the following drawings and specific embodiments. The following combines Figures 1-5 Describe the control method of the present invention in detail, but it is not a limitation to the present invention.

[0082] Step S1, establish the kinematic and dynamic models of the pneumatic flexible manipulator.

[0083] S1.1. Use the D-H method to conduct kinematic analysis on the multi-degree-of-freedom pneumatic flexible manipulator as follows:

[0084]

[0085]

[0086] Among them, L 1 = 29 cm, L 2 = 28.5 cm, L 3 = 29 cm, respectively representing the initial lengths of the first joint, the second joint, and the third joint; i = 1, 2,..., 6 is the i-th degree of freedom, θ i is the joint angle with a range of [-20°, 20°], d i is the link offset length, a i is the link length, α i is the link twist angle; thus, the kinematic model of the manipulator is obtained as follows:

[0087]

[0088] Among them, is the pose matrix, p x (t), p y (t), p z (t) are the position coordinates of the pneumatic flexible manipulator respectively;

[0089] S1.2. Based on this kinematic analysis model, further establish the dynamic model of the pneumatic flexible manipulator using the Euler-Lagrange method:

[0090]

[0091] Among them, H(t) is the inertia matrix, C(t) is the Coriolis matrix, G(t) represents the gravity matrix, D(t) represents the damping matrix, E(t) refers to the preloading matrix, U c (t) is the control matrix, x 1 (t) is the deflection angle matrix;

[0092] Rewrite the dynamic model into the form of a second-order mathematical model:

[0093]

[0094] In the formula: τ u (t) = H -1 (t)D(t)U C (t) = BU C(t) represents the control input, and f(t) = H -1 (t)(E(t) - G(t) - C(t)x 1 (t)) represents the load disturbance.

[0095] Step S2: According to the grasping and handling tasks, perform joint space trajectory planning for the pneumatic flexible manipulator. Perform trajectory planning for each angle according to the Figure 1 shown joint space trajectory planning process diagram to avoid singular configurations;

[0096] S2.1: Use the Monte Carlo method to traverse the six joint angles θ i in the working range [-20°, 20°] to obtain the working space point cloud map of the end of the manipulator, and store the end position of the pneumatic flexible manipulator in the working space and the corresponding angle data in the dataset;

[0097] S2.2: Intercept the plane cross-section parallel to the Z-axis and passing through the two target points. Use the bisection method to equally sample the working points between the two target points on this cross-section as reference points. Then, obtain the joint angle values corresponding to the two target points and the reference points between them by retrieving the dataset as the known angles;

[0098] S2.3: Interpolate between the known angles based on the cubic spline interpolation method to make the angle trajectory smoother. Specifically: Use the known angles as the interpolation nodes of the cubic spline interpolation method, and set the angular accelerations at the starting point and the ending point to zero as the boundary conditions. Use the joint angle values corresponding to the target points, interpolation points, and reference points to draw the angle trajectory of the cubic polynomial. Based on considering the motion characteristics and task requirements of the pneumatic flexible manipulator, perform time planning to generate a continuous and smooth cubic spline interpolation trajectory to ensure the smoothness and accuracy of the trajectory;

[0099] S2.4: In order to generate a smooth and energy-optimal trajectory, use the particle swarm optimization algorithm to optimize the numerical values of the interpolation points. Specifically: Take the minimum value of the integral of the joint angle trajectory as the optimization objective. After optimizing the numerical values of the interpolation points through the particle swarm optimization algorithm, a smooth and energy-optimal joint angle trajectory can be obtained; this trajectory not only meets the requirements of motion planning but also can effectively reduce the energy consumption of the robot.

[0100] Step S3: Design an adaptive RBF neural network to perform real-time estimation of the load disturbance according to the Figure 2 shown structure schematic diagram of the RBF neural network:

[0101] S3.1: The RBF neural network is usually used to approximate continuous bounded smooth functions and general high-order nonlinear systems. Therefore, the load disturbance f(t) of the pneumatic flexible manipulator can be estimated using the RBF neural network as shown in the following formula:

[0102]

[0103] where is the estimate of the load disturbance f(t), is the estimation weight, and h j (t) is a Gaussian basis function:

[0104]

[0105] In the formula, b j is the width of the j-th neuron, and c j = [c 1j , c 2j is the center vector, is the input value, where e(t) is the tracking error, is the auxiliary variable obtained by the controller;

[0106] The adaptive law of the estimated weighted vector is:

[0107]

[0108] where Γ is a positive diagonal constant matrix, and k p is a positive adjustable parameter in the backstepping integral sliding mode control; through the above iteration, the load disturbance f(t) can be estimated in real time by the RBF neural network.

[0109] Step S4, based on the ideas of the adaptive RBF neural network and the backstepping technique, a backstepping integral sliding mode controller is proposed to achieve disturbance compensation and robust motion control, specifically:

[0110] S4.1, to improve the dynamic performance of the pneumatic flexible manipulator, a backstepping integral sliding mode controller is designed, and its integral sliding mode surface is designed as:

[0111] s 1 (t) = k p e(t) + k i ∫ρ(t)dt

[0112] where, e(t) = x 1 (t) - y 1 (t) is the tracking error, and k i is a positive adjustable parameter. In the formula:

[0113] ρ(t) = |e(t)| δ sign(e(t))

[0114] ρ(t) is a bounded differentiable function, where 0 < δ < 1, and satisfies:

[0115]

[0116] S4.2. Combine the integral sliding mode surface and the second-order mathematical model to obtain the following spatial model:

[0117]

[0118] Based on the ideas of the adaptive RBF neural network and the backstepping technique, a backstepping integral sliding mode controller is proposed to achieve disturbance compensation and robust motion control. The backstepping integral sliding mode controller is designed as:

[0119]

[0120] where

[0121]

[0122] α 1 (t) = ξ|s 1 (t)| r sign(s 1 (t))

[0123] where ξ and r are positive adjustable parameters, is an auxiliary variable, Δ 1 (t) is a virtual variable; The control block diagram of the pneumatic flexible manipulator is as Figure 3 shown. Among them, the angle trajectory obtained from the joint space trajectory planning is used as the reference trajectory x 1 (t) of the control block diagram. The tracking error e(t) of the system and the auxiliary variable obtained by the backstepping integral sliding mode controller are used as the input values of the RBF neural network. The estimated value of the RBF neural network is input into the backstepping integral sliding mode controller to output the control quantity U C (t) to achieve the motion control of the manipulator.

[0124] Step S5. Use the Lyapunov method to conduct a convergence test on the estimated value of the RBF neural network and the backstepping integral sliding mode controller. Specifically:

[0125] S5.1. Design the first Lyapunov function as:

[0126]

[0127] Derive V 1 (t) to obtain:

[0128]

[0129] Since ξ > 0, then when When it is close to 0, it is negative definite, that is, the integral sliding mode surface s 1 (t) converges to zero;

[0130] S5.2, design the second Lyapunov function as:

[0131]

[0132] Taking the derivative of V 2 (t) gives:

[0133]

[0134] where ξ and k 1 are two positive parameters. If the weight error is bounded, then holds, that is, the auxiliary variable can converge to zero;

[0135] S5.3, design the third Lyapunov function as:

[0136]

[0137] Taking the derivative of V 3 (t) gives:

[0138]

[0139] Therefore, the weight error is bounded and convergent, that is, the estimated value of the RBF neural network can effectively estimate the load disturbance f(t), and the integral sliding mode surface modal surface s 1 (t) converges to zero;

[0140] S5.4, design the fourth Lyapunov function as:

[0141]

[0142] Taking the derivative of V 4 (t) gives:

[0143]

[0144] Therefore, the tracking error e(t) converges to zero, and the second-order mathematical model composed of the backstepping integral sliding mode controller is stable.

[0145] Example:

[0146] To verify the effectiveness of the trajectory planning of the pneumatic flexible manipulator and the motion control based on the RBF neural network proposed in this embodiment, a six-degree-of-freedom pneumatic flexible manipulator is used as an experimental platform here. Its task of grasping and handling loads is set, and its experimental verification is given as follows:

[0147] The initial deflection angle of the joint of the pneumatic flexible manipulator is 0°, corresponding to the initial position coordinates (0m, 0m, 0.865m); the spatial trajectory of the end of the manipulator planned according to the actual task is as Figure 4 shown. In Figure 4 , the gripper at the end of the manipulator is at point "A" in the initial state, moves to point "B" to grasp the load, then the gripper transports the load to point "C", and then returns to the initial position "A" again; the coordinates of "A", "B" and "C" are (0m, 0m, 0m, 0.865m), (-0.195m, 0.196m, 0.804m) and (0.196m, -0.195m, 0.804m) respectively; according to the cubic spline interpolation method and the particle swarm optimization algorithm, the reference trajectories of each joint angle are finally obtained, so that the manipulator can avoid falling into a singular configuration and reduce energy consumption. The reference trajectories of each joint angle are sent as inputs to the Figure 3 control block diagram of the pneumatic flexible manipulator, and the experimental trajectories and error diagrams of its end position in the X, Y, and Z axis directions are as Figure 5 shown.

[0148] From Figure 5 the experimental results, it can be seen that the actual trajectory of grasping the load can effectively track the reference trajectory, and is hardly affected by grasping and placing the load at points "B" and "C"; from the tracking error diagram, it can be seen that the dynamic tracking error always remains bounded, and the steady-state error can finally converge to zero.

[0149] The trajectory planning proposed by the present invention can effectively avoid the pneumatic flexible manipulator from falling into a singular configuration, and the proposed backstepping integral sliding mode controller based on the RBF neural network can quickly and accurately achieve the grasping and handling tasks.

Claims

1. Pneumatic flexible manipulator trajectory planning and control method based on RBF neural network, characterized in that: The following steps are involved: S1, establish the kinematic and dynamic models of the pneumatic flexible manipulator; S2, performs joint space trajectory planning for the pneumatic flexible manipulator according to the grasping and handling tasks; S3, design an adaptive RBF neural network to estimate load disturbances in real time; S4, based on the adaptive RBF neural network and backstepping technology, a backstepping integral sliding mode controller is designed to achieve disturbance compensation and robust motion control; S5, the Lyapunov method is used to check the convergence of the estimated value of the RBF neural network and the backstepping integral sliding mode controller.

2. The pneumatic flexible manipulator trajectory planning and control method based on RBF neural network according to claim 1 is characterized in that: The step S1 specifically includes: S1.1, the kinematic analysis of the multi-DOF pneumatic flexible manipulator is carried out using the DH method, and the kinematic model of the manipulator is obtained as follows: in, is the pose matrix, p x (t), p y (t), p z (t) are the position coordinates of the pneumatic flexible manipulator; S1.2, based on the above kinematic model, the Euler-Lagrange method is further used to establish the dynamic model of the pneumatic flexible manipulator: Among them, H(t) is the inertia matrix, C(t) is the Coriolis matrix, G(t) represents the gravity matrix, D(t) represents the damping matrix, E(t) refers to the preload matrix, and U c (t) is the control matrix, x1(t) is the deflection angle matrix; The dynamic model is rewritten into a second-order mathematical model: Where: τ u (t) = H -1 (t)D(t)U C (t) = BU C (t) represents the control input, f(t) = H -1 (t)(E(t)-G(t)-C(t)x1(t)) represents the load disturbance.

3. The pneumatic flexible manipulator trajectory planning and control method based on RBF neural network according to claim 2 is characterized in that: The step S2 specifically includes: S2.1, using the Monte Carlo method to calculate the six joint angles θ in the working range [-20°, 20°] i Traverse to obtain the workspace point cloud map of the end of the robot arm, and store the position of the end of the pneumatic flexible robot arm in the workspace and the corresponding angle data in the data set; S2.2, intercept a plane cross section parallel to the Z axis and passing through the two target points, and use the bisection method to equidistantly sample the working points between the two target points as reference points on the cross section; then retrieve the data set to obtain the joint angle values ​​corresponding to the two target points and the reference points between them as known angles; S2.3, interpolation between known angles based on cubic spline interpolation method: using known angles as interpolation nodes of cubic spline interpolation method, setting the angular acceleration of the starting point and the end point to zero as boundary conditions; using the joint angle values ​​corresponding to the target point, interpolation point and reference point to draw the angle trajectory of the cubic polynomial; considering the motion characteristics and task requirements of the pneumatic flexible manipulator, time planning is performed to generate a continuous and smooth cubic spline interpolation trajectory; S2.4, use the particle swarm optimization algorithm to optimize the values ​​of the interpolation points: take the minimum value of the integral of the joint angle trajectory as the optimization target, and optimize the values ​​of the interpolation points through the particle swarm optimization algorithm to obtain a smooth and energy-optimal joint angle trajectory.

4. The pneumatic flexible manipulator trajectory planning and RBF neural network-based control method according to claim 3 is characterized in that: The step S3 specifically includes: S3.1, the load disturbance f(t) of the pneumatic flexible manipulator is estimated using the RBF neural network as shown in the following formula: in is the estimate of the load disturbance f(t), is the estimated weight, h j (t) is the Gaussian basis function: Where b j is the width of the jth neuron, c j =[c 1j ,c 2j ] is the center vector, is the input value, where e(t) is the tracking error, is an auxiliary variable obtained by the controller; Estimated weights The adaptive law is: Where Γ is a positive diagonal constant matrix, k p It is a positive adjustable parameter in the backstepping integral sliding mode control; through the above iteration, the load disturbance f(t) is estimated in real time using the RBF neural network.

5. The pneumatic flexible manipulator trajectory planning and control method based on RBF neural network according to claim 4 is characterized in that: The step S4 specifically includes: S4.1, the integral sliding mode surface in the backstepping integral sliding mode controller is designed as: s1(t)=k p e(t)+k i ∫ρ(t)dt Among them, e(t) = x1(t) - y1(t) is the tracking error, k i is a positive adjustable parameter, where ρ(t)=|e(t)| δ sign(e(t)) ρ(t) is a bounded differentiable function with 0<δ<1, satisfying: S4.2, combining the integral sliding surface and the second-order mathematical model, the following spatial model is obtained: Based on the adaptive RBF neural network and backstepping technology, a backstepping integral sliding mode controller is designed to achieve disturbance compensation and robust motion control. The backstepping integral sliding mode controller is designed as follows: In the formula α1(t)=ξ|s1(t)|rsign(s1(t)) where ξ and r are positive adjustable parameters, is an auxiliary variable and α1(t) is a dummy variable.

6. The pneumatic flexible manipulator trajectory planning and RBF neural network-based control method according to claim 5 is characterized in that: The step S5 specifically includes: S5.1, design the first Lyapunov function as: Taking the derivative of V1(t) we get: Since ξ>0, then when When it is close to 0, is negative definite, that is, the integral sliding mode surface s1(t) converges to zero; S5.2, design the second Lyapunov function as: Taking the derivative of V2(t) we get: Where ξ and k1 are two positive parameters; if the weight error is bounded, then holds, that is, the auxiliary variable can converge to zero; S5.3, design the third Lyapunov function as: Taking the derivative of V3(t) we get: Therefore, the weight error It is bounded convergent, that is, the estimated value of the RBF neural network The load disturbance f(t) can be effectively estimated, and the integral sliding mode surface s1(t) converges to zero; S5.4, design the fourth Lyapunov function as: Taking the derivative of V4(t) we get: Therefore, the tracking error e(t) converges to zero and the second-order mathematical model composed of the backstepping integral sliding mode controller is stable.

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