Self-adaptive predetermined time trajectory tracking control method for rigid-flexible coupling tendon-driven mechanical arm

Abstract

The invention provides an adaptive predetermined time trajectory tracking control method for a rigid-flexible coupling tendon-driven mechanical arm. The adaptive predetermined time trajectory tracking control method comprises the following steps: establishing a dynamic model of the rigid-flexible coupling tendon-driven mechanical arm which comprehensively considers the flexible deformation of an arm lever structure and the elastic deformation of a rope; designing a nonsingular terminal sliding mode surface according to the trajectory tracking error, and estimating system lumped interference by adopting an RBF neural network; and designing a self-adaptive predetermined time nonsingular terminal sliding mode controller, adjusting parameters through a self-adaptive law to suppress and control input buffeting, and controlling a joint trajectory tracking error to converge within a predetermined time range. The vibration of the tail end of the mechanical arm is restrained, and meanwhile it is ensured that the joint trajectory tracking error converges within the preset time range; the influence of initial conditions is avoided; according to the method, system uncertainty and external disturbance are estimated through the RBF neural network, and control robustness is improved; a self-adaptive parameter adjusting mechanism is introduced, the control input buffeting problem is effectively solved, and the tail end operation precision of the mechanical arm is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of robotic arm control, and in particular to a method for adaptively tracking and controlling a rigid-flexible coupled tendon-driven robotic arm with a predetermined time trajectory. Background Art

[0002] In space exploration missions, robotic arms are core equipment for tasks such as capturing and repairing large spacecraft, constructing ultra-large space facilities, and exploring asteroid resources. Traditional robotic arms utilize a modular structure consisting of carbon composite tubes connected by joints. These joints drive the arm's motion, with the joints accounting for 85% to 90% of the arm's mass. This severely limits their operational range and dexterity, and increases launch costs.

[0003] To address this issue, tendon actuation has been introduced, replacing traditional joints with cables to achieve lightweight, high-torque actuation. This novel tendon-driven joint boasts ±180° of motion and can be fully folded without bias. Its lightweight boom structure replaces the traditional gear reduction mechanism, achieving high joint torque at a low mass cost. Multi-cable coordinated actuation enhances variable stiffness control and compliant operation. Passive cables can be added to strengthen the overall stiffness of the manipulator arm, achieving high stiffness for ultra-long manipulators at a low mass cost. Its modular design also provides strong versatility. However, during long-distance operations, flexible deformation of the boom structure and cable elasticity can lead to reduced end-of-line precision, a critical issue that needs to be addressed. Therefore, it is necessary to consider incorporating structural flexible deformation into dynamic analysis and controller design.

[0004] Existing control studies for tendon-driven manipulators often fail to fully consider the rigid-flexible coupling characteristics, resulting in large trajectory tracking errors and poor vibration suppression. To more accurately adjust the system's settling time, finite-time control strategies have been proposed. These methods ensure that the system state converges to the desired value within a finite time, T. While finite-time control strategies can achieve rapid convergence, the settling time, T, of finite-time stable systems depends not only on the control parameters but also on the system's initial conditions, significantly limiting their practical engineering applications. To overcome this shortcoming, fixed-time control methods have been proposed, making the settling time, T, independent of the system's initial conditions. Consequently, fixed-time control methods have been widely used in trajectory tracking control of flexible manipulators. While fixed-time control eliminates the influence of initial conditions, it is difficult to predetermine the required settling time. Therefore, a control method that can achieve high-precision trajectory tracking within a predetermined time and suppress terminal vibration is urgently needed. Summary of the Invention

[0005] In response to the shortcomings of the existing technology, the present invention provides a rigid-flexible coupling tendon-driven robotic arm with adaptive predetermined time trajectory tracking control method, aiming to solve the problems of low trajectory tracking accuracy, insufficient vibration suppression and unpredictable convergence time in the existing technology of the rigid-flexible coupling tendon-driven robotic arm.

[0006] The technical solution of the present invention is: a method for adaptively tracking a predetermined time trajectory of a rigid-flexible coupled tendon-driven robotic arm, comprising the following steps:

[0007] S1) Establish a dynamic model of the rigid-flexible coupled tendon-driven manipulator that comprehensively considers the flexible deformation of the arm structure and the elastic deformation of the rope;

[0008] S2), defining a trajectory tracking error, and designing a non-singular terminal sliding surface according to the trajectory tracking error, and designing an equivalent control term through the non-singular terminal sliding surface;

[0009] S3), using an RBF neural network to estimate the system lumped interference, and designing a switching control item based on the estimated system lumped interference; the input of the RBF neural network is the system state variable, and the output is the interference estimate;

[0010] S4) Design an adaptive predetermined time non-singular terminal sliding mode controller, which includes an equivalent control term and an adaptive switching term. The controller adjusts parameters through an adaptive law to suppress control input chattering and control the joint trajectory tracking error to converge within a predetermined time range.

[0011] Preferably, in step S1), the dynamic model is derived based on the Lagrangian method, the flexible arm is regarded as an Euler-Bernoulli beam, and the assumed modal method is used to describe the lateral elastic deformation of the arm.

[0012] Preferably, in step S1), the dynamic model of the rigid-flexible coupling tendon-driven manipulator that comprehensively considers the flexible deformation of the arm structure and the elastic deformation of the rope is:

[0013]

[0014] Where, θ=[θ1…θ i …θ n ] T is the joint angle matrix of the manipulator; M(θ) is a positive definite, symmetric mass matrix; is the column matrix containing the Coriolis force and the centripetal force; K is the flexible arm stiffness matrix; is the joint angular velocity; is the joint angular acceleration; τ e represents the rope elastic loss torque, J m Represents the equivalent mapping relationship between motor current and joint torque, i mRepresents the current vector of each driving motor of the robotic arm system.

[0015] Preferably, in step S2), the trajectory tracking error is:

[0016]

[0017] Where, e1 and e2 are trajectory tracking errors; θ r is the actual joint angle of the trajectory; is the actual joint angular velocity of the trajectory; θ d 、 are the desired joint angle and the desired joint angular velocity, respectively.

[0018] Preferably, in step S2), the non-singular terminal sliding surface s is:

[0019] s=e2+h1sign 1-γ (e1)+h2sign 1+γ (e1); (10)

[0020] Where 0<γ<1 is the fractional power parameter; h1 and h2 are the synovial parameters; sign is the sign function.

[0021] As a preference, in step S2), the equivalent control item u eq for:

[0022]

[0023] Where, is the actual joint angular acceleration of the trajectory; k1 and k2 are controller parameters; sat σ is a saturation function; α>0 indicates a control parameter, β>0 indicates a control parameter, T c2 >0 indicates the preset time; n indicates the number of degrees of freedom of the robot arm; is an element of M(θ); C rr for elements of ; Λ1 and Λ2 represent positive definite diagonal matrices respectively.

[0024] As a preference, in step S3), the system aggregate interference estimated by the RBF neural network for:

[0025]

[0026] Where, is the estimated weight coefficient; φ(x) is the Gaussian radial basis function.

[0027] As a preference, in step S3), the switching control item usw for:

[0028]

[0029] Where η>0 represents the switching coefficient; sgn(s) represents the sign function.

[0030] As a preference, in step S3), according to the equivalent control item u eq and switch control u sw The predetermined time non-singular terminal sliding mode controller is obtained, namely:

[0031]

[0032] Where, u represents the total control input of the system; u eq is an equivalent control item; u sw is the switching control term; η>0 represents the switching coefficient; sgn(s) represents the sign function.

[0033] Preferably, in step S4), an adaptive parameter adjustment mechanism is introduced to replace the switching item of the predetermined time non-singular terminal sliding mode controller to obtain an adaptive predetermined time non-singular terminal sliding mode controller, and its expression is:

[0034]

[0035] Where; is the adaptive adjustment item, for The estimated value of N represents the preset estimation error; is the design parameter.

[0036] Preferably, in step S4), the adaptive law of the adaptive predetermined time non-singular terminal sliding mode controller is:

[0037]

[0038] Where, represents the derivative of the adaptive law; ι1 and ι2 represent the adaptive law parameters respectively; κ>0 represents the gain.

[0039] The beneficial effects of the present invention are:

[0040] 1. The present invention suppresses the vibration of the end of the manipulator while ensuring that the joint trajectory tracking error converges within a predetermined time range;

[0041] 2. The rigid-flexible coupling dynamic model established by the present invention comprehensively considers the flexibility of the arm structure and the elastic deformation of the rope, which is more in line with actual working conditions and provides an accurate model basis for controller design;

[0042] 3. The adaptive scheduled time non-singular terminal sliding mode controller of the present invention enables the manipulator to complete trajectory tracking within the scheduled time and is not affected by initial conditions, meeting the strict operating time requirements of space operations;

[0043] 4. The present invention estimates system uncertainty and external disturbances through RBF neural network, thereby improving the robustness of control; and by introducing an adaptive parameter adjustment mechanism, effectively solves the problem of control input chattering, suppresses end vibration, and improves the end operation accuracy of the manipulator. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a flowchart of the method of Example 1 of the present invention;

[0045] Figure 2 This is a schematic structural diagram of a rigid-flexible coupled tendon-driven robotic arm according to Example 1 of the present invention;

[0046] Figure 3 This is a schematic structural diagram of the Euler-Bernoulli beam of the rigid-flexible coupled tendon-driven robotic arm in Example 1 of the present invention;

[0047] Figure 4 This is a schematic diagram of a robotic arm simulated in Example 2 of the present invention;

[0048] Figure 5 This is a comparison diagram of joint trajectory tracking simulated in Example 2 of the present invention;

[0049] Figure 6 This is a comparison diagram of trajectory tracking errors simulated in Example 2 of the present invention;

[0050] Figure 7 This is a comparison diagram of the joint equivalent torque simulated in Example 2 of the present invention;

[0051] Figure 8 This is a comparison diagram of the first-order modal amplitude of the robotic arm end simulated in Example 2 of the present invention;

[0052] Figure 9 This is a comparison diagram of the second-order modal amplitude of the robotic arm end simulated in Example 2 of the present invention;

[0053] Figure 10 This is a comparison diagram of the vibration of the end of the robotic arm simulated in Example 2 of the present invention;

[0054] Figure 11 This is a diagram showing the changing trends of adaptive parameters simulated in Example 2 of the present invention. DETAILED DESCRIPTION

[0055] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0056] like Figure 1 As shown, this embodiment provides a method for adaptively tracking a predetermined time trajectory of a rigid-flexible coupled tendon-driven robotic arm, comprising the following steps:

[0057] S1) Establishing a dynamic model of a rigid-flexible coupled tendon-driven manipulator that comprehensively considers the flexible deformation of the arm structure and the elastic deformation of the rope; specifically comprising the following steps:

[0058] S11), such as Figure 2 As shown in (a), the m-DOF rigid-flexible coupled tendon-driven manipulator is installed on the base of a large spacecraft, and the end is connected to an operating weight. The equivalent schematic diagram of the system is shown in 2(b), where OXY, O0x0y0 and O P x p y p They represent the inertial coordinate system, the base mass center coordinate system and the end weight coordinate system respectively. and They represent the fixed coordinate system of the i-th flexible arm and the i-th boom of the manipulator system respectively; r C ,r0,r p Represent the center of mass position vector of the entire system, the base position vector, and the end mass center position vector, respectively. They represent the center of mass position of the i-th flexible arm and the center of mass position vector of the i-th boom, respectively. Represent the origin To the centroid The distance between arrive The distance between Represent the origin To the centroid The distance between arrive The distance between them.

[0059] In order to derive the dynamic model of the rigid-flexible coupled tendon-driven manipulator, the following assumptions are made:

[0060] Assume that the flexible arm is a homogeneous slender rod, the flexibility and damping of the spreader are negligible; ignore the axial deformation and shear deformation, and only consider the bending deformation; the flexible arm is regarded as Figure 3 The Euler-Bernoulli beam shown.

[0061] S12) Using the assumed modal method, the lateral elastic deformation of the i-th flexible arm is expressed as:

[0062]

[0063] Where W i (x i ,t) is the cross section of the flexible arm The deformation of is the j-th modal function of the flexible arm, δ ij (t) is The time-varying amplitude of , m is the number of truncation terms of the flexible arm mode;

[0064] S13) Establish the second kind of Lagrangian function L of the robotic arm system, namely:

[0065] L=TV; (2)

[0066] Where T is the total kinetic energy of the robotic arm system; V is the total potential energy of the robotic arm system;

[0067] in,

[0068]

[0069] Where T0 is the kinetic energy of the base in the rigid-flexible coupled tendon-driven manipulator system; is the kinetic energy of each flexible arm; n represents the number of degrees of freedom of the manipulator; is the kinetic energy of each spreader; T p is the kinetic energy of the end weight; EI represents the bending stiffness; represents the length of the flexible arm of section i;

[0070] Select the generalized coordinates q=[q0,θ1…θ i …θ n ,δ 11 …δ 1m …δ n1 …δ nm ] T And the generalized output torque is τ=[τ0…τ i …τ n ,0 T ] T ; The Lagrangian dynamic equation can be obtained as:

[0071]

[0072] in, represents the first-order derivative of the generalized coordinate q; q0 is the base posture; θ i is the joint angle of the i-th flexible arm; δ ij for The time-varying amplitude of is the j-th modal function of the flexible arm; τ i is the torque output by the flexible arm of section i; T is the transposition operation;

[0073] The dynamic equation of the flexible arm tendon-driven manipulator system with uncontrolled carrier position and controlled posture is obtained as follows:

[0074]

[0075] Where M q (q) is a positive definite, symmetric mass matrix; is the matrix of Coriolis force and centripetal force; K q is the flexible arm stiffness matrix; u=[τ0…τ i …τ n ] T is the control input column matrix of the system; is the second-order derivative of the generalized coordinate q;

[0076] S14) Since the flexible arm tendon driven manipulator is installed on a large spacecraft, the base attitude q0 = 0, then Assuming that the spacecraft base attitude is in a controlled fixed state, the dynamic equation is simplified to the following form:

[0077]

[0078] Where, θ=[θ1…θ i …θ n ] T is the joint angle matrix of the manipulator; M(θ) is a positive definite, symmetric mass matrix; is the column matrix containing the Coriolis force and the centripetal force; K is the flexible arm stiffness matrix; u m =[τ1…τ i …τ n ] T is the control input column matrix of the system; is the joint angular velocity; is the joint angular acceleration;

[0079] S15), comprehensively considering the mapping relationship between the tendon-driven manipulator motor current, rope tension, and joint torque, the dynamic model of the rigid-flexible coupled tendon-driven manipulator that comprehensively considers the flexible deformation of the arm structure and the elastic deformation of the rope is obtained as follows:

[0080]

[0081] Where, τ e represents the rope elastic loss torque, J m Represents the equivalent mapping relationship between motor current and joint torque, i m Represents the current vector of each driving motor of the robotic arm system.

[0082] S2) defining a trajectory tracking error, designing a non-singular terminal sliding surface based on the trajectory tracking error, and designing an equivalent control term through the non-singular terminal sliding surface; specifically comprising the following steps:

[0083] S21) Define the trajectory tracking error as:

[0084]

[0085] Where, e1 and e2 are trajectory tracking errors; θ r is the actual joint angle of the trajectory; is the actual joint angular velocity of the trajectory; θ d 、 are the desired joint angle and the desired joint angular velocity, respectively.

[0086] S22) Design the non-singular terminal sliding surface s as:

[0087] s=e2+h1sign 1-γ (e1)+h2sign 1+γ (e1); (10)

[0088] Where, 0<γ<1 is the fractional power parameter; h1 and h2 are the synovial parameters; sign is the sign function;

[0089] in,

[0090]

[0091] Where α>0 represents the control parameter, β>0 represents the control parameter, T c1 >0 indicates the preset time; n indicates the number of degrees of freedom of the robot arm;

[0092] S23) By using formula (9) to find the time derivative, we get:

[0093]

[0094] make, The system's lumped interference term δ = 0, and substituting it into equation (11) yields the equivalent control term u eq :

[0095]

[0096] Where, is the actual joint angular acceleration of the trajectory; k1 and k2 are controller parameters; sat σ is a saturation function; α>0 indicates a control parameter, β>0 indicates a control parameter, T c3 >0 indicates the preset time; n indicates the number of degrees of freedom of the robot arm; is an element of M(θ); C rr for The element Λ1=diag(|e 11 | -γ ,…,|e1n | -γ ),Λ2=diag(|e 21 | -γ ,…,|e 2n | -γ ) respectively represent; e 1i 、e 2i Represent the i-th component of e1 and e2 respectively;

[0097] sat σ (Λ1)=diag(sat σ (Λ 11 ),…,sat σ (Λ 11 )); (15)

[0098]

[0099] Where diag represents the diagonal matrix symbol; Λ 1i represents the i-th component of Λ1; σ represents the preset amplitude.

[0100] The actual joint angular acceleration of the trajectory Expressed as:

[0101]

[0102] Where δ is the lumped interference term of the system.

[0103] S3), using RBF neural network to estimate the system aggregate interference, and designing switching control items based on the estimated system aggregate interference;

[0104] The lumped disturbance includes flexible vibration, rope elastic loss torque and external disturbance. The input of the RBF neural network is the system state variable, and the output is the disturbance estimation value. The structure of the RBF neural network is that the number of input layer nodes is the dimension of the system state variable, the number of hidden layer nodes is a preset value, and the number of output layer nodes is 1.

[0105] The system aggregate interference δ=w T φ(x)+∈, where w=[w1,w2,…,w n ] T represents the weight coefficient under ideal conditions, ∈ represents the RBF neural network estimation error; φ(x) is the Gaussian radial basis function.

[0106] The system aggregate interference estimated by using the RBF neural network for:

[0107]

[0108] Where, is the estimated weight coefficient; φ(x) is the Gaussian radial basis function, that is:

[0109]

[0110] Among them, c i =[c i1 ,c i2 ,…,c in ] T and b i Represent the center and width of the i-th neuron node respectively; is the system state variable, which serves as the input of the RBF neural network; δ represents the modal coordinate variable of the slow subsystem; is θ δ The first-order derivative of ; e1 and e2 are trajectory tracking errors;

[0111] The switching control item u sw for:

[0112]

[0113] Where η>0 represents the switching coefficient; sgn(s) represents the sign function.

[0114] According to the equivalent control term u eq and switch control u sw The predetermined time non-singular terminal sliding mode controller is obtained, namely:

[0115]

[0116] Where, u represents the total control input of the system; u eq is an equivalent control item; u sw To switch control items;

[0117] S4), designing an adaptive predetermined time non-singular terminal sliding mode controller, adjusting parameters through an adaptive law to suppress control input chattering, and controlling the joint trajectory tracking error to converge within a predetermined time range;

[0118] By introducing an adaptive parameter adjustment mechanism to replace the switching term of the scheduled time non-singular terminal sliding mode controller, an adaptive scheduled time non-singular terminal sliding mode controller is obtained, and its expression is:

[0119]

[0120] Where, is the adaptive adjustment item, for The estimated value of N Indicates the preset estimation error; satσ is a saturation function; Λ1 and Λ2 are positive definite diagonal matrices; is the design parameter.

[0121] In this embodiment, the adaptive law of the adaptive predetermined time non-singular terminal sliding mode controller is:

[0122]

[0123] Where, represents the derivative of the adaptive law; ι1 and ι2 represent the adaptive law parameters respectively; κ>0 represents the gain.

[0124] Example 2

[0125] This embodiment uses Matlab / Simulink tools to build a simulation platform, and applies the adaptive scheduled time non-singular terminal sliding mode controller of Example 1 to a planar single-joint module tendon-driven robotic arm; Figure 4 As shown, similarly, considering that the tendon-driven manipulator is installed on a large spacecraft, the mass of the manipulator is much smaller than the mass of the spacecraft base, and the manipulator base can be considered fixed. Considering the accuracy of the system model and the complexity of the calculation, the elastic modal number of the system is set to m = 2. In addition, this embodiment is compared with the finite-time controller for simulation, and its expression is: Among them, k1>0, k2>0, α>0, β=2α / (1+α).

[0126] In the simulation, the expected trajectory of the rigid-flexible coupled tendon-driven manipulator joint is set as The initial state of the robotic arm is uniformly set to θ r0 =0.35(rad),

[0127] The parameters of the adaptive scheduled time non-singular terminal sliding mode controller are preset as follows: α=1, β=1, σ=10,κ=1,T c1 =15,T c2 =15; the control parameters of the finite time controller are set as: k1=1, k2=1, The parameters of the preset time non-singular terminal sliding mode controller are: α=1, β=1, η=0.01,σ=10,T c1 =15,T c2 =15; the simulation results are as follows Figure 5-11 shown.

[0128] in, Figure 5 and Figure 6The robot arm joint trajectory tracking and tracking error under the action of three controllers are demonstrated. It can be seen that within the scheduled time, the preset adaptive scheduled time non-singular terminal sliding mode controller ANTSM and the scheduled time non-singular terminal sliding mode controller NTSM quickly adjust the initial state and track the desired trajectory. The system response speed is better than the finite time controller FTC.

[0129] Figure 7 It reflects the equivalent torque of the robot arm joint under the action of the three controllers. It can be seen that after the introduction of the parameter adaptive adjustment mechanism, the control input of the control strategy ANTSM is smoother than that of NTSM and FTC.

[0130] Figure 8 、 Figure 9 and Figure 10 The first-order modal vibration shape, second-order modal vibration shape and amplitude of the end of the robotic arm under the action of three controllers. It can be seen that the amplitude of the end of the robotic arm is mainly dominated by the first-order modal amplitude. Figure 11 represents the adaptive parameter of the adaptive scheduled time non-singular terminal sliding mode controller ANTSM From the changes in the data, we can see that the adaptive parameter values ​​eventually converge to a specific value over time.

[0131] The above embodiments and descriptions are only for explaining the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, which shall fall within the scope of the invention to be protected.

Claims

1. A method for adaptively tracking and controlling a rigid-flexible coupled tendon-driven robotic arm with a predetermined time trajectory, characterized in that: The steps include: S1) Establish a dynamic model of the rigid-flexible coupled tendon-driven manipulator that comprehensively considers the flexible deformation of the arm structure and the elastic deformation of the rope; S2), defining a trajectory tracking error, and designing a non-singular terminal sliding surface according to the trajectory tracking error, and designing an equivalent control term through the non-singular terminal sliding surface; S3), using an RBF neural network to estimate the system lumped interference, and designing a switching control item based on the estimated system lumped interference; the input of the RBF neural network is the system state variable, and the output is the interference estimate; S4) Design an adaptive predetermined time non-singular terminal sliding mode controller, which includes an equivalent control term and an adaptive switching term. The controller adjusts parameters through an adaptive law to suppress control input chattering and control the joint trajectory tracking error to converge within a predetermined time range.

2. The method for adaptively tracking and controlling a rigid-flexible coupled tendon-driven robotic arm in predetermined time according to claim 1, characterized in that: In step S1), the dynamic model is derived based on the Lagrangian method, assuming that the flexible arm is a homogeneous slender rod; ignoring axial deformation and shear deformation, and considering only bending deformation; the flexible arm is regarded as an Euler-Bernoulli beam, and the assumed modal method is used to describe the lateral elastic deformation of the arm; the lateral elastic deformation of the flexible arm of section i is expressed as: Where W i (x i ,t) is the cross section of the flexible arm The deformation of is the j-th modal function of the flexible arm, δ ij (t) is The time-varying amplitude of , m is the number of modal truncation terms of the flexible arm, and t represents time.

3. The method for adaptively tracking and controlling a rigid-flexible coupled tendon-driven robotic arm in predetermined time according to claim 2, characterized in that: The established dynamic model of the rigid-flexible coupled tendon-driven manipulator, which comprehensively considers the flexible deformation of the arm structure and the elastic deformation of the cable, is as follows: Where, θ=[θ1…θ i …θ n ] T is the joint angle matrix of the manipulator; M(θ) is a positive definite, symmetric mass matrix; is the column matrix containing the Coriolis force and the centripetal force; K is the flexible arm stiffness matrix; is the joint angular velocity; is the joint angular acceleration; τ e represents the rope elastic loss torque, J m Represents the equivalent mapping relationship between motor current and joint torque, i m Represents the current vector of each driving motor of the robotic arm system, and T represents the transposition operation.

4. The method for adaptively tracking and controlling a rigid-flexible coupled tendon-driven robotic arm in predetermined time according to claim 1, characterized in that: In step S2), the trajectory tracking error is defined as: e1=θ r -θ d , Where, e1 and e2 are trajectory tracking errors; θ r is the actual joint angle of the trajectory; is the actual joint angular velocity of the trajectory; θ d 、 are the desired joint angle and the desired joint angular velocity, respectively.

5. The method for adaptively tracking and controlling a rigid-flexible coupled tendon-driven robotic arm in predetermined time according to claim 4, characterized in that: In step S2), the non-singular terminal sliding surface s is: s=e2+h1sign 1-γ (e1)+h2sign 1+γ (e1); (10) Where 0<γ<1 is the fractional power parameter; h1 and h2 are the synovial parameters; sign is the sign function.

6. The method for adaptively tracking and controlling a rigid-flexible coupled tendon-driven robotic arm in predetermined time according to claim 5, characterized in that: In step S2), the equivalent control item u eq for: Where, is the actual joint angular acceleration of the trajectory; k1 and k2 are controller parameters; sat σ is a saturation function; α>0 indicates a control parameter, β>0 indicates a control parameter, T c3 >0 indicates the preset time; n indicates the number of degrees of freedom of the robot arm; is an element of M(θ); C rr for elements of ; Λ1 and Λ2 represent positive definite diagonal matrices respectively.

7. The method for adaptively tracking and controlling a rigid-flexible coupled tendon-driven robotic arm in predetermined time according to claim 6, characterized in that: In step S3), the system aggregate interference estimated by the RBF neural network is for: Where, is the estimated weight coefficient; φ(x) is the Gaussian radial basis function, and x is the system state variable, which serves as the input of the RBF neural network.

8. The method for adaptively tracking and controlling a rigid-flexible coupled tendon-driven robotic arm in predetermined time according to claim 7, characterized in that: In step S3), the switching control item u sw for: Where η>0 represents the switching coefficient; sgn(s) represents the sign function; And according to the equivalent control term u eq and switch control u sw The predetermined time non-singular terminal sliding mode controller is obtained, namely: Where, u represents the total control input of the system; u eq is an equivalent control item; u sw is the switching control term; η>0 represents the switching coefficient; sgn(s) represents the sign function.

9. The method for adaptively tracking and controlling a rigid-flexible coupled tendon-driven robotic arm in predetermined time according to claim 8, characterized in that: In step S4), an adaptive parameter adjustment mechanism is introduced to replace the switching term ηsgn(s) of the predetermined time non-singular terminal sliding mode controller to obtain an adaptive predetermined time non-singular terminal sliding mode controller, which is expressed as follows: Where; is the adaptive adjustment item, for The estimated value of N represents the preset estimation error; is the design parameter.

10. The method for adaptively tracking and controlling a rigid-flexible coupled tendon-driven robotic arm in predetermined time according to claim 9, characterized in that: In step S4), the adaptive law of the adaptive predetermined time non-singular terminal sliding mode controller for: Where ι1 and ι2 represent the adaptive law parameters respectively; κ>0 represents the gain.

Images