Finite time dynamic mechanical arm control method based on speed reconstruction strategy

Abstract

A finite time dynamic mechanical arm control method based on a speed reconstruction strategy comprises the steps that firstly, a mechanical arm system physical model containing joint torque is constructed, joint tracking errors are defined, and a mechanical arm system state space model is obtained; 2, constructing a finite-time high-bandwidth gain speed estimator, defining a state estimation error, and obtaining an estimation error dynamic equation; 3, defining an auxiliary state to obtain an auxiliary state dynamic equation; 4, constructing a finite time non-recursive adaptive controller; and 5, obtaining a final input torque of the controlled system, and outputting the final input torque as a joint torque. According to the method, through the processes of error modeling, state estimation, auxiliary conversion, control law design and closed-loop feedback, the dynamic tracking problem of the mechanical arm is converted into the finite time convergence problem of the error state, meanwhile, dynamic gain and robust compensation are introduced, the adaptability of a system to parameter uncertainty and external disturbance is improved, and the system reliability is improved. And a high-precision and high-robustness control target is realized.

Claims

1. A finite-time dynamic manipulator control method based on a velocity reconstruction strategy, comprising the following steps: first step: Based on the Lagrangian dynamic equations, the joint angle position information of each joint is collected using the joint angle sensors on the robotic arm system. The inertia matrix, centripetal force and Coriolis force matrices, and gravity vector obtained through pre-parameter identification are used to construct a physical model of the robotic arm system including the joint torque τ. Define joint angle and velocity tracking errors x1 and x2; Based on the physical model of the manipulator system and the definition of tracking error, the state space model of the manipulator system including the definition of control law u is obtained. The dynamic tracking problem is transformed into a convergence problem of the error state, and the output angle tracking error y = x1 is used for closed-loop control. Step 2: Construct a control law u and angle tracking error y = x1 as input, and use joint angle and velocity tracking error estimates is the output of a finite-time high-bandwidth gain velocity estimator; Error redefinition based on angle, velocity tracking error x1, x2 and joint angle, velocity tracking error estimates Define the angle and velocity state estimation errors e1 and e2; Based on the state-space model of the manipulator system, the finite-time high-bandwidth gain velocity estimator, and the angle and velocity state estimation errors e1 and e2, the estimation error dynamic equation is derived. The actual joint state and the estimated state are related, which facilitates the design of estimation-based robust compensation when constructing the control law u in the fourth step. Step 3: Define the auxiliary state and track the joint angle and velocity error estimates Convert to scaled auxiliary states z1 and z2, unify joint angle and velocity tracking error estimates The dynamic gain magnitude; Based on the auxiliary state definition and the finite time high bandwidth gain velocity estimator in the second step, the auxiliary state dynamic equation is obtained, and the joint angle and velocity tracking error estimation values ​​are converted to Dynamic conversion into auxiliary states z1 and z2 that can be directly called by the control law u; The fourth step is to build a finite-time non-recursive adaptive controller: First construct the dynamic gain adaptive update law The amplitude of L is adaptively adjusted online using the angle tracking error y=x1 and the angle estimation error x1 as the driving signal; Then, the dynamic gain L and auxiliary states z1 and z2 are used as inputs, and the control law u is output after gain and robust compensation. The control law u is fed back to the state space model of the manipulator system to change the angle and speed tracking errors x1 and x2; the control law u is fed back to the auxiliary state dynamic equation to change the joint angle and speed tracking error estimates Force estimated state Track the actual states x1 and x2, let the angle state estimation error and velocity state estimation error e1 and e2 converge to 0 within a finite time, and eventually approach the reference trajectory to form a closed control loop; The dynamic gain L is fed back to the finite time high bandwidth gain speed estimator to estimate the error dynamic equation, auxiliary state, auxiliary state dynamic equation and control law u, and the adaptive update law is used to calculate the error dynamic equation, auxiliary state dynamic equation and control law u. Dynamically match the control strength of the control loop to system requirements; Step 5: Based on the control law u defined in the first step and the control law u output in the fourth step, the final input torque of the controlled system is obtained, and its output is used as the joint torque τ acting on the robotic arm in the first step.

2. The finite-time dynamic manipulator control method based on velocity reconstruction strategy according to claim 1, characterized in that: In the first step, the physical model of the robotic arm system is: Where: q is the collected joint angle position data; is the joint angular velocity; is the joint acceleration; τ is the joint torque; M(q) is the 6-dimensional positive definite symmetric inertia matrix, is the 6-dimensional centripetal force and Coriolis force matrix, G(q,θ) is the 6-dimensional manipulator gravity vector, F ric is the friction force inside the manipulator; θ is the identification error in the centripetal force and Coriolis force matrix and the manipulator gravity vector; The tracking error is defined as: Where: q ref is the expected angle of each joint of the system, is the expected velocity of each joint of the system; x1 is the joint angle tracking error, and x2 is the joint velocity tracking error; The state space model of the robotic arm system is: in: is the time derivative of joint angle tracking error and joint velocity error; M -1 (x1+q ref ) is the inverse matrix of the inertia matrix M(q); define the control law is the expected acceleration of each joint of the system; nonlinear term Expressed as:

3. The finite-time dynamic manipulator control method based on velocity reconstruction strategy according to claim 1, characterized in that: In the second step, the finite-time high-bandwidth gain velocity estimator is: Among them: α1, α2 are gain coefficients; ω is the homogeneity parameter, The symbol sig is defined as sig r (·)=|·| r sign(·); are the estimated values ​​of x1 and x2, i.e., the estimated values ​​of joint angle tracking error and joint velocity tracking error respectively; the dynamic gain L is the bandwidth parameter, L>1; The state estimation error is defined as: Where: e1 is the angle state estimation error, e2 is the speed state estimation error after scaling; The dynamic equation of the estimation error is: in: They are the time derivatives of e1 and e2, respectively, representing the dynamic changes of the error.

4. The finite-time dynamic manipulator control method based on velocity reconstruction strategy according to claim 3 is characterized in that: α1>0，α2>0。 5. The finite-time dynamic manipulator control method based on velocity reconstruction strategy according to claim 3 is characterized in that: described 6. The finite-time dynamic manipulator control method based on velocity reconstruction strategy according to claim 1, characterized in that: In the third step, the auxiliary state is defined as: The auxiliary state dynamic equation is:

7. The finite-time dynamic manipulator control method based on velocity reconstruction strategy according to claim 1, characterized in that: In the fourth step, the finite-time non-recursive adaptive controller is: in: is the update rate of the dynamic gain L; L0 is the initial value of L, L>1; k1, k2 are the design gain parameters; δ is the threshold parameter; λ is the update rate coefficient of the dynamic gain L, λ>0.

8. The finite-time dynamic manipulator control method based on velocity reconstruction strategy according to claim 7, characterized in that: Said k1, k2>0.

9. The finite-time dynamic manipulator control method based on velocity reconstruction strategy according to claim 7, characterized in that: The 0<δ<0.

5.

10. The finite-time dynamic manipulator control method based on velocity reconstruction strategy according to claim 1, characterized in that: In the fifth step, the final input torque of the controlled system is:

Images