Method for programming repeating motion of redundant robotic arm

A method for performing a repeating motion of a robotic arm on the basis of a variable parameter convergence differential neural network, comprising:

• providing a robotic arm, the robotic arm having an end and a plurality of joints;
• providing a system for operating the robotic arm by the following steps:
• a) establishing an inverse kinematics equation of the robotic arm at a velocity level by tracking the end of the robotic arm;
• b) generating an inverse kinematics problem as a time-varying convex quadratic programming problem constrained by an equality;
• c) obtaining an initial joint state θ(0) of the robotic arm and a joint state θ(t) during the motion of the robotic arm, and introducing a repeating motion indicator into the time-varying convex quadratic programming problem;
• wherein the repeating motion indicator is obtainable by means of the performance indicator coefficient c, which is designed as c=ζ(θ(t)−θ(0)), where ζ represents the response coefficient to a joint offset;
• d) converting the time-varying convex quadratic programming problem, into a time-varying matrix equation by using a Lagrangian function;
• e) solving the time-varying matrix equation by the variable parameter convergence differential neural network;
• wherein the error of the time-varying matrix equation converges to zero based on the variable parameter convergence differential neural network, an error function is constructed as:
• ε(t)=Qy−u
• where ε(t) represents the error of the time-varying matrix equation, and then based on a neurodynamic method, the error is designed to converge to zero in the following way:
• d
• ⁢
• ⁢
• ɛ
• ⁡
• (
• t
• )
• dt
• =
• -
• γ
• ⁢
• ⁢
• exp
• ⁡
• (
• t
• )
• ⁢
• Φ
• ⁡
• (
• ɛ
• ⁡
• (
• t
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• )
• where γ is a parameter for adjusting a convergence rate, Φ(•) is an activation function, and the error function is substituted into the above formula to obtain a variable parameter convergence differential neural network solver, namely:
• Q{dot over (y)}=−{dot over (Q)}y−γ exp(t)Φ(Qy−u)+{dot over (u)}
• where the variable parameter convergence differential neural network solver obtains an optimal solution y* of the time-varying matrix equation, and the first n terms thereof are an optimal solution x* of the time-varying convex quadratic programming problem, i.e., an optimal solution of a joint angular velocity;
• f) integrating the optimal solution x* of the robotic arm at the velocity level to obtain an optimal solution θ* of a joint angle;
• and
• g) using the optimal solution θ* of the joint angle to operate the robotic arm to perform the repeating motion, so that after the end of the robotic arm completes a cycle of actions, all the joints of the robotic arm can return to an initial position.