Trajectory optimization method of terminal self-reconfiguring live working robot based on Fourier series

Abstract

End-effector self-reconfiguring live working robot autonomously replaces the end actuator of the robot arm for different tasks, and at the same time completes high-altitude work tasks according to the designed motion plan. In order to ensure uninterrupted operation on power transmission lines, the research methods to enhance the efficiency of robot arm work while reducing energy consumption is of significant importance. Based on this, the paper proposes a time-energy optimal trajectory optimization method for a six-joint robotic arm of a reconfigurable robot for power line maintenance based on Fourier series, taking into account the influence of both robot kinematics and dynamics on the motion trajectory, the positions, velocities, accelerations and joint torques are all considered as constraints. Time and energy are chosen as objective functions. By utilizing the Lagrangian equation method establish an energy-based robot dynamic model in generalized coordinates. The motion curves of each joint are obtained by the cubic spline interpolation method in the joint space, and the boundary conditions of the motion curves are optimized by Fourier series, so as to establish the optimal trajectory mathematical model. The time-energy optimal trajectory planning problem is transformed into a convex optimization problem, the DTW (Dynamic Time Warping) algorithm is used to regularize the difference between the time function and the energy function in the displacement sequence under the known trajectory, and the number of terms in the Fourier series of the minimum hour of the objective function is obtained by the GA-DQN (Genetic Algorithm-Deep Q-Network) algorithm. Finally, with the actuator replacement at the end of the robotic arm as the operation objective, the time-energy optimal trajectory is obtained from the desired positional attitude at the initial and termination of the end of the robotic arm. Simulation analysis is carried out under MATLAB and compared with the motion trajectory obtained by the fifth degree polynomial interpolation method, and the results show that by optimizing the motion trajectory with Fourier series, the motion time is shortened by about 35.67% and the energy consumption is reduced by about 39.63%. And online experiments were conducted in the field to measure the output errors of joints 2 and 5, as well as the actual energy and time consumption of outputting the optimal trajectories, which verified that the trajectories obtained under this optimization algorithm have better performance and can meet the requirements of online robot end self-reconfiguration operation.