Gain-optimization trajectory planning method for hyper-redundant manipulator with joint constraints

Because their inverse kinematics do not have analytical solutions, hyper-redundant manipulators cannot be directly solved by the geometric method. To realize real-time planning, this study proposes an artificial potential field trajectory planning method based on the Jacobian transposition matrix. Trajectory planning must satisfy not only the requirements of end-tracking accuracy but also the joint velocity and angular constraints. The joint velocity is mainly determined by the gain of the trajectory planning algorithm. Through the optimization of the potential field function and use of weighted joint velocities, the joint speed norms can be reduced under the precondition of avoiding joint restriction. Thus, a larger gain can be selected to help the system achieve a better steady-state performance. The Monte Carlo method was used to establish the relationship between the maximum joint speed and gain, which is necessary to determine the gain range for selecting an appropriate gain. The correctness and effectiveness of the algorithm can be proved by selecting different gains in point-to-point and trajectory tracking motion. The study also introduces velocity feedforward in trajectory tracking motion and proves the stability of the two motion formal algorithms by the Lyapunov stability theorem. Results of a simulation verification of the hyper-redundant manipulator independently designed and manufactured by our laboratory revealed that the end position deviation and attitude deviation were less than 10-4 mm and 1×10-5 rad, respectively, based on the premise of ensuring rapid point-to-point movement. In addition, the trajectory tracking movement position deviation and altitude deviation were less than 10-3 mm and 1×10-4 rad, respectively. Finally, experimental verification revealed that although the trajectory deviation in the experimental process increased by an order of magnitude compared to the simulation, the requirements of the experimental task were still met. © 2019, Science Press. All right reserved.