High Order Curvature and Torsion Continuous Trajectory Planning Method for Space Flight Robot

Abstract

Aiming at the propulsion disturbance problem brought by the discontinuity of the rotation angular acceleration in the freedom flight course of space robot at microgravity condition, a flight trajectory which conforms to cubic curvature polynomials and cubic torsion polynomials in carrier coordinate of robot in 3D space in the trajectory planning stage. The robot's rotation angular velocity, angular acceleration and angular jerk can be continuous if the robot flies along the robot trajectory. According to the kinematics transform between the carrier coordinate system and the global coordinate system, the flight trajectory in the global coordinate system is a nonlinear transcendental equation set with quadratic integral. Separate polynomial parameters and other parameters separately, using partial differential Jacobi matrix to express the local linear relationship of the gradients of polynomial parameters and the gradients of other parameters, and Newton-Rap son iterative is used to draw near the real solution. At last, all approximate values are got. Thus it is concluded that the functions of the curvature polynomial, the torsion polynomial and the expression of trajectory in the global coordinate. The simulation experiment shows that the trajectory planning method can ensure that the angular velocity of robot is high order continuous at the same time, and effectively avoiding the control disturbance and burden of control system caused by the mutations of command speed, acceleration and jerk.