Control Optimization for Space Robots in Target Detumbling

Abstract

Space robots have significantly advanced space technology by performing various in-orbit missions, including spacecraft maintenance, large-scale spacecraft assembly, and the capture and removal of noncooperative space objects. Safely and autonomously capturing a tumbling defunct satellite, a typical noncooperative object, poses a significant challenge for free-floating space robots (FFSR). After the end-effector of an FFSR securely reaches the tumbling target, the FFSR can decelerate its rotation and stabilize it to a stationary state, completing the capture mission. Given the limitations in control energy and the urgency of rapid stabilization for safety, the investigation of optimal control methods for space robots grasping noncooperative tumbling targets is a significant area of research. This article offers an optimal control solution for FFSRs to engage and bring a rotating object in space to rest. Initially, we develop a nonlinear optimal control method for FFSRs using the Hamilton–Jacobi–Bellman (HJB) equation for optimization in multiple performance indices, ensuring detailed proof of stability and convergence. The successive Galerkin approximation (SGA) method is specifically developed to approximate the analytical solution for the HJB equation for FFSRs. Computational simulations support the viability of the proposed method to arrest a tumbling target. Compared to the customary computed torque control before the optimization, computational simulation results show the proposed SGA optimal control approach achieves quicker stabilization of the tumbling target with reduced control energy consumption.