Optimal Control of a Space Robot to Approach a Tumbling Object for Capture with Uncertainties in the Boundary Conditions

Abstract

This paper presents an optimal control strategy for a space robot to approach a tumbling object, such as an out-of-control satellite or a piece of space debris, for capture with minimal impact to the base satellite (also called servicing satellite or chaser satellite) with consideration of random uncertainties in the initial and final boundary conditions. The method consists of two steps. The first step is to determine an optimal future time and the target object’s corresponding motion state for the robot to capture the tumbling object, such that, at the time when the tip of the robot intercepts it, the resulting impact or disturbance on the attitude of the base satellite will be minimal. In the second step, the space robot will be controlled to reach the tumbling object at the predicted optimal time along an optimal trajectory. Uncertainties in the initial and final boundary conditions are introduced as errors inevitably exist in the tracking sensing data. Markov Chain Monte Carlo (MCMC) method is employed to solve the optimal control problem with boundary uncertainties. The performance of the method is demonstrated using a dynamics simulation example.