Optimal Trajectory Planning for Orbital Robot Rendezvous and Docking

TL;DR

This work tackles the problem of safely approaching tumbling space debris for robotic capture by formulating a nonlinear optimization framework that generates a close-range, feasible approach trajectory in a two-dimensional plane. A dynamic Keep-Out Sphere (KOS) adapts to the relative pose, enabling near-docking access while preserving safety, and the trajectory is reproduced on hardware-feasible discrete ON/OFF thrusters via a PWM-based allocation scheme. The method is validated in both ideal continuous-control simulations and high-fidelity MuJoCo simulations, including two case studies that vary target spin and attitude at closest approach; results show a final relative velocity around $0.03~\mathrm{m/s}$ and a final positional error on the order of $0.09~\mathrm{m}$, with notable increases in error when approaching from the rear. The framework provides a clear, implementable pathway toward practical debris-removal missions, with demonstrated robustness under diverse approach scenarios and a clear plan for extending to three dimensions and hardware experiments.

Abstract

Approaching a tumbling target safely is a critical challenge in space debris removal missions utilizing robotic manipulators onboard servicing satellites. In this work, we propose a trajectory planning method based on nonlinear optimization for a close-range rendezvous to bring a free-floating, rotating debris object in a two-dimensional plane into the manipulator's workspace, as a preliminary step for its capture. The proposed method introduces a dynamic keep-out sphere that adapts depending on the approach conditions, allowing for closer and safer access to the target. Furthermore, a control strategy is developed to reproduce the optimized trajectory using discrete ON/OFF thrusters, considering practical implementation constraints.

Figures (9)

• Figure 1: Simulation of a thruster-mounted chaser satellite approaching a target satellite in rotational motion (top-right) and simulated approach trajectory of the chaser achieving a precise adjustment of the pose (bottom).
• Figure 2: Placement of thrusters and direction of thrust.
• Figure 3: Different KOS patterns changed depending on the relative pose between the target and the chaser.
• Figure 4: Optimized trajectory for a closest approach (dot line) and the corresponding two satellites' poses in time series (two colored squares). In this case, the trajectory was planned to achieve the closest approach when the target is tilted at $3\pi/4$ to the $x$-axis.
• Figure 5: Thruster operation sequence (Control cycle: 10 Hz).