Optimal Trajectory Planning for Space Object Tracking with Collision-Avoidance Constraints

TL;DR

This paper introduces an optimization-based method for planning collision-free trajectories of a chaser spacecraft near a target object, efficiently balancing fuel use and safety over long durations.

Contribution

It presents a novel mixed-integer nonlinear programming approach with convex reformulation and heuristics for efficient, collision-free space trajectory planning.

Findings

Effective collision avoidance in numerical case study

Reduced computational overhead for long-horizon planning

Validated approach for practical space missions

Abstract

A control optimization approach is presented for a chaser spacecraft tasked with maintaining proximity to a target space object while avoiding collisions. The target object trajectory is provided numerically to account for both passive debris and actively maneuvering spacecraft. Thrusting actions for the chaser object are modeled as discrete (on/off) variables to optimize resources (e.g., fuel) while satisfying spatial, dynamical, and collision-avoidance constraints. The nonlinear equation of motion is discretized directly using a fourth-order Runge-Kutta method without the need for linearized dynamics. The resulting mixed-integer nonlinear programming (MINLP) formulation is further enhanced with scaling techniques, valid constraints based on a perspective convex reformulation, and a combination of continuous relaxations of discrete actions with rounding heuristics to recover high-quality feasible solutions. This methodology enables efficient, collision-free trajectory planning over extended time horizons while reducing computational overhead. The effectiveness and practicality of the proposed approach is validated through a numerical case study.