Reachability-Based Safe-Start Regions for Approach to a Tumbling Target with Rotating LOS Constraints

Abstract

This paper presents a reachability-aware guidance architecture for autonomous approach to a tumbling, uncooperative target under a rotating line-of-sight (LOS) docking corridor. The LOS admissible set rotates with the target body frame, producing time-varying polyhedral constraints on the chaser's relative motion, and the design problem is to establish the initial states from which the chaser can safely approach and synchronize with the rotating hold point. A closed-form answer is derived from bounded-thrust relative orbital dynamics, in the form of two analytical safe-start criteria: a directional per-constraint erosion margin, quantifying the corridor margin consumed by rotation-induced drift before the thruster can arrest it, and a synchronization radius, bounding the range over which the apparent rotational velocity can still be cancelled. Closed-loop guidance combines a three-regime tracking law, spanning far-field approach, close body-frame tracking, and synchronized hold, with a receding-horizon quadratic program carrying the rotating corridor constraints and exact discrete relative-motion prediction. The criteria are benchmarked against four standard reachability engines, namely backward and forward polytopic reachable sets, Hamilton--Jacobi level sets, and closed-loop Monte Carlo simulation. The closed-form test is orders of magnitude cheaper than grid-based Hamilton--Jacobi reachability while tracking closed-loop feasibility closely across a parametric sweep. The residual optimism and the gap against Hamilton--Jacobi are structural rather than a method error: requiring the chaser to reach the hold point and co-rotate with it is strictly stronger than requiring it to arrive with arbitrary velocity, and the gap widens with tumble rate. The criteria therefore serve as an onboard go/no-go bound where Hamilton--Jacobi reachability is prohibitively expensive.

10 pages, 3 figures, 3 tables. Preprint of paper IAC-26,C1,3,6,x110087 submitted to the 77th International Astronautical Congress (IAC 2026), Antalya, Türkiye, 5-9 October 2026