Control Barrier Functions for Safe Free-Flying Robotic Spacecraft Operations in Tumbling Target Capture

Multi-robot Control Barrier Function (CBF) safety filters can become infeasible, but a failed quadratic program (QP) does not indicate why the conflict occurred or how to resolve it. To address this, we develop an exact feasibility certificate for multi-agent CBF filters with heterogeneous control-affine dynamics and convex input sets. The certificate quantifies a feasibility reserve by separating the demand imposed by safety constraints from the available actuator supply. This decomposition shows when CBF gain tuning or increased actuation can and cannot resolve infeasibility, and identifies the agents and interactions responsible for the conflict. We further propose an algorithm to optimally allocate shared safety constraints by maximizing the worst local feasibility margin, yielding a linear program for polyhedral input sets. In $320$ paired closed-loop simulations, the proposed allocation reduces infeasible control steps from roughly $50\%$ to $6.2\%$, and reduces safety-violating runs from $118/160$ to $24/160$. In addition, across $52$ infeasibility events, the certificate identifies an interaction whose relaxation restores feasibility in $94\%$ of cases.

Control barrier functions for input-constrained systems place the admissible input set inside the definition of the safe set, yet the resulting barrier is almost always a function of the state alone; On a quadrotor this is not cosmetic: because the thrust vector must be reoriented before it can decelerate an approach, and reorientation is limited by the attainable body rate, a state-only barrier certifies states from which no escape is reachable in time; We characterize the certification gap in closed form and show its width is proportional to closing speed and inversely proportional to the body-rate limit; We then define an escape barrier on the augmented pair of state and previously applied input, with escape authority measured over the one-step reachable thrust cap; It admits a closed form and an analytic inverse for the maximum certifiable closing speed, and embeds in a predictive controller at no additional state cost; Across 550 paired closed-loop episodes on a 13-state quadrotor, the proposed controller completes every tested scenario, whereas the stopping-distance barrier enforced over the same horizon fails 15% and 25% of episodes in exactly the two scenarios that enter the predicted gap; Against an online backup-CBF baseline enforcing the same escape condition at the reached state, it holds a 29-74 degree larger directional margin and 3-18 times the clearance, and an independent conservative rollout referee finds no certified state from which escape fails.

We propose a safety-critical framework for the cooperative transportation of passive targets in microgravity, where a team of chaser robots acts through unilateral pushing contacts to track a human-provided desired twist while ensuring safe target motion. The pushing-only nature of the interaction introduces sparse, configuration-dependent actuation constraints requiring chasers to physically relocate on the target body when the desired pushing allocation changes. To address these challenges, we formulate a delay-aware feedback control architecture leveraging Control Lyapunov Function (CLF) and Control Barrier Function (CBF) constraints within a mixed-integer thrust allocation program to enforce stability and safety of the target, respectively. The proposed framework enables reference tracking while guaranteeing obstacle avoidance with a circular obstacle despite intermittent control authority, providing a foundation for human-supervised cooperative transportation of free-flyers in space environments. The proposed framework is validated through Gazebo simulations.