Escape-Aware Control Barrier Functions for Quadrotor Safety under Body-Rate Limits

• URL: http://arxiv.org/abs/2609.17292v1
• Date: Tue, 15 Sep 2026 15:06:37 GMT
• Title: Escape-Aware Control Barrier Functions for Quadrotor Safety under Body-Rate Limits
• Abstract summary: Control barrier functions for input-constrained systems place the admissible input set inside the definition of the safe set.<n>On a quadrotor this is not cosmetic: because the thrust vector must be reoriented before it can decelerate an approach, a state-only barrier certifies states from which no escape is reachable in time.<n>We 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.
• Score: 4.665549640473909
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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