Extent-compatible control barrier functions

Safety requirements in dynamical systems are commonly enforced with set invariance constraints over a safe region of the state space. Control barrier functions, which Lyapunov-like functions for guaranteeing invariance, an effective tool to enforce such and guarantee safety when system is represented as point In this paper, we introduce extent-compatible control explicitly accounting its volume (extent) within ambient workspace. order implement framework, first propose sum-of-squares optimization program that solved pointwise time ensure safety. Since programs can be computationally prohibitive, next approach instead considers finite number points sampled on extent boundary. The result quadratic guaranteed retains computational advantage traditional functions. While alternative generally more conservative than approach, show conservatism reduced by increasing points. Simulation robotic implementation results provided.