Extent-compatible control barrier functions

M. Srinivasan, M. Abate, G. Nilsson, S. Coogan
Systems and Control Letters, 2021


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