Extent-compatible control barrier functions
M. Srinivasan, M. Abate, G. Nilsson, S. Coogan
Systems and Control Letters, 2021
Abstract
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.