Robust Time-Varying Control Barrier Functions with Sector-Bounded Nonlinearities

Abstract: This paper presents a novel approach for ensuring safe operation of systems subject to input nonlinearities and time-varying safety constraints. We formulate robust time-varying control barrier functions by combining two ingredients: (i) time-varying control barrier functions which capture the time-varying safety constraints, and (ii) pointwise-in-time quadratic constraints that bound the nonlinearity. These ingredients are used to design a safety filter. This filter ensures safety while minimally altering the command from a given baseline controller. The safety filter is implemented as the solution of a second-order cone program, which can be efficiently computed online. The approach is demonstrated on a simple car obstacle avoidance scenario.