Adaptation for Validation of Consolidated Control Barrier Functions

We develop a novel adaptation-based technique for safe control design in the presence of multiple state constraints. Specifically, we introduce an approach for synthesizing any number of candidate control barrier functions (CBFs), each encoding a different state constraint, into one consolidated CBF (C-CBF) candidate. We then propose a parameter adaptation law for the weights of the C-CBF's constituent functions such that its controllable dynamics are non-vanishing. We prove that the adaptation law certifies the consolidated CBF candidate as valid for a class of nonlinear, control-affine, multi-agent systems, which permits its use in a quadratic program based control law. We highlight the success of our approach in simulation on a multi-robot goal-reaching problem in a warehouse environment, and further demonstrate its efficacy via a laboratory study with an AION ground rover operating amongst other vehicles behaving both aggressively and conservatively.