Adaptation for Validation of a Consolidated Control Barrier Function based Control Synthesis

Abstract

We develop a novel adaptation-based technique for safe control design in the presence of multiple control barrier function (CBF) constraints. Specifically, we introduce an approach for synthesizing any number of candidate CBFs into one consolidated CBF candidate, and propose a parameter adaptation law for the weights of its constituents such that the controllable dynamics of the consolidated CBF are nonvanishing. We then prove that the use of our adaptation law serves to certify 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 multirobot goal-reaching problem in a crowded warehouse environment, and further demonstrate its efficacy experimentally in the laboratory via AION ground rovers operating amongst other vehicles behaving both aggressively and conservatively. c i=1 Si. C(k) is shown here with a dotted white boundary for gains k0 at time t0 and k1 at t1.

Rate-Tunable Control Barrier Functions: Methods and Algorithms for Online Adaptation

“…When multiple constraints are present, [6], [7] combine barrier functions into a single barrier constraint through smoothed minimum (or maximum) operator. [20] proposes a novel weighted-summation technique, where the weights are tuned for performance and to avoid singular states where the control input has no contribution to barrier function derivatives (usually the latter is only assumed, but not guaranteed, to not happen in the literature). The authors in [5] perform nonsmooth analysis to construct a barrier function with the nonsmooth minimum (or maximum) operation.…”