Feasibility for CBF-Based Optimal Control Using Machine Learning

Abstract

In this chapter, we continue the discussion on feasibility guarantees for the CBF/HOCBF-based optimization in OCP-CBF (2.20) following the methods presented in Chap. 4. Here, however, we rely on the use of machine-learning techniques in which actual data are used in two different ways. First, in Sect. 5.1 we introduce a metric for feasibility robustness that measures the extent to which the feasibility of the QPs in (2.21) is maintained in the presence of time-varying and unknown unsafe sets. We then parameterize the HOCBFs and describe ways to learn parameter values that maximize this feasibility robustness metric. This learning compensates for the myopic feature of the QP-based approach and is particularly effective when unsafe sets are regular (to be defined later) and do not depend on initial conditions. Next, in Sect. 5.2 we present an alternative approach better suited for irregular unsafe sets in which the QP problem feasibility heavily depends on initial conditions. In this case, the goal is to learn a new feasibility constraint that guarantees the QP feasibility; this is then enforced by a HOCBF and added to the QPs. Simulation examples illustrating the applicability of the developed methods for robot control are presented in Sects. 5.1.5 and 5.2.6.