Online Adaptation for Safe Control of Constrained Dynamical Systems

Abstract

Advances in sensing modalities and computational power have led to the prospect of a widespread deployment of robots in our society. Central to this objective is developing control and navigation stacks that avoid conservatism, presumed to be measured by a performance metric, while being provably and practically safe. A crucial element that must be accounted for is that controllers, which are typically designed for and tuned in laboratory or highly monitored industrial settings for a specific scenario, may experience a drop in performance and lose their safety guarantees when used elsewhere. It is of paramount importance therefore to import robots with the capability to adapt their controllers online to customize responses to a priori untested environments.

In brief, this dissertation presents (1) tools to adapt any parametric controller using a model-based approach to achieve simultaneous satisfaction of multiple state constraints and enhanced performance; (2) a numerical scheme for predicting future state distributions in systems governed by stochastic dynamics with state-dependent disturbances, which can be utilized in model-predictive approaches; and (3) a method to assist decision-making on dropping (disregarding) constraints when it is not feasible to satisfy all constraints simultaneously.

A significant part of the dissertation focuses on a specific safety-critical control method called control barrier functions (CBF). The CBF-based controllers have garnered interest in recent years due to their ease of implementation. However, finding a theoretically valid CBF remains a challenge and in practice, they are prone to performance degradation and safety violations, especially when multiple CBFs are imposed together. This dissertation introduces a new notion of CBFs, called Rate-Tunable CBFs, that allows for time-varying parameters in theory and online tuning in practice.