Barrier-certified Learning-based Control of Systems with Uncertain Safe Set

Abstract

This paper focuses on the problem of safe control design for systems that operate in cluttered environments and proposes a safe controller that ensures safety of the ego system despite the uncertain behavior of the surrounding external agents. To model the interaction between the ego system and other agents, two sets of decoupled dynamics are utilized: the dynamics of the ego system which is known and controllable and the dynamics of external agent which is unknown and out of control of the ego system. The safety criterion is represented as a function of both ego system's and external agent's states. An uncertain safe set is then formed as a set for which its forward invariance assures that safety specifications of the ego system are satisfied. Control barrier function (CBF) is then employed to ensure forward invariance of the safe set and thus assuring the safety of ego system. Since the trajectory information of external agents is also required to satisfy the safety specifications of the ego system, the external agent dynamics are learned through the data collected from their behavior observations. However, inaccurate approximation might lead to violation of safety. To overcome this challenge, a modified CBF is proposed that uses the instantaneous sensory observations to avoid imminent safety violation by ensuring the forward invariance of a sub-set of the safety set that satisfies safety. It results in safety guarantee with simplified approximation and even during learning. This set then expands toward the exact safe set by improvement of the approximation. The efficacy of the proposed method is demonstrated in the simulation.