Optimizable Control Barrier Functions to Improve Feasibility and Add Behavior Diversity while Ensuring Safety

Abstract

Ensuring safety while retaining maximum performance is a basic requirement for automatic cyber-physical systems, especially for safety-critical applications. A quadratic programming optimization framework called MPC-CBF has recently been presented, which directly unifies model predictive control (MPC) with control barrier functions (CBFs) over the prediction time horizon. However, the conservative nature of CBFs can lead to feasibility problems in real applications. Based on the analysis of the role of the decay rate and the conservative accumulation phenomenon in standard CBF formulations, this paper proposes to directly optimize CBF constraints within the MPC framework. By regarding CBFs as a safety restriction level indicator and an optimizable constraint within the MPC framework, the trade-off between feasibility and safety can be adaptively optimized. The proposed Optimizable CBF (OCBF) model removes the hyper-parameters selection problem in standard CBFs and can adaptively adjust the safety restriction level and increase behavior diversity by adding the corresponding objects in the cost function in MPC. To eliminate the accumulation effects of actual values of the CBF constraints in previous time steps, this paper further proposes a General OCBF (GOCBF) formulation. Compared with existing formulations, the safety margin defined in our GOCBF has intuitive physical meanings and thus provides a more flexible and intuitive mechanism to compromise different objects in terms of ensuring safety while not undermining basic feasibility. Experimental results demonstrate that our algorithm provides a more flexible and intuitive mechanism to achieve this, thus improving feasibility and adding behavior diversity in the MPC-CBF framework.