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Safety Planning Using Control Barrier Function: A Model Predictive Control Scheme

This paper presents a control barrier function-based model predictive control (MPC) scheme which trades off between safety and performance. The control barrier function and the control Lyapunov function are unified in an unconstrained time-invariant MPC framework which not only guarantees safety but also performs look-ahead optimal planning. This approach provides a smooth transition in interior points of the set of feasible states and ensures safety for a broader class of feasible sets for which the safety criteria is a function of possibly all state variables. Compared to existing methods, it addresses the case of conflict between safety and optimality and safe set does not necessarily contain the origin. Also, the proposed barrier function candidate does not need a zeroing factor to ensure stability. In addition, it can be applied to the cases where the feasible sets are open or do not have a global minimizer. Moreover, a tuning parameter is incorporated to specify the required level of conservativeness of the controller depending on the application. The provided simulation results show the effectiveness of the proposed method.