Control barrier functions with the notion of viability kernels solve state-constrained problems under input constraints. However, it is not clear that how viability kernels are obtained for general systems and whether an optimal safety assist controller satisfying both state and input constraints is continuous. In this paper, we consider a four-wheeled vehicle model and demonstrate how to obtain its viability kernel. Then, by explicitly solving an optimization problem, we design a human assist controller that ensures the safety of the system with minimal intervention. Moreover, we show that the proposed explicit controller is continuous. Lastly, we confirm the effectiveness of the proposed method by computer simulation.

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