In this paper we consider autonomous driving of miniature race cars. The viability kernel is used to efficiently generate finite look-ahead trajectories that maximize progress while remaining recursively feasible with respect to static obstacles (e.g., stay inside the track). Together with a low-level model predictive controller, this method makes real-time autonomous racing possible. The viability kernel computation is based on space discretization. To make the calculation robust against discretization errors, we propose a novel numerical scheme based on game theoretical methods, in particular the discriminating kernel. We show that the resulting algorithm provides an inner approximation of the viability kernel and guarantees that, for all states in the cell surrounding a viable grid point, there exists a control that keeps the system within the kernel. The performance of the proposed control method is studied in simulation where we determine the effects of various design choices and parameters and in experiments on an autonomous racing set-up maintained at the Automatic Control Laboratory of ETH Zurich. Both simulation and experimental results suggest that the more conservative approximation using the discriminating kernel results in safer driving style at the cost of a small increase in lap time.
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