  This paper presents an optimisation-based approach for an obstacle avoidance
problem within an autonomous vehicle racing context. Our control regime
leverages online reachability analysis and sensor data to compute the maximal
safe traversable region that an agent can traverse within the environment. The
idea is to first compute a non-convex safe region, which then can be
convexified via a novel coupled separating hyperplane algorithm. This derived
safe area is then used to formulate a nonlinear model-predictive control
problem that seeks to find an optimal and safe driving trajectory. We evaluate
the proposed approach through a series of diverse experiments and assess the
runtime requirements of our proposed approach through an analysis of the
effects of a set of varying optimisation objectives for generating these
coupled hyperplanes.
