Time-optimal control of the race car: a numerical method to emulate the ideal driver

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Abstract
A numerical method for the time-optimal control of the race car is presented. The method is then used to perform the role of the driver in numerical simulations of manoeuvres at the limit of race car performance. The method does not attempt to model the driver but rather replaces the driver with methods normally associated with numerical optimal control. The method simultaneously finds the optimal driven line and the driver control inputs (steer, throttle and brake) to drive this line in minimum time. In principle, the method is capable of operation with arbitrarily complex vehicle models as it requires only limited access to the vehicle model state vector. It also requires solution of the differential equation representing the vehicle model in only the forward time direction and is hence capable of simulating the full vehicle transient response.