  The problem of autonomous navigation is to generate a set of navigation
references which when followed move the vehicle from a starting position to and
end goal location while avoiding obstacles. Autonomous racing complicates the
navigation problem by adding the objective of minimising the time to complete a
track. Solutions aiming for a minimum time solution require that the planner is
concerned with the optimality of the trajectory according to the vehicle
dynamics. Neural networks, trained from experience with reinforcement learning,
have shown to be effective local planners which generate navigation references
to follow a global plan and avoid obstacles. We address the problem designing a
reward signal which can be used to train neural network-based local planners to
race in a time-efficient manner and avoid obstacles. The general challenge of
reward signal design is to represent a desired behavior in an equation that can
be calculated at each time step. The specific challenge of designing a reward
signal for autonomous racing is to encode obstacle-free, time optimal racing
trajectories in a clear signal We propose several methods of encoding ideal
racing behavior based using a combination of the position and velocity of the
vehicle and the actions taken by the network. The reward function candidates
are expressed as equations and evaluated in the context of F1/10th autonomous
racing. The results show that the best reward signal rewards velocity along,
and punishes the lateral deviation from a precalculated, optimal reference
trajectory.
