Neuro-Genetic Truck Backer-Upper Controller

Marc Schoenauer and Edmund Ronald Abstract|The precise docking of a truck at a loading dock has been proposed in [Nguyen & Widrow 90] as a benchmark problem for non-linear control by neural-nets. The main di culty is that back-propagation is not a priori suitable as a learning paradigm, because no set of training vectors is available: It is non-trivial to nd solution trajectories that dock the truck from anywhere in the loading yard. In this paper we show how a genetic algorithm can evolve the weights of a feedforward 3-layer neural net that solves the control problem for a given starting state, achieving a short trajectory from starting point to goal. The tness of a net in the population is a function of both the nearest position from the goal and the distance travelled. The in uence of input data renormalisation on trajectory precision is also discussed. I. PLANT DESCRIPTION The plant to be controlled here is a truck with trailer, which should be backed up to a loading dock; the truck is initially located at some random position in the parking lot. The truck backs up by small uniform steps, denoted by r, while steering is e ected by re-orienting the front wheels before each step. There is thus only one control variable, the angle of the steering wheels with respect to the cab, denoted u. Our truck is the same as that described in the pioneering studies of [Nguyen & Widrow 90], who devised backpropagation through time to investigate the system. We have followed [Nguyen & Widrow 90] in chosing the observable state variables which together de ne a state: The coordinates of the center back of the trailer, and the orientation of the cab and the trailer with repect to the x axis. The constraints on the steering range and the sizing of the truck have been retained. We have however adopted a di erent set of dynamic equations, which allow us to resolve more easily the uncertainty on the angles S and C occasioned by the use of the arctangent in the paper cited above. The reader may verify that both derivations are equivalent in the rst order, and thus de ne similar trajectories. Both authors can be reached at Centre de Math ematiques Appliqu ees, URA CNRS 756, Ecole Polytechnique, 91128 Palaiseau, France. Email should be adressed to [email protected] (x,y) θ θ