The brachistochronic motion of a wheeled vehicle

The paper considers the brachistochronic motion of a wheeled vehicle on a horizontal plane surface. The objective is to transfer the vehicle from the specified initial position with given initial kinetic energy to the specified terminal position in minimum time with conserved total mechanical energy of the vehicle. The problem is solved by applying Pontryagin’s maximum principle and singular optimal control theory. The projection of the reaction force of the horizontal plane applied on the front vehicle wheels onto the axis of the front vehicle axle is taken for a control variable. The cases of unbounded and bounded value of this projection are considered. The shooting method is used to solve the two-point boundary value problem arising from Pontryagin’s maximum principle and singular optimal control theory.