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In this paper, a model of a pair of Dubin’s vehicles is considered. The vehicles move from an initial position and orientation to final position and orientation. A long the motion, the two vehicles are not allowed to collide however the two vehicles cann’t to far each other. The optimal control of the vehicle is found using the Pontryagin’s Maximum Principle (PMP). This PMP leads to a Hamiltonian system consisting of a system of differential equation and its adjoint. The originally differential equation has initial and final condition but the adjoint system doesn't have one. The classical difficulty is solved numerically by the greatest gradient descent method. Some simulation results are presented in this paper.

The Numerical Control Design for a Pair of Dubin's Vehicles