The Numerical Control Design for a Pair of Dubins Vehicles

TL;DR

This paper develops an optimal control framework for a pair of Dubins vehicles to navigate from start to end positions without collision, using Pontryagin's Maximum Principle and numerical gradient descent, with simulation validation.

Contribution

It introduces a novel control approach for dual Dubins vehicles considering collision avoidance and inter-vehicle distance constraints, solved via PMP and numerical methods.

Findings

Successful simulation of vehicle trajectories under the proposed control.

Effective avoidance of collisions and maintaining distance constraints.

Validation of the control method through numerical experiments.

Abstract

In this paper, a model of a pair of Dubins 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 cant to far each other. The optimal control of the vehicle is found using the Pontryagins 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.