Optimal Path Tracking With Dubins' Vehicles

In this article, patrolling with Dubins' vehicles is investigated. The vehicles have significant kinematic constraints such as minimum-turning radius, and are unable to move in a reverse direction, i.e., they can only track planar curvature-bounded paths. The problem is more challenging than the conventional patrolling problem because the Euclidean traveling salesmen problem (ETSP) solution provides poor estimates of the actual travel time and vehicle location in this case. An algorithm called the pulley algorithm (PA) is developed to convert the ETSP optimal solution to a kinematically feasible optimal Dubins path that can be tracked by Dubins' vehicles. The PA guarantees that its corresponding optimal path is suitable for patrolling, i.e., for repetitive tracks among the way points. In addition, an upper bound for the PA is presented to show the difference between it and the ETSP optimal solution. This article also introduces enhancements to some of the existing algorithms in the literature in terms of the solution approach. This is followed by practical implementation to control two-wheeled mobile robots using model predictive control to track the Euclidean and the Dubins paths obtained for the patrolling operation.