Relaxed Dubins Problems through Three Points
Zheng Chen, Tal Y. Shima · 2019
In this paper, we study the Relaxed 3-Point Dubins Problem (R3PDP), which consists of steering a Dubins vehicle through three consecutive waypoints with prescribed heading orientation angle at the initial waypoint. From a geometric point of view, we show that the shortest path must lie in a sufficient family of 12 candidates, and a formula in terms of the parameters of the R3PDP is established for all the 12 candidates. Analyzing the formula indicates that the shortest path of the R3PDP is determined by the zeros of some nonlinear equations. We propose some efficient algorithms to find the zeros of those nonlinear equations so that any R3PDP can be efficiently solved. Finally, some numerical examples are simulated, illustrating the developments of the paper.