Optimal Spherical Geodesic Curvature Constrained Paths
Abstract
Path planning for vehicles is an essential study that must be undertaken to make good use
of resources such as fuel (which is always a limited resource) to ascertain that a vehicle/robot
completes its mission efficiently. The current study deals with the path planning of a Dubins’
vehicle on a sphere. A Dubins’ vehicle is one that moves only forwards, with a constant speed
and with a minimum turning radius constraint; and is named after L.E. Dubins due to his seminal
work [1] on the nature of optimal curves in the plane. The result being that optimal paths must be
of the following types only: CSC, CCC, SC, CS, CC, or C can be optimal. This study aims to
understand the nature of optimality of the Dubins’ type paths on a sphere.
The main tools employed are Pontryagin’s Minimum Principle and the Sabban frame (same
setup as in Monroy-Pérez’s work [2]). The final result obtained as a result of analytical study and
corroboration with numerical computation is that Dubins’ type paths are optimal on the sphere for r in the interval (0,(1/sqrt(2))] on account of the CCCC type path being non-optimal in the same interval.
Subject
Path planningDubins' vehicle
optimal spherical Dubins' paths
Pontryagin's Minimum Principle
Sabban frame
Citation
Pavan, Athindra (2021). Optimal Spherical Geodesic Curvature Constrained Paths. Master's thesis, Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /195065.