Autonomous vehicles, which include Unmanned Aerial Vehicles (UAVs), have increasing civilian and military applications. Hence, motion planning for such vehicles to tackle various scenarios they might encounter is increasingly important. Among various advantages that such vehicles have, such as the ability to reach dangerous and hard-to-reach terrains, they have limitations, such as an inability to rotate about its own axis and a constraint on the rate of change of the heading angle. Motion planning for such a vehicle, denoted as a curvature-constrained vehicle, involves identifying the candidate paths to travel from one configuration (location and orientation) to another such that an objective functional (for example, time taken or fuel consumed) is minimized. Addressing such problems typically involves formulating the path planning problem as an optimal control problem, followed by employing Pontryagin's Minimum Principle (PMP) to obtain optimal control actions. A systematic analysis is then performed to identify the candidate optimal paths for the considered problem.

In this talk, the “Weighted Markov-Dubins Problem”, which is a planar problem applicable for modeling and obtaining optimal paths for a UAV with hardware failure, will first be presented. Following this, two path planning problems on a sphere will be presented: one wherein a vehicle needs to attain a desired final configuration on the sphere, and another wherein the vehicle needs to attain a desired final location on the sphere. Such problems are applicable to plan paths for curvature-constrained vehicles moving over the surface of the earth (which is approximated to be a sphere).