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This article considers two variants of a shortest path problem for a car-likerobot visiting a set of waypoints. The sequence of waypoints to be visited isspecified in the first variant while the robot is allowed to visit thewaypoints in any sequence in the second variant. Field of view constraints arealso placed when the robot arrives at a waypoint, i.e., the orientation of therobot at any waypoint is restricted to belong to a given interval of angles atthe waypoint. The shortest path problem is first solved for two waypoints withthe field of view constraints using Pontryagin's minimum principle. Using theresults for the two point problem, tight lower and upper bounds on the lengthof the shortest path are developed for visiting n points by relaxing therequirement that the arrival angle must be equal to the departure angle of therobot at each waypoint. Theoretical bounds are also provided on the length ofthe feasible solutions obtained by the proposed algorithm. Simulation resultsverify the performance of the bounds for instances with 20 waypoints.

Path Planning Algorithms for a Car-Like Robot visiting a set of Waypoints with Field of View Constraints