Dubins Path with Terminal Range and Field-of-View Constraints

This paper addresses a path planning problem for a turn-constrained vehicle equipped with a sensor that has a limited range and field-of-view (FOV). The vehicle is models by Dubins kinematics, and the objective is to determine the shortest path that reaches the target within the sensor’s range and lies in its FOV. The limited range of the sensor manifests as a constraint to reach a circle centered at target’s position and radius equal to sensor range. The field of view constraints are expressed as coupled constraints on terminal position and heading. Using Pontryagin’s minimum principle, we show that optimal solution could have at most two segments, a turn or a straight line for each segment. Straight line segments occur exclusively when the final position is located on the boundary of the target circle. Furthermore, we provide an analytical approach for computing optimal paths in scenarios where the optimality conditions lead to complex geometric configurations.