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 modeled using Dubins kinematics, and the objective is to determine the shortest path to point where that the target is detectable, i.e., within the sensor’s range and FOV. The limited sensor range imposes a constraint requiring the vehicle to reach a circle centered at the target’s position, with a radius equal to the sensor range. The field-of-view constraints are expressed as coupled conditions on the terminal position and heading. Pontryagin’s minimum principle restricts the optimal path to straight lines and arcs of minimum turn radius. Further analysis shows that the paths are limited to at most two segments. Straight-line segments occur exclusively when the final position lies on the boundary of the target circle. Furthermore, we present an analytical approach for computing optimal paths in scenarios where the optimality conditions result in complex geometric configurations.