DubinsSpanier

DubinsSpanier is a computational geometry algorithm used to compute the shortest path between two points in a planar environment with polygonal obstacles. It is named after the mathematicians who developed it, Daniel Dubins and John Spanier. The algorithm finds a path that consists of straight line segments and circular arcs, where the arcs are tangent to the obstacles.

The core idea behind DubinsSpanier is to break down the problem into smaller, manageable parts. First, it identifies all possible "tangent lines" between the start and end points and the obstacles. These tangent lines represent potential straight-line segments in the shortest path. Next, it considers circular arcs that can be traced by a vehicle with a minimum turning radius as it moves along the boundary of an obstacle.

The algorithm then explores combinations of these straight line segments and circular arcs to find the shortest overall path. This exploration often involves constructing a graph where nodes represent points of tangency and edges represent the feasible segments and arcs. A shortest path search algorithm, such as Dijkstra's algorithm, is then applied to this graph to find the optimal path.

DubinsSpanier has applications in robotics, autonomous navigation, and motion planning. It is particularly useful in scenarios where a vehicle has constraints on its turning radius, such as cars or drones. The algorithm's ability to find provably shortest paths under these constraints makes it a valuable tool in various engineering and research fields. Its complexity arises from the number of possible tangent connections and the need to efficiently search through the resulting state space.