An Exact Geometry–Based Algorithm for Path Planning

A novel, exact algorithm is presented to solve the path planning problem that involves finding the shortest collision-free path from a start to a goal point in a two-dimensional environment containing convex and non-convex obstacles. The proposed algorithm, which is called the shortest possible path (SPP) algorithm, constructs a network of lines connecting the vertices of the obstacles and the locations of the start and goal points which is smaller than the network generated by the visibility graph. Then it finds the shortest path from start to goal point within this network. The SPP algorithm generates a safe, smooth and obstacle-free path that has a desired distance from each obstacle. This algorithm is designed for environments that are populated sparsely with convex and nonconvex polygonal obstacles. It has the capability of eliminating some of the polygons that do not play any role in constructing the optimal path. It is proven that the SPP algorithm can find the optimal path in O(nn ) time, where n is the number of vertices of all polygons and n ̓ is the number of vertices that are considered in constructing the path network (n ̓ ≤ n). The performance of the algorithm is evaluated relative to three major classes of algorithms: heuristic, probabilistic, and classic. Different benchmark scenarios are used to evaluate the performance of the algorithm relative to the first two classes of algorithms: GAMOPP (genetic algorithm for multi-objective path planning), a representative heuristic algorithm, as well as RRT (rapidly-exploring random tree) and PRM (probabilistic road map), two well-known probabilistic algorithms. Time complexity is known for classic algorithms, so the presented algorithm is compared analytically.