Navigation of car-like mobile robots in obstructed environments using convex polygonal cells

Abstract Due to their kinematics, car-like mobile robots cannot follow an arbitrary path. Besides obstacle avoidance, the path planning problem for such platforms has to satisfy two additional constraints: a lower bounded radius of turn and a non-holonomic constraint. When the robot is not circular, precise manuevering always implies working in the configuration space of the vehicle. Due to the complexity of representing this space, the planning of a path typically involves computer intensive methods, and rarely allows for real-time applications. In environments described with two-dimensional convex polygonal cells, we show that maneuvering can be completely handled with geometric reasoning. Within a convex cell, joining any two configurations of the vehicle only requires computation of maneuvers related to the beginning and the end of the trajectory. Just a few boundary configurations have to be checked to avoid collision. Because of the convexity of the cell, maneuvers related to the initial configuration and to the final configuration can be connected by a straight trajectory. This geometric reasoning approach allows not only precise calculation of the trajectories within the convex cells, but also extremely fast path-planning computation since it avoids representation of the whole configuration space. In generatl environments, a graph connecting adjacent convex cells is generated. To find a path between two distant configurations, the graph is searched to identify the cells that have to be traversed. Intermediate configurations are computed at the boundary of adjacent cells and the trajectory planning algorithm is applied to each set of consecutive configurations. Finally, the trajectories generated inside each cell are assembled to produce global collision-free paths in complex environments.