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## List of results

**A Motion Planner for Nonholonomic Robots +***(This paper considers the problem of motion … This paper considers the problem of motion planning for a car-like robot (i.e., a</br>mobile robot with a nonholonomic constraint whose turning radius is lower-bounded). We</br>present a fast and exact planner for our mobile robot model, based upon recursive</br>subdivision of a collision-free path generated by a lower-level geometric planner that</br>ignores the motion constraints. The resultant trajectory is optimized to give a path that</br>is of near-minimal length in its homotopy class. Our claims of high speed are supported by</br>experimental results for implementations that assume a robot moving amid polygonal</br>obstacles. The completeness and the complexity of the algorithm are proven using an</br>appropriate metric in the configuration space R2 x S1 of the robot. This metric is defined</br>by using the length of the shortest paths in the absence of obstacles as the distance</br>between two configurations. We prove that the new induced topology and the classical one</br>are the same. Although we concentration upon the car-like robot, the generalization of</br>these techniques leads to new theoretical issues involving sub-Riemannian geometry and to</br>practical results for nonholonomic motion planning. results for nonholonomic motion planning.)*