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This research presents two novel approaches to nonholonomic motion planning. The methodologies presented are based on the standard fast marching square path planning method and its application to car-like robots. Under the first method, the environment is considered as a three-dimensional C-space, with the first two dimensions given by the position of the robot and the third dimension by its orientation. This means that we operate over the configuration space instead of the bi-dimensional environment map. Moreover, the trajectory is computed along the C-space taking into account the dimensions of the vehicle, and thus guaranteeing the absence of collisions. The second method uses the standard fast marching square, and takes advantage of the vector field of the velocities computed during the first step of the method in order to adapt the motion plan to the control inputs that a car-like robot is able to execute. Both methods ensure the smoothness and safety of the calculated paths in addition to providing the control actions to perform the trajectory

Nonholonomic Motion Planning Using the Fast Marching Square Method