This research presents two novel approaches for nonholonomic motion
planning. The methodologies presented are based on the standard Fast
Marching Square path planning method and its application to car-like
robots. In the first method, the environment is considered as a 3D
C-Space, with the first two dimensions given by the position of the
robot, and the third dimension by its orientation. This means we operate
over the configuration space instead of the bi-dimensional environment
map. Besides, 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 velocities computed
in 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
assure smoothness and safety of the calculated paths and, besides, they
provide the control plan to perform the trajectory.