This article deals with trajectory planning for non-holonomic mobile robots. We call trajectory the association of a path, which is the geometrical restriction of the motion, and of a time schedule given by a time table, a velocity or an acceleration profile. The robots considered are non-holonomic, as their motion's direction is limited by the robot's position. However, two types of robot are considered: car-like vehicles have a lower bounded turning radius, while manoeuvrable robots do not. This article shows that optimal paths for car-like vehicles correspond to optimal trajectories for manoeuvrable robots, and presents how these paths can thus be followed faster by manoeuvrable robots than paths made of line segments, along which these robots have to stop at each direction's discontinuity.