Controlling independently the heading and the position of a Dubins car using Lie brackets

In this paper, we give a control approach to follow a trajectory for a Dubins car controlling the heading independently. The difficulty is that the Dubins car should have a heading corresponding to the argument of the vector speed of the vehicle. This non holonomic constraint can be relaxed thanks to a specific control which uses Lie brackets. We will show such a control will allow us, at least from a theoretical point of view, to control independently the moving position of the car and the heading.