Mobile robots trajectories with continuously differentiable curvature: an optimal control approach

We consider the problem of generating smooth trajectories for a fast moving mobile robot in a cluttered environment, when online path updating is performed. The well-known smoothing methods using clothoids, cubic spirals or polynominal curves are extended by taking into account the conditions for a continuously differentiable path update. We use the Hamilton-Jacobi framework to create a continuously differentiable interpolation of an existing path of straight lines and arcs of circles. The smoothing approach is combined with the generation of an appropriate velocity profile along the path. The results are compared to those obtained by more classical smoothing methods and to the polynominal approach implemented on the car-like robot MoViLaR of our institute. Finally an embedding of this method into the robot's hierarchical control structure is presented.