Trajectory generation with curvature constraint based on energy minimization

The trajectory generation problem for mobile robots consists in providing a set of trajectories that are `smooth´ and meet certain boundary conditions. The authors present a method to generate curvature continuous trajectories for which the curvature profile is a polynomial function of arc length. An algorithm based on the deformation of a curve by energy minimization allows one to solve general geometric constraints which was not possible by previous methods. Furthermore, it is able to take into account the limitation of radius of curvature of the robot by controlling the extrema of curvature along the path