Smooth and acceleration minimizing trajectories for mobile robots

An approach to generating smooth piecewise local trajectories for mobile robots is proposed. Given the configurations (position and direction) of two points, one searches for the trajectory that minimizes the integral of acceleration (tangential and normal). The resulting trajectory should not only be smooth but also safe in order to be applicable in real-life situations, so the authors investigate two different obstacle-avoidance constraints that satisfy the minimization problem. Unfortunately, in this case the problem becomes more complex and unsuitable for real-time implementations. Therefore, the authors introduce two simple solutions, based on the idea of polynomial fitting to generate safe trajectories, once a collision is detected with the original smooth trajectory. Simulation results for the different algorithms are presented