An Optimal and Real-Time Solution to Parameterized Mobile Robot Trajectories in the Presence of Moving Obstacles

In this paper, the problem of determining an optimal collision-free path is studied for a mobile robot moving in a dynamically changing environment. A polynomial parametrization is used to represent the family of mobile robot’s paths and to solve for feasible trajectories. Then a suitable performance index is set up and the trajectory generation problem is formulated as a constrained optimization problem subject to motion constraints and the collision avoidance criterion. The optimal solution is analytical and simple. It is good for realtime trajectory planning. Finally, the framework is applied to a car-like mobile robot. The validity of our approach is supported by computer simulations.