مسيرهاي كوتاه ترين زمان براي يك ربات ديفرانسيلي

Time Optimal Trajectories for a Differential Drive Robot

Robot control algorithms are divided into two stages, namely, trajectory planning and path tracking. In this paper, we study trajectory planning for a differential drive robot, moving on a plane without obstacle toward a fixed target. We consider the geometry of motion and find the compatible Lagrangian related to this problem. We prove that the mentioned geometry is a generalization of Finsler geometry, named Lagrange geometry. Hence, time optimal trajectories are the geodesies of this geometry. Finally, we give a real world example of a differential drive robot. The differential equations of optimal path are found, and the trajectory is plotted by the Maple program,.