Time-Distance Optimal Trajectory Planning For Mobile Robots On Straight And Circular Paths

Trajectories generally used to describe the space and time required to performa desired motion task for a mobile robot or manipulator system. In this paper, weconsidered a cubic polynomial trajectory for the problem of moving a mobile robotfrom its initial position to a goal position in over a continuous set of time. Along thepath, the robot requires to observe a certain acceleration profile. Then, weformulated an optimization approach to generate optimal trajectory profiles for themobile robot in the cases of maximum-distance and minimum-time problems. Theoptimization problem presented to find the trajectory strategy that would give therobot time-distance optimality to move from a start point to an end point where therobot should stay inside its acceleration limits all the time. The problem solvedanalytically because as it is well known, numerical solutions and iterative methodsare time-consuming, therefore, our closed-form solutions demand low computationtime. Finally, the results are verified by simulations.

Keywords:

Mobile Robots , Trajectory Planning , Constrained Optimization , Acceleration limits