time-distance optimal trajectory planning for mobile robots on straight and circular paths

trajectories generally used to describe the space and time required to perform a desired motion task for a mobile robot or manipulator system. in this paper, we considered a cubic polynomial trajectory for the problem of moving a mobile robot from its initial position to a goal position in over a continuous set of time. along the path, the robot requires to observe a certain acceleration profile. then, we formulated an optimization approach to generate optimal trajectory profiles for the mobile robot in the cases of maximum-distance and minimum-time problems. the optimization problem presented to find the trajectory strategy that would give the robot time-distance optimality to move from a start point to an end point where the robot should stay inside its acceleration limits all the time. the problem solved analytically because as it is well known, numerical solutions and iterative methods are time-consuming, therefore, our closed-form solutions demand low computation time. finally, the results are verified by simulations.