Planning of mobile robots under limitted velocity and acceleration

Manipulator systems or mobile vehicles are designed to perform a desired motion task, where they need to provide the space and time required for the task in trajectory equation forms. The most common form of a trajectory is polynomial. In this paper, we considered a 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 certain acceleration limits. Then, we formulated an optimization approach to generate optimal trajectory profiles for the mobile robot in the cases of maximum distance problem. 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 had been solved analytically. Finally, the results are verified by simulations.