Optimal trajectory planning for an omni-directional mobile robot with static obstacles: a polynomial based approach

This paper presents a polynomial based optimal trajectory planning for an omni-directional mobile robot in presence of static obstacles with considering a limitation on velocity and acceleration of the robot. First, optimal trajectory planning problem is formulated as an optimal control problem which minimize a cost function of states and control efforts respect to constraints of the problem. To solve this optimal control problem, a state parameterization method is used. In fact, state variables of system are approximated by polynomial functions of time with unknown coefficients. Thus optimal control problem converts to a constraint optimization problem which is too easier than original optimal control problem. Then the polynomials coefficients are computed such that satisfy all the problem requirements and constraints. Simulation results show effectiveness of the proposed method under different situations.