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

Abstract

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.

Optimal trajectory planning for Omni-directional mobile robots using direct solution of optimal control problem

“…Also simulation results are compared with the result obtained in [15]. Table I shows the simulation data in SI units for scenarios 1 and 2.…”

“…Table II compares Also old J and new J present the optimal value of performance index in proposed method and the method in [15], respectively. Approximation polynomial trajectories for scenario 2 are obtained as follows: 2 3 4…”

“…A state parameterization is utilized to convert nonlinear optimal control problem to a NLP. In [15], we presented a solution method which solves the NLP in arbitrary points of time interval (0, ).…”

Trajectory planning for mechanical systems in the presence of dynamic obstacles

“…Motion planning problems are of high importance for various robotic systems and the last decades have witnessed a lot of attention paid to this area of research among control theorists and engineers. Meanwhile, typical approaches to reference trajectories construction are based on using time polynomials which proved to be an effective tool, e.g., for differentially flat dynamical systems (see [1,2,3,4,5,6,7,8,9]). Numerical optimization procedures to meet geometrical, velocity and acceleration constraints are discussed in [1,6,7].…”

Trajectory planning and optimisation method for intelligent vehicle lane changing emergently

“…In previous studies, automobile lane‐changing trajectory planning methods were based on search [12–14], optimisation [15–17] and function [18–21]. The first two methods are not suitable for real time because of their complexity, extended search and optimisation duration, which is not suitable for the planning of urgent lane‐changing trajectory.…”