Path planning for a group of vehicles in 2D obstructed environment

摘要

Path planning problem for a vehicle group in a two-dimensional obstructed environment is addressed. The kinematics equations of the vehicles on a plane with ideal connections are considered. Then a method is proposed for planning motion paths based on the interpretation of all the neighboring objects as repellers. The method on the basis of simple algorithms implemented in design of vehicles enables organization of the group motion without using a centralized algorithm. A new method for introduction of repellers which is based on formation of an unstable position in the vehicles phase space is proposed. Repulsive forces are generated as outputs of dynamic elements that integrate non-linear functions of the distance to the obstacles. As a result, we obtained the principles of changing speed and direction of the vehicles' motion. The stability analysis of the obtained paths was made using the method of Lyapunov functions. We showed steady state regime of a group of vehicles and its asymptotic stability. Modification of the planning algorithm with no setting of the trajectory is being proposed. The developed algorithms are implemented within a decentralized structure of the control system. Numerical modeling of a goup of five robots in an environment with stationary obstacles was carried out. Conclusions were made about using the proposed method in practice based on this analysis and the modeling results. A modification of this path planning method is being discussed - the one that uses kinematics equations and dynamics equations; this allows to take into consideration the speed of approaching to the obstacles. Also using this method in three-dimensional environment and in an environment with nonstationary obstacles is being discussed.