Algorithms for Path Planning in a Group of Mobile Robots in an Environment with Obstacles with a Given Template

Abstract

A method is proposed for solving the problem of planning the movement of a group of ground-based robotic platforms (UGR) with the requirement to maintain a given formation of the system in the presence of stationary obstacles and sources of disturbances. The task of calculating the trajectory of the leading UGR, coupled with the use of a displacement planner and subsequent smoothing of the resulting trajectory according to the method considered in the first part of this work, is highlighted. The trajectories of the slaved elements of the group are determined by constructing offset spatial curves along which these elements should move, taking into account a given configuration or the requirements of preserving some average kinematic parameters of the elements along their trajectory. To solve the problem of evading the group from the influence of sources of disturbances, the method considered in the previous works of the authors is proposed. It is based on the calculation of the probabilities of successful passage of the elements of the group of their trajectories. These probabilities can be found after evaluating the parameters of the characteristic probability functions of the sources describing the nature of their impact on moving objects over small time intervals. In this article, this method is modified by additional optimization of the resulting spatial trajectory along the length for each UGR, taking into account a given degree of permissible deviation from the original curve. A technique has been developed that allows to find the target trajectories of the leading and driven UGR of the group, the probability of successful passage of which exceeds the specified target value. The methodology is generalized to the case when the optimization criterion is the probability of successful completion of only part of the UGR group. Simulation results confirms the effectiveness of the proposed method of planning the trajectories of robots forming a group in the field of repeller sources.