Path Planning for Formations using Global Optimization with Sparse Grids

M. Saska, I. Ferenczi, M. Hess, and K. Schilling (Germany)


mobile robot, formations, splines, global optimization, sparse grids


This paper proposes an original path planning method developed for leader following formations of car-like robots. In this approach a reference path calculated by the leader should be feasible for all following robots without changing a relative distance in the formation. This require ment can be satisfied using a solution which is composed of smoothly connected cubic splines and can be calculated in real time. Qualities of the result like the length and minimal radius of the resulting path as well as the distance to obsta cles are merged into a discontinuous penalty function. The resulting global minimization problem is solved with a de terministic approach based on sparse grids. This algorithm has been tested for several applications in real robotics en vironments and compared with the results from a stochastic Particle Swarm Optimization method. Some of the deter mined solutions were then verified by simulations of for mation movements.

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