Abstract
This paper describes a robust algorithm for mobile robot formations based on the Voronoi Fast Marching path planning method. This is based on the propagation of a wave throughout the model of the environment, the wave expanding faster as the wave's distance from obstacles increases. This method provides smooth and safe trajectories and its computational efficiency allows us to maintain a good response time. The proposed method is based on a local-minima-free planner; it is complete and has an O(n) complexity order where n is the number of cells of the map. Simulation results show that the proposed algorithm generates good trajectories.
Highlights
Formation control is currently a highly popular topic of research
Virtual structure, where the entire formation is treated as a single structure whose desired motion is translated into the desired motion of each vehicle [4]. Another possible criterion takes into account the rigidity of the formation geometry: some authors specify the full geometry, e.g., the distances and bearings between the vehicles of the formation and control each vehicle to ensure that these are accurately achieved [5], requiring a coordination architecture to switch between geometries when required by environment characteristics [6]; others see the formation as a dynamic geometry structure that naturally becomes distorted in the presence of obstacles and/or environment geometry changes [7]
The level set ሼ࢞Ȁܦሺ࢞ሻ ൌ ݐሽ of the solution represents the wave front advancing with a medium velocity ܲሺ࢞ሻ, which is the inverse of the medium refraction index ܴሺ࢞ሻ
Summary
Formation control is currently a highly popular topic of research. Different approaches can be classified according to different criteria. Virtual structure, where the entire formation is treated as a single structure whose desired motion is translated into the desired motion of each vehicle [4] Another possible criterion takes into account the rigidity of the formation geometry: some authors specify the full geometry, e.g., the distances and bearings between the vehicles of the formation and control each vehicle to ensure that these are accurately achieved [5], requiring a coordination architecture to switch between geometries when required by environment characteristics (e.g., narrow passages, open spaces) [6]; others see the formation as a dynamic geometry structure that naturally becomes distorted in the presence of obstacles and/or environment geometry changes [7]. If the medium is non‐homogeneous and the velocity ܲ is not constant, the function ܦrepresents the distance function measured with the metrics ܲሺ࢞ሻ or the arrival time of the wave front to point ࢞
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