Planning robot formations with fast marching square including uncertainty conditions

Abstract

This paper presents a novel algorithm to solve the robot formation path planning problem working under uncertainty conditions such as errors the in robot's positions, errors when sensing obstacles or walls, etc. The proposed approach provides a solution based on a leaderfollowers architecture (real or virtual leaders) with a prescribed formation geometry that adapts dynamically to the environment. The algorithm described herein is able to provide safe, collision-free paths, avoiding obstacles and deforming the geometry of the formation when required by environmental conditions (e.g. narrow passages). To obtain a better approach to the problem of robot formation path planning the algorithm proposed includes uncertainties in obstacles' and robots' positions. The algorithm applies the Fast Marching Square (FM 2 ) method to the path planning of mobile robot formations, which has been proved to work quickly and efficiently. The FM 2 method is a path planning method with no local minima that provides smooth and safe trajectories to the robots creating a time function based on the properties of the propagation of the electromagnetic waves and depending on the environment conditions. This method allows to easily include the uncertainty reducing the computational cost significantly. The results presented here show that the proposed algorithm allows the formation to react to both static and dynamic obstacles with an easily changeable behavior.

An Automatic Navigation System for Unmanned Surface Vehicles in Realistic Sea Environments

“…Hence, USVs should be as far away from obstacles as possible for safety. The literature [33] has proposed a new algorithm named the fast marching square (FMS) method to tackle this problem, which adds one step to the conventional FMM algorithm. First, the FMS method generates a security potential map (V) with the FMM executing from all the points in obstacle area (see Figure 6a) by using the previous planning space.…”

Path planning algorithm for unmanned surface vehicle formations in a practical maritime environment

“…Besides, the gradient of such a potential field is smoother than conventional one, which is more suitable for a vehicle to track. Gomez et al (2013) further improved the FM method to the fast marching square (FMS) method and increased the safety of planned trajectories.…”

“…In this paper, the authors improve upon the work of Gomez et al (2013) and developing its application specifically for USV formation with emphasis on path planning in a dynamic environment. A new constrained FM method is proposed to model the dynamic behaviour of moving ships for collision avoidance.…”

“…To tackle this problem, the FMS method proposed by Gomez et al (2013) for indoor mobile robots is used in this paper. The basic concept behind the FMS is to apply the conventional FM algorithm twice but with different purposes:…”

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“…Zhang et al [11] utilized artificial potential field algorithm to avoid obstacles for leader-follower formation in unknown environments. Gomez et al [12] used the Fast Marching Square method with no local minima problem for leader-follower formation with obstacle avoidance. Liu et al [13] developed an improved rapidly exploring random tree to plan the path for each robot and developed a dynamic priority strategy to solve the conflicts caused by orders of robots in forming the formation.…”