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.
Bi-directional search is a widely used strategy to increase the success and convergence rates of sampling-based motion planning algorithms. Yet, few results are available that merge both bi-directional search and asymptotic optimality into existing optimal planners, such as PRM*, RRT*, and FMT*. The objective of this paper is to fill this gap. Specifically, this paper presents a bi-directional, sampling-based, asymptotically-optimal algorithm named Bi-directional FMT* (BFMT*) that extends the Fast Marching Tree (FMT*) algorithm to bidirectional search while preserving its key properties, chiefly lazy search and asymptotic optimality through convergence in probability. BFMT* performs a two-source, lazy dynamic programming recursion over a set of randomly-drawn samples, correspondingly generating two search trees: one in cost-to-come space from the initial configuration and another in cost-to-go space from the goal configuration. Numerical experiments illustrate the advantages of BFMT* over its unidirectional counterpart, as well as a number of other state-of-the-art planners.
The Fast Marching Method is a very popular algorithm to compute times-of-arrival maps (distances map measured in time units). Since their proposal in 1995, it has been applied to many different applications such as robotics, medical computer vision, fluid simulation, etc. Many alternatives have been proposed with two main objectives: to reduce its computational time and to improve its accuracy. In this paper, we collect the main approaches which improve the computational time of the standard Fast
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