Fast Marching Tree: a Fast Marching Sampling-Based Method for Optimal Motion Planning in Many Dimensions
Lucas Janson, Edward Schmerling, Ashley Clark, Marco Pavone

TL;DR
The paper introduces FMT*, a novel probabilistic sampling-based motion planning algorithm that is asymptotically optimal, converges faster than existing methods, and provides convergence rate bounds in high-dimensional spaces.
Contribution
The paper presents FMT*, a new algorithm that improves convergence speed and provides the first convergence rate bounds for sampling-based motion planning.
Findings
FMT* converges faster than PRM* and RRT* in high-dimensional spaces.
The algorithm achieves a convergence rate of order O(n^{-1/d+ ho}).
Numerical experiments show FMT* yields better solutions within the same time frame.
Abstract
In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional configuration spaces. This algorithm is proven to be asymptotically optimal and is shown to converge to an optimal solution faster than its state-of-the-art counterparts, chiefly PRM* and RRT*. The FMT* algorithm performs a "lazy" dynamic programming recursion on a predetermined number of probabilistically-drawn samples to grow a tree of paths, which moves steadily outward in cost-to-arrive space. As a departure from previous analysis approaches that are based on the notion of almost sure convergence, the FMT* algorithm is analyzed under the notion of convergence in probability: the extra mathematical flexibility of this approach allows for convergence…
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Taxonomy
TopicsRobotic Path Planning Algorithms · Optimization and Search Problems · Robotics and Sensor-Based Localization
