Effective metrics for multi-robot motion-planning

Abstract

We study the effectiveness of metrics for Multi-Robot Motion-Planning (MRMP) when using RRT-style sampling-based planners. These metrics play the crucial role of determining the nearest neighbors of configurations and in that they regulate the connectivity of the underlying roadmaps produced by the planners and other properties like the quality of solution paths. After screening over a dozen different metrics we focus on the five most promising ones-two more traditional metrics, and three novel ones which we propose here, adapted from the domain of shape-matching. In addition to the novel multi-robot metrics, a central contribution of this work are tools to analyze and predict the effectiveness of metrics in the MRMP context. We identify a suite of possible substructures in the configuration space, for which it is fairly easy (i) to define a so-called natural distance, which allows us to predict the performance of a metric. This is done by comparing the distribution of its values for sampled pairs of configurations to the distribution induced by the natural distance; (ii) to define equivalence classes of configurations and test how well a metric covers the different classes. We provide experiments that attest to the ability of our tools to predict the effectiveness of metrics: those metrics that qualify in the analysis yield higher success rate of the planner with fewer vertices in the roadmap. We also show how combining several metrics together leads to better results (success rate and size of roadmap) than using a single metric.

Machine Learning Based Relative Orbit Transfer for Swarm Spacecraft Motion Planning

“…Neural network training aims to minimize the error function E, which is the mean squared error (MSE) that quantifies the difference between the computed output trajectory (feedforward neural network) and the actual trajectory (mathematical model). The number of layers and parameters were determined empirically by examining the performance of several different layers (3)(4)(5)(6)(7)(8)(9)(10)(11)(12) and parameters . We found that 100 parameters per layer and 4 total layers gave the least mean squared error (M SE < 0.001).…”

“…As with swarm trajectory planning, collision-free paths must be generated, which is well-known to be NP-hard [11]. Many works such as [12], [13], [14], [15] have explored multi-robot path planning in more general contexts.…”

dRRT*: Scalable and informed asymptotically-optimal multi-robot motion planning

“…Later, dRRT was applied to motion planning of a free-flying multi-link robot (Salzman et al, 2016). In that case, dRRT allowed to efficiently decouple between costly self-collision checks, which were done offline, and robot-obstacle collision checks, by traversing an implicitly-defined roadmap, whose structure resembles to that of Ĝ. dRRT has also been used in the study of the effectiveness of metrics for MMP, which are an essential ingredient in sampling-based planners (Atias et al, 2017).…”

Review of Multi-Agent Algorithms for Collective Behavior: a Structural Taxonomy

“…Several sampling-based motion planning algorithms have been proposed for multi-agent systems [348]- [351]; in particular, [349], [351] offer optimality guarantees. A key problem in sampling-based motion planning is to efficiently assess the "distance" between sampled points -the work in [352] proposes and assesses the performance of different metrics to efficiently estimate the "distance" between samples in the multi-agent setting.…”