This paper presents a novel approach, named the Group Marching Tree (GMT*) algorithm, to planning on GPUs at rates amenable to application within control loops, allowing planning in real-world settings via repeated computation of near-optimal plans. GMT*, like the Fast Marching Tree (FMT) algorithm, explores the state space with a "lazy" dynamic programming recursion on a set of samples to grow a tree of near-optimal paths. GMT*, however, alters the approach of FMT with approximate dynamic programming by expanding, in parallel, the group of all active samples with cost below an increasing threshold, rather than only the minimum cost sample. This group approximation enables low-level parallelism over the sample set and removes the need for sequential data structures, while the "lazy" collision checking limits thread divergence---all contributing to a very efficient GPU implementation. While this approach incurs some suboptimality, we prove that GMT* remains asymptotically optimal up to a constant multiplicative factor. We show solutions for complex planning problems under differential constraints can be found in ~10 ms on a desktop GPU and ~30 ms on an embedded GPU, representing a significant speed up over the state of the art, with only small losses in performance. Finally, we present a scenario demonstrating the efficacy of planning within the control loop (~100 Hz) towards operating in dynamic, uncertain settings.
Optimal Sampling-Based Motion Planning under Differential Constraints: the Driftless Case
Institute for Computational & Mathematical Engineering, Stanford University（斯坦福大学计算与数学工程研究所）；Department of Statistics, Stanford University（斯坦福大学统计系）；Department of Aeronautics and Astronautics, Stanford University（斯坦福大学航空航天系）
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA（电气与计算机工程学院，佐治亚理工学院，亚特兰大，GA）；School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA（航空航天工程学院，佐治亚理工学院，亚特兰大，GA）
Towards reliable real-time trajectory optimization
University of Tartu（塔尔图大学）；Institute of Technology（技术学院）；Institute of Robotics（机器人研究所）；Johannes Kepler University（约翰内斯·开普勒大学）；Institute of Computer Science（计算机科学研究所）
Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs
Carnegie Mellon University（卡内基梅隆大学）；Canadian Space Agency（加拿大航天局）；Defence Research and Development Canada（加拿大国防研究与发展部）；Massachusetts Institute of Technology（麻省理工学院）；National Aeronautics and Space Administration（美国国家航空航天局）；Northern Centre for Advanced Technology Inc.（北方先进技术中心公司）；Ontario Drive and Gear Ltd.（安大略传动与齿轮有限公司）；Office of Naval Research（美国海军研究办公室）；University of Toronto（多伦多大学）；University of Waterloo（滑铁卢大学）；University of Toronto Institute for Aerospace Studies（多伦多大学航空航天研究所）
