解算器
运动规划
渐近最优算法
数学优化
动力系统理论
状态空间
采样(信号处理)
计算机科学
动力系统(定义)
数学
图形
边界(拓扑)
多样性(控制论)
机器人
理论计算机科学
人工智能
数学分析
统计
物理
滤波器(信号处理)
量子力学
计算机视觉
作者
Yanbo Li,Zakary Littlefield,Kostas E. Bekris
标识
DOI:10.1177/0278364915614386
摘要
Sampling-based algorithms are viewed as practical solutions for high-dimensional motion planning. Recent progress has taken advantage of random geometric graph theory to show how asymptotic optimality can also be achieved with these methods. Achieving this desirable property for systems with dynamics requires solving a two-point boundary value problem (BVP) in the state space of the underlying dynamical system. It is difficult, however, if not impractical, to generate a BVP solver for a variety of important dynamical models of robots or physically simulated ones. Thus, an open challenge was whether it was even possible to achieve optimality guarantees when planning for systems without access to a BVP solver. This work resolves the above question and describes how to achieve asymptotic optimality for kinodynamic planning using incremental sampling-based planners by introducing a new rigorous framework. Two new methods, STABLE_SPARSE_RRT (SST) and SST*, result from this analysis, which are asymptotically near-optimal and optimal, respectively. The techniques are shown to converge fast to high-quality paths, while they maintain only a sparse set of samples, which makes them computationally efficient. The good performance of the planners is confirmed by experimental results using dynamical systems benchmarks, as well as physically simulated robots.
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