Probabilistic Feasibility for Nonlinear Systems with Non-Gaussian Uncertainty using RRT
Probabilistic Feasibility for Nonlinear Systems with Non-Gaussian Uncertainty using RRT
复制标题
使用 RRT 计算具有非高斯不确定性的非线性系统的概率可行性
DOI：
10.2514/6.2011-1589
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
J. How
中科院分区：
文献类型：
--
作者：
Brandon Luders;J. How
对于涉及许多或无界形式的不确定性的运动规划问题，它可能无法确定一条路径保证是可行的，需要考虑规划者的保守性和不可行的风险之间的权衡。最近的工作开发了机会约束快速探索随机树（CC-RRT）算法，一个实时规划算法，可以eciently计算在每个时间步的风险，以保证概率的可行性。然而，在该文件中的结果需要一个线性系统和高斯不确定性的双重假设，这两个假设往往不适用于许多现实生活中的路径规划方案。本文提出了几个扩展CC-RRT框架，允许这些假设放宽。对于受高斯过程噪声影响的非线性系统，通过在每个时间步对动态进行线性化，可以将状态分布近似为高斯分布;仿真结果表明了这种方法对开环和闭环动态的有效性。对于具有非高斯不确定性的系统，我们提出了不确定性的基于粒子的表示，从而得到状态分布;随着粒子数量的增加，粒子接近真正的不确定性。相对于以前的工作，这种方法的一个关键方面是考虑约束满足的概率界限，无论是在每一个时间步和整个路径的持续时间。
For motion planning problems involving many or unbounded forms of uncertainty, it may not be possible to identify a path guaranteed to be feasible, requiring consideration of the trade-o between planner conservatism and the risk of infeasibility. Recent work developed the chance constrained rapidly-exploring random tree (CC-RRT) algorithm, a real-time planning algorithm which can eciently compute risk at each timestep in order to guarantee probabilistic feasibility. However, the results in that paper require the dual assumptions of a linear system and Gaussian uncertainty, two assumptions which are often not applicable to many real-life path planning scenarios. This paper presents several extensions to the CC-RRT framework which allow these assumptions to be relaxed. For nonlinear systems subject to Gaussian process noise, state distributions can be approximated as Gaussian by considering a linearization of the dynamics at each timestep; simulation results demonstrate the eective of this approach for both open-loop and closed-loop dynamics. For systems subject to non-Gaussian uncertainty, we propose a particle-based representation of the uncertainty, and thus the state distributions; as the number of particles increases, the particles approach the true uncertainty. A key aspect of this approach relative to previous work is the consideration of probabilistic bounds on constraint satisfaction, both at every timestep and over the duration of entire paths.