【MR】现代机器人学-第十章-运动规划（附官方视频）

首先附上官方视频英文字幕自动转中文字幕的录屏。

10.1 Overview of Motion Planning 运动规划概述

10.2 C-Space Obstacles 配置空间障碍 C-障碍物

10.2.3 Graphs and Trees 图和树

10.2.4  Graph Search 图搜索

10.3 Complete Path Planners 完整路径规划器

10.4 Grid Methods for Motion Planning 运动规划的网格方法

10.5.1 Sampling Methods for Motion Planning 1  RRT算法

10.5.2 Sampling Methods for Motion Planning2 概率路线图PRM算法

10.6  Virtual Potential Fields 虚拟势场

10.7 Nonlinear Optimization 非线性优化

本章小结：

1. A fairly general statement of the motion planning problem is as follows. Given an initial state x(0) = xstart and a desired final state xgoal, find a time T and a set of controls u : [0, T] → U such that the motion satisfies x(T) ∈ Xgoal and q(x(t)) ∈ Cfree for all t ∈ [0, T].

2. Motion planning problems can be classified in the following categories: path planning versus motion planning; fully actuated versus constrained or underactuated; online versus offline; optimal versus satisficing; exact versus approximate; with or without obstacles。

3. Motion planners can be characterized by the following properties: multiplequery versus single-query; anytime planning or not; complete, resolution complete, probabilistically complete, or none of the above; and their degree of computational complexity.

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5. A conservative check of whether a configuration q is in collision uses a simplified “grown” representation of the robot and obstacles. If there is no collision between the grown bodies, then the configuration is guaranteed collision-free. Checking whether a path is collision-free usually involves sampling the path at finely spaced points and ensuring that if the individual configurations are collision-free then the swept volume of the robot path is collision-free.

6. The C-space geometry is often represented by a graph consisting of nodes and edges between the nodes, where edges represent feasible paths. The graph can be undirected (edges flow in both directions) or directed (edges flow in only one direction). Edges can be unweighted or weighted according to their cost of traversal. A tree is a directed graph with no cycles in which each node has at most one parent.

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9. A grid-based path planner discretizes the C-space into a graph consisting of neighboring points on a regular grid. A multi-resolution grid can be used to allow large steps in wide open spaces and smaller steps near obstacle boundaries.

10. Discretizing the control set allows robots with motion constraints to take advantage of grid-based methods. If integrating a control does not land the robot exactly on a grid point, the new state may still be pruned if a state in the same grid cell has already been achieved with a lower cost.

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The End