机器人运动规划

动态窗口方法 (Dynamic Window Approach)

在$(v,\omega )$空间下，确定

• 静态窗口（最大/最小速度&角速度）
• 动态窗口（由当前速度+最大加速度&角加速度所能达到的速度）
• 无碰撞范围

在此范围内确定最优方案，评价指标包括

• 当前朝向与目标方向的偏差
• 与目标点的距离
• 速度（在终点刹车范围外越快越好）

缺点

• 目标函数局部最优
• 假设障碍物静止

改进一：运动障碍物 Velocity Obstacles

改进二：协作避障Reciprocal Velocity Obstacles

• 坐标系为两个机器人之间的相对速度和角速度
• 如当前速度和角速度在障碍区域内，作当前点到障碍区域切线的垂线，两个机器人沿着垂线方向各走至少一半。

图搜索

Open Set: Unexpanded Nodes
Closed: 已访问的，不再更新

广度优先

• Complete (will find the solution if it exists)
• First solution found is the optimal path

深度优先

• Lower memory footprint than BFS with high-branching
• DFS not complete for infinite trees

Dijkstra’s Algorithm

• Open queue is ordered according to currently known best cost to arrive
  

A* Heuristic Search

The cost function is a sum of two functions:

• Past path-cost function, which is a known cost from the starting node to the current node
• Future path-cost function, which is a “heuristic estimate” of the distance from the current node to the goal

SAMPLING-BASED MOTION PLANNING

• Sampling algorithm
• distance function
• collision detection approach

Probabilistic Road Maps

• Step 1: Build a roadmap by connecting nearby (sampled, free-space) configurations using simple planners to construct a graph of valid path segments
• Step 2: Query: Search the graph using a graph search technique (A*)
• 适用于multiple-queries

Rapidly Exploring Dense Trees

• 适用于single-query
• 节点之间具有方向性
• 易于与机器人的运动限制相结合