RRT基本概念

  原文地址

快速探索随机树(RRT)是一种通过随机构建空间填充树来有效搜索非凸,高维空间的算法。树是从搜索

空间中随机抽取的样本逐步构建的,并且本质上倾向于朝向大部分未探测区域生长。 RRTSteven M. LaValle

James J. Kuffner Jr. [1].[2]开发,它们可以轻松处理障碍物和差分约束(非完整和动力学)的问题,

并被广泛应用于自主机器人运动规划

RRT可以被看作是一种为具有状态约束的非线性系统生成开环轨迹的技术。一个RRT也可以被认为是

一个蒙特卡罗方法。用来将搜索偏向一个配置空间中图形的最大Voronoi区域一些变化甚至可以被认

为是随机分形[3]

   目录 
1描述
2算法
3运动规划的变体和改进
4另见
5参考
6外部链接    
1.描述

RRT通过使用来自搜索空间的随机样本来生长以起始配置为根的树。 随着每个样本的绘制,都会

尝试与树中最近的状态进行连接。 如果连接可行(完全通过空闲空间并服从任何约束),则会导致

新状态添加到树中。通对搜索空间进行均匀采样,扩展现有状态的概率与其Voronoi区域的大小成

正比。 由于最大的Voronoi地区属于搜索前沿的state,这意味着该树优先向大型未探测地区扩展。

树与新状态之间的连接长度经常受到增长因素的限制。 如果随机样本与树中最近状态的距离超

过此限制允许的范围,则使用随机样本沿树的最大距离处的新状态,而不是随机样本本身。 随机样本

可以被视为控制树木生长的方向,而生长因子决定其速率。 This maintains the space-filling bias of

the RRT while limiting the size of the incremental growth.

RRT增长可以通过增加特定区域采样状态的可能性而产生偏差。 RRT的大多数实际应用都利用这一

点来指导对规划问题目标的搜索。这是通过在状态抽样过程中引入一个向目标采样的小的概率来实现

的。这个概率越高,树越向着目标生长。

2.算法

For a general configuration space C, the algorithm in pseudocode is as follows:
Algorithm BuildRRT
  Input: Initial configuration qinit, number of vertices in RRT K, incremental distance Δq)
  Output: RRT graph G

  G.init(qinit)
  for k = 1 to K
    qrand ← RAND_CONF()
    qnear ← NEAREST_VERTEX(qrand, G)
    qnew ← NEW_CONF(qnear, qrand, Δq)
    G.add_vertex(qnew)
    G.add_edge(qnear, qnew)
  return G
"←" is a shorthand for "changes to". For instance, "largest ← item" means that the value of largest changes to the value of item.
"return" terminates the algorithm and outputs the value that follows.
   在上面算法中," RAND_CONF "在C中抓取一个随机配置qrand,这可以用一个函数“RAND_FREE_CONF”来代替,该函数使用Cfree中的样本,而使用某种碰撞检测算法拒绝Cobs中的那些函数。

   “NEAREST_VERTEX”是贯穿图G中的所有顶点v的函数,使用某个测量函数计算qrand和v之间的距离,从而返回最近的顶点。
“NEW_CONF”通过在qrand的方向上从qnear移动增量距离Δq来选择新的配置qnew。(根据[4]中

的完整问题,这应该被省略,qrand被用来代替qnew。)

3.运动规划的变体和改进

Parti-game directed RRTs (PDRRTs),[5] a method that combines RRTs with the parti-game method[6] to refine the search

where it is needed (for example around obstacles) to be able to plan faster and solve more motion planning problems

than RRT

Parti-game directed RRTs (PDRRTs),[5]一种将RRT和parti-game方法[6]结合在一起的方法,在需要的地方(例如围绕障碍物)

细化搜索,以便能够比RRT更快地计划和解决更多的运动规划问题


Closed-loop rapidly-exploring random (CL-RRT),[7] an extension of RRT that samples an input to a stable closed-loop

system consisting of the vehicle and a controller

Closed-loop rapidly-exploring random (CL-RRT),[7]RRT的一个扩展,将采样输入到一个由车辆和控制器组成稳定的闭环系

It has been shown that, under 'mild technical conditions', the cost of the best path in the RRT converges almost surely to

a non-optimal value.[8] For that reason, it is desirable to find variants of the RRT that converges to the optimum:

已经表明,在“温和的技术条件下”,RRT中的最佳路径的成本几乎肯定会收敛到非最优值。 出于这个原因,最好找到收敛到最优

的RRT变体:

  • Rapidly-exploring random graph (RRG) and RRT*,[8][9][10] a variant of RRT that converges towards an optimal
  • solution
  • Rapidly-exploring random graph (RRG) and RRT*,[8][9][10] RRT的一个变体,趋于最佳的解决方案

  • RRT*-Smart,[11] a method for accelerating the convergence rate of RRT* by using path optimization (in a similar
  • fashion to Theta*) and intelligent sampling (by biasing sampling towards path vertices, which – after path
  • optimization– are likely to be close to obstacles)
  • RRT*-Smart,[11] 通过使用路径优化(以类似于Theta *的方式)和智能采样(通过对路径顶点进行偏置采样(其在路径优化之后可能接近障碍))
  • 来加速RRT *的收敛速率的方法,

  • A*-RRT and A*-RRT*,[12] a two-phase motion planning method that uses a graph search algorithm to search for
  • an initial feasible path in a low-dimensional space (not considering the complete state space) in a first phase,
  • avoiding hazardous areas and preferring low-risk routes, which is then used to focus the RRT* search in the
  • continuous high-dimensional space in a second phase
  • A*-RRT and A*-RRT*,[12]  一种两阶段运动规划方法,采用图搜索算法在第一阶段在低维空间(不考虑完整状态空间)搜索初始可行路径,
  • 避开危险区域,偏好低风险路线, 然后用于在第二阶段将RRT *搜索集中在连续的高维空间中

  • RRT*FN,[13][14][15] RRT* with a fixed number of nodes, which randomly removes a leaf node in the tree in every
  • iteration
  • RRT*FN,[13][14][15] RRT *具有固定数量的节点,在每次迭代中随机地移除树中的叶节点

  • RRT*-AR,[16] sampling-based alternate routes planning
  • RRT*-AR,[16]基于采样的替代路径规划

  • Informed RRT*,[17][18] improves the convergence speed of RRT* by introducing a heuristic, similar to the way in
  • which A* improves upon Dijkstra's algorithm
  • 通过引入启发式来提高RRT *的收敛速度,类似于A *改进Dijkstra算法的方式

  • Real-Time RRT* (RT-RRT*),[19] a variant of RRT* and informed RRT* that uses an online tree rewiring strategy
  • that allows the tree root to move with the agent without discarding previously sampled paths, in order to
  • obtain real-time path-planning in a dynamic environment such as a computer game
  • Real-Time RRT* (RT-RRT*),[19]RRT *和RRT *的变体,它使用在线树重新布线策略,允许树根与代理一起移动,而不必丢弃先前采样的路径,
  • 以便在动态环境中获得实时路径规划,例如计算机 游戏

  • Theta*-RRT,[20] a two-phase motion planning method similar to A*-RRT* that uses a hierarchical combination
  • of any-angle search with RRT motion planning for fast trajectory generation in environments with complex
  •  nonholonomic constraints
  • 一种类似于A * -RRT *的两阶段运动计划方法,其使用任意角度搜索与RRT运动规划的分层组合,用于具有复杂非完整约束的环境中的快速轨迹
  • 生成

4.另见

  • Any-angle path planning
  • Probabilistic roadmap
  • Space-filling tree
  • Motion planning
  • Randomized algorithm

5.参考

1.  LaValle, Steven M. (October 1998). "Rapidly-exploring random trees: A new tool for path planning" (PDF)
Technical Report. Computer Science Department, Iowa State University (TR 98-11).
2.LaValle, Steven M.; Kuffner Jr., James J. (2001). "Randomized Kinodynamic Planning" (PDF)The International Journal of Robotics Research
(IJRR)20 (5): 378–400. doi:10.1177/02783640122067453.
3. http://msl.cs.uiuc.edu/rrt/about.html About RRTs, by Steve LaValle

4.Rapidly-Exploring Random Trees: Progress and Prospects (2000), by Steven M. Lavalle , James J. Kuffner , Jr. Algorithmic and Computational
Robotics: New Directions, http://eprints.kfupm.edu.sa/60786/1/60786.pdf
5. Ranganathan, Ananth; Koenig, Sven. PDRRTs: "Integrating Graph-Based and Cell-Based Planning". In Proceedings of the IEEE International
Conference on Intelligent Robots and Systems (IROS), pages 2799–2808, 2004.
6. Moore, A. W.; Atkeson, C. G., "The parti-game algorithm for variable resolution reinforcement learning in multidimensional state-spaces,"
 Machine Learning, vol. 21, no. 3, pages 199–233, 1995.
7.Kuwata, Yoshiaki; Teo, Justin; Fiore, Gaston; Karaman, Sertac; Frazzoli, Emilio; How, Jonathan P. (September 2009).
 "Real-time Motion Planning with Applications to Autonomous Urban Driving" (PDF).
 IEEE Transactions on Control Systems and TechnologyIEEE Control Systems Society17 (5): 1105–1118. doi:10.1109/tcst.2008.2012116.
Retrieved 10 April 2017. 
8.  Karaman, Sertac; Frazzoli, Emilio (3 May 2010). "Incremental Sampling-based Algorithms for Optimal Motion Planning". arXiv:1005.0416 Freely accessible [cs.RO].
Jump up to:
9. Karaman, Sertac; Frazzoli, Emilio (5 May 2011). "Sampling-based Algorithms for Optimal Motion Planning".  arXiv : 1105.1186 
10.OlzhasAdi (Jan 26, 2015). "RRT* Brief Explanation" (video)YouTube. Retrieved 3 August 2016.
11. Islam, Fahad; Nasir, Jauwairia; Malik, Usman; Ayaz, Yasar; Hasan, Osman; "RRT*-Smart: Rapid convergence implementation of RRT* towards optimal solution",
in Proceedings of IEEE International Conference on Mechatronics and Automation (ICMA), pages 1651–1656, Chengdu, China, August 2012.
12. Brunner, M.; Bruggemann, B.; Schulz, D.. " Hierarchical rough terrain motion planning using an optimal sampling-based method ,"
in  Int. Conf. on Robotics and Automation (ICRA) , Karlsruhe, Germany, 2013.
13. Adiyatov, Olzhas; Varol, Huseyin Atakan. "Rapidly-exploring random tree based memory efficient motion planning".
In Mechatronics and Automation (ICMA), 2013 IEEE International Conference on, pages 354–359, 2013. doi:10.1109/ICMA.2013.6617944
14. Adiyatov, Olzhas; Varol, Atakan (2013).  "MATLAB Toolbox of RRT, RRT* and RRT*FN algorithms" . Retrieved 3 August 2016 .
15. OlzhasAdi (Jan 26, 2015). "RRT*FN Brief Explanation" (video)YouTube. Retrieved 3 August 2016.
16. Choudhury, Sanjiban; Scherer, Sebastian; Singh, Sanjiv.
"RRT*-AR: Sampling-based alternate routes planning with applications to autonomous emergency landing of a helicopter".
In Robotics and Automation (ICRA), 2013 IEEE International Conference on, Karlsruhe, 6–10 May 2013, pages 3947–3952.
 doi:10.1109/ICRA.2013.6631133
17. Gammell, Jonathan D.; Srinivasa, Siddhartha S.; Barfoot, Timothy D. (8 Apr 2014). "Informed RRT*: Optimal Sampling-based Path Planning
Focused via Direct Sampling of an Admissible Ellipsoidal Heuristic".  2014 IEEE/RSJ International Conference on Intelligent Robots and Systems
arXiv:1404.2334 Freely accessible [cs.RO]. doi:10.1109/IROS.2014.6942976.
18.utiasASRL (Jul 4, 2014). "Informed RRT* @ UTIAS (IROS 2014)" (video)YouTube. Retrieved 3 August 2016.
19.Naderi, Kourosh; Rajamäki, Joose; Hämäläinen, Perttu (2015). "RT-RRT*: a real-time path planning algorithm based on RRT*".
In Proceedings of the 8th ACM SIGGRAPH Conference on Motion in Games (MIG '15). ACM, New York, NY, USA, 113–118. 
20. Palmieri, Luigi; Koenig, Sven; Arras, Kai O. "RRT-Based Nonholonomic Motion Planning Using Any-Angle Path Biasing".
In Robotics and Automation (ICRA), 2016 Proceedings of the IEEE International Conference on, pages 2775-2781, 2016.
6.外部链接
  • Media related to Rapidly exploring random tree at Wikimedia Commons
  • Java visualizer of RRT and RRT* including map editor



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