Rapidly Exploring Random TreesRRT-Connected: An Efficient Approach to Single-Query
Path Planning
Rapidly Exploring Random TreesData structure/algorithm to facilitate path
planningDeveloped by Steven M. La Valle (1998)Originally designed to handle problems with
nonholonomic constraints and high degrees of freedom
Rapidly Exploring Random TreesAlgorithm: BUILD_RRT(qinit)1 T.init(qinit);2 for k=1 to K do3 qrand ← RANDOM_CONFIG();4 EXTEND(T, qrand);5 Return T;
Rapidly Exploring Random TreesEXTEND(T,q)1 qnear ← Nearest_NEIGHBOUR(q,T);2 if NEW_CONFIG(q, qnear, qnew) then3 T.add_vertex(qnew);4 T.add_edge(qnear, qnew);5 if qnew = q then6 Return Reached;7 else 8 Return Advanced;9 Return Trapped;
Rapidly Exploring Random Trees
Rapidly Exploring Random TreesMain advantage: biased towards unexplored
regionsProbability node selected for extension proportional
to size voronoi region
Rapidly Exploring Random TreesNice properties: Expansion heavily biased towards
unexplored areas of state space Distribution nodes approaches the sampling
distribution (important for consistency), usually uniform but not necessarily!
Relatively simple algorithm Always remains connected
RRT-Connect Path PlannerHow to use RRT in a path planner?RRT-Connect:
Single shot methodGrow two RRTs one from the start position and
one from the goal positionAfter every extension try to connect the treesIf the trees connect a path has been found
RRT-Connect Path PlannerAlgorithm:RRT_CONNECT_PLANNER(qinit, qgoal)1 Ta.init(qinit); Tb.init(qgoal);2 for k=1 to K do3 qrand ← RND_CFG();4 if not(EXTEND(Ta, qrand)= Trapped) then5 if(CONNECT(Tb, qnew) = Reached) then6 Return PATH(Ta, Tb);7 SWAP(Ta, Tb);8 Return Failure;
RRT-Connect Path PlannerCONNECT(T, q)1 repeat2 S ← EXTEND(T, q)3 until not (S = Advanced)4 Return S;
RRT-Connect Path Planner
RRT-Connect Path PlannerVariations:
RRT_EXTEND_EXTENDRRT_CONNECT_CONNECTIn CONNECT step only add last vertex to graphGrow more RRTs
RRT-Connect Path PlannerAnalysis:
RRT-Connect is probabilistic completeDistribution vertices in RRT converges toward
sampling distributionNo theoretical characterization of the rate of
converge!
RRT-Connect Path PlannerExperiments:
Average 100 trialsScene 1: 0.228sScene 2: 5,94sScene 3: 2.92sUsing 3D non incremental collision checking algorithm
RRT-Connect Path PlannerExperiments:
In uncluttered scenes connect heuristic 3 to 4 times faster than other RRT-based variants
Useful for complicated 3D scenes7-DOF kinematic chain, over 8000 triangle
primitivesaverage 2 s for each motion to reach, grasp and move
RRT-Connect Path PlannerExperiments:
over 13.000 triangles80 s SGI Indigo215 s high-end SGI
RRT-Connect Path PlannerConclusion:
Randomised approach that yields good experimental performances withno parameter tuningno pre-processingsimple and consistent behaviourbalance between greedy searching and uniform
explorationwell suited for incremental distance computation
and fast nearest neighbour algorithms
RRT-Connect Path PlannerTo do:
optimise distance travelled during each step by using the radius of a collision free ball
use approximate nearest neighbour methodsuse incremental collision detection algorithm compare performance to other path planning
approachesidentify conditions that lead to poor
performance
RRT-Connect Path PlannerIssues:
Randomness can cause great variance in runtime due to ‘unlucky instance’
RRT-Connect Path PlannerIssues:
Ugly paths
References RRT-connect: An efficient approach to single-query path
planning. J. J. Kuffner and S. M. LaValle. In Proceedings IEEE International Conference on Robotics and Automation, pages 995--1001, 2000
On Heavy-tailed Runtimes and Restarts in Rapidly-exploring Random Trees. Nathan A. Wedge and Michael S. Branicky. 2008
Chapter 5: Sampling-Based Motion Planning, Planning Algorithms. S. M. LaValle. Cambridge University Press, Cambridge, U.K.,
Rapidly-exploring random trees: A new tool for path planning. S. M. LaValle. TR 98-11, Computer Science Dept., Iowa State University, October 1998 2006.
http://msl.cs.uiuc.edu/rrt/gallery.html Rapidly-Exploring Random Trees in Highly Constrained
Environments. Amjad Almahairi. 2010.