tree-based planning
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http://parasol.tamu.edu
Tree-Based Planning
Nancy M. AmatoParasol Lab,Texas A&M University
‘Single Shot’ Planning
Given Start and Goal configurations, determine a motion plan connecting them without preprocessing (don’t build roadmap)
• Also, can be applied when do not have specific goal, but want to find space reachable from start
Start
Goal
Bi-Directional Search: Iteratively grow trees from start and goal
S0
G0
S1
S3
S2
G2
G3
G1
Obstacle1
Obstacle2
Obstacle3
• Build two trees: one from start and one from goal•partial progress saved & added to evolving trees
• Original query solved when start & goal trees meet
G4
Ariadne’s Clew Algorithm [Bessiere et al IROS 1993]
Start
Goal
EXPLORE random walk terminus
new Landmark
SEARCH random walk terminus[Bessiere et al, IROS 1993]
Rapidly Exploring Random Trees (RRT) [Kuffner & LaValle ICRA 1999]
Start
Goal
Nodes in current RRT-VAR tree
Configurations around closest to random in treeRandom configuration
xrand
xnear
New node added to the RRT tree
Rapidly Exploring Random Trees (RRT) [Kuffner & LaValle ICRA 1999]
RRT approaches
GENERATE_RRT(xinit, K, t)1. T.init(xinit);
2. For k = 1 to K do
3. xrand RANDOM_STATE();
4. xnear NEAREST_NEIGHBOR(xrand, T);
5. u SELECT_INTPUT(xrand, xnear);
6. xnew NEW_STATE(xnear, u, t);
7. T.add_vertex(xnew);
8. T.add_edge(xnear, xnew, u);
9. Return T;
xnear
xrand
xinit
xnew
LaValle, 1998; LaValle, Kuffner, 1999, 2000; Frazzoli, Dahleh, Feron, 2000; Toussaint, Basar, Bullo, 2000; Vallejo, Jones, Amato, 2000; Strady, Laumond, 2000; Mayeux, Simeon, 2000; Karatas, Bullo, 2001; Li, Chang, 2001; Kuffner, Nishiwaki, Kagami, Inaba, Inoue, 2000, 2001; Williams, Kim, Hofbaur, How, Kennell, Loy, Ragno, Stedl, Walcott, 2001; Carpin, Pagello, 2002.
The result is a tree rooted at xinit:
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