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: