1. http://parasol.tamu.edu Tree-Based Planning Nancy M. Amato Parasol Lab,Texas A&M University

2. ‘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

3. Bi-Directional Search: Iteratively grow trees from start and goal S0S0 G0G0 S1S1 S3S3 S2S2 G2G2 G3G3 G1G1 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 G4G4

4. 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]

5. Rapidly Exploring Random Trees (RRT) [Kuffner & LaValle ICRA 1999] Start Goal Nodes in current RRT-VAR tree Configurations around closest to random in tree Random configuration x rand x near New node added to the RRT tree

6. Rapidly Exploring Random Trees (RRT) [Kuffner & LaValle ICRA 1999]

7. RRT approaches GENERATE_RRT(x init, K,  t) 1. T.init(x init ); 2. For k = 1 to K do 3. x rand  RANDOM_STATE(); 4. x near  NEAREST_NEIGHBOR(x rand, T); 5. u  SELECT_INTPUT(x rand, x near ); 6. x new  NEW_STATE(x near, u,  t); 7. T.add_vertex(x new ); 8. T.add_edge(x near, x new, u); 9. Return T; x near x rand x init x new 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 x init :