Tree-Based Planning Nancy M. Amato Parasol 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 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

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 tree Random configuration x rand x near New node added to the RRT tree

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

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, The result is a tree rooted at x init :