Multi-Heuristic A* Sandip Aine, Siddharth Swaminathan,Venkatraman Narayanan,Victor Hwang, and Maxim Likhachev IIIT Delhi Case for Multiple Heuristics An Example Problem Full-body mobile manipulation: 12D planning The Robotics Institute, Carnegie Mellon University Experiments: Mobile Manipulation MHA*: Algorithms • • Independent MHA* (IMHA*): separate g, h values and priority queues for each search Shared MHA* (SMHA*): separate h values and queues for each search, but shared g MHA*: Details • • • • • Performance of informed search algorithms depends greatly on the quality of heuristics h0: base distance (2D BFS) available h1: base distance + orientation difference with goal Hard to design a single admissible heuristic h2: base distance + orientation difference with vertical that captures all the complexities of the problem, and is yet free of local-minima Easier to develop a set of inadmissible heuristics, each addressing a subset of the problem complexities Relieves the user from spending a lot of time h0 engineering one great admissible heuristic-i.e, heuristics can now be actual ‘rules of thumb’ Proposed algorithm uses several inadmissible heuristics in addition to one consistent h1 h2 heuristic for performing informed search, with Multi-Heuristic A* (MHA*) provable guarantees on bounded • 1 consistent heuristic (h0) + n inadmissible heuristics suboptimality of the solution (h1, h2 .., hn) • Designing “local minima free” heuristic is not easy for complex problems Round robin exploration while goal state has not yet been expanded for i in 1:n if min. key(OPENi)<= w2* min. key(OPEN0) expand from OPENi else expand from OPEN0 end for end while Anchor Search OPEN0 key = g0+ w1*h0 consistent heuristic Inad. Search 1 Inad. Search 2 Inad. Search n OPEN1 key = g1+ w1*h1 OPEN2 key = g2+ w1*h2 OPENn key = gn+ w1*hn IMHA*: Independent Expansions 90% 60% 30% 0% Comparison with Weighted A* 1.20 1.5 ✔ 1.1 ⨯ 0.80 0.8 0.40 0.4 0 Success rate WA* Runtime (Ratio) IMHA* 0 Solution Cost (Ratio) SMHA* Comparison with Sampling-based Planners ✔ 100% ︸ 6.0 ⨯ 2.0 75% 4.5 1.5 50% 3.0 1.0 25% 1.5 0.5 0% 0 Success rate PRM ✔ Runtime (Ratio) RRT-Con 0 RRT*(F) ⨯ ︸ ⨯ ︸ ✔ ✔ Base distance End-effector distance (Ratios) IMHA* SMHA* Other domains: 3D navigation, Sliding tile puzzles OPEN1 key = g+ w1*h1 OPEN2 key = g+ w1*h2 OPENn key = g+ w1*hn SMHA*: Shared Expansions (successor states are inserted/updated in all queues) MHA* Properties IMHA* SMHA* Subopt. bound w1*w2 w1*w2 Max. re-expansions n+1 2 Easy ✔ ? Parallelization Path sharing No ✔ Yes ✔ [1] Fast Downward Search (Roger/Helmert ’10) [2] Explicit Estimation Search (Thayer/Ruml ’11) [3] MPWA* (Valenzano et al. ’10)