Implan: Scalable Incremental Motion Planning for Multi-Robot Systems
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1 Implan: Scalable Incremental Motion Planning for Multi-Robot Systems Indranil Saha UC Berkeley and UPenn Joint work with Rattanachai Ramaithitima (UPenn), Vijay Kumar (UPenn), George Pappas (UPenn) and Sanjit Seshia (UC Berkeley) Annual Meeting 2015 ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 1/15
2 Motion Planning Problem An input problem instance P = R, I, PRIM, Workspace, ξ R - The set of robots I - Initial state of the group of robots PRIM = [PRIM 1, PRIM 2,..., PRIM R ] Workspace - Workspace dimension, position of obstacles ξ - Specification given in Linear Temporal Logic Definition (Motion Planning Problem) Given an input problem P with specification ξ, synthesize a trajectory that satisfies ξ ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 2/15
3 Trajectory Synthesis via SMT Solving [IROS 2014] Complan (COmpositional Motion PLANner) isaha/complan.shtml Φ(0) Prim 1 Φ(1) Prim 2 Φ(2)... Φ(L 1) Prim L Φ(L) Constraints: (Φ(0) I) Transition Specification Boolean combination of constraints from Linear Arithmetic and Equality with Uninterpreted Functions theories Complan solves for the L motion primitives using an SMT solver ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 3/15
4 Limitation of Complan The motion planning problem is reduced to a monolithic SMT solving problem The number of constraints for collision avoidance increases quadratically with the number of robots Complan has limited scalability ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 4/15
5 Motion Plan Synthesis for a Swarm of Robots Implan (Incremental Motion PLANner) Specification: ( collision) U reach ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 5/15
6 Outline of the Algorithm R1 R2 R1' R2' Synthesize optimal trajectory for each robot independently Assign Priority to find R1 ar2feasible R2' ordering R1' for the robots Synthesize final trajectories according to the assigned priorities Treat the robots with higher priorities as dynamic obstacles Introduce minimum delay to execute the optional trajectory to avoid collision ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 6/15
7 Priority Assignment Algorithm InitObs(j) : The set of robots whose initial locations obstruct the optimal trajectory of Robot R j FinalObs(j) : The set of robots whose final locations obstruct the optimal trajectory of Robot R j Algorithm: 1. Generate the following constraints: R j R, R k R\{R j } : R k InitObs(j) prio(k) > prio(j) R j R, R k R\{R j } : R k FinalObs(j) prio(j) > prio(k) 2. Solve the constraints using an SMT solver ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 7/15
8 Example1: Motion Plan Synthesis for 6 Robots 15 i1 i i y i f1 f5 i5 f x f2 i6 f3 f6 Ordering: 1: R 3 2: R 6 3: R 2 4: R 4 5: R 1 6: R 5 ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 8/15
9 Example1: Motion Plan Synthesis for 6 Robots 15 i1 i i y i f1 f5 i5 f x f2 i6 f3 f6 Ordering: 1: R 3 2: R 6 3: R 2 4: R 4 5: R 1 6: R 5 Computation Time: Complan: 27m40s Implan: 7s ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 8/15
10 Priority Assignment Algorithm What if a priority assignment does not exist? ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 9/15
11 R1 Priority Assignment Algorithm R2 R1' R2' What if a priority assignment does not exist? R1 R2 R2' R1' prio(1) < prio(2) prio(1) > prio(2) ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 9/15
12 R1 Priority Assignment Algorithm R2 R1' R2' What if a priority assignment does not exist? R1 R2 R2' R1' prio(1) < prio(2) prio(1) > prio(2) Dependent robots are placed into a group Groups are found by unsatisfiable cores generated by the SMT solver ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 9/15
13 Example2: Motion Plan Synthesis for 6 Robots 15 i1 i i y i f1 f5 i5 f x f2 i6 f3 f6 Ordering: 1: R 2 2: R 4, R 5, R 6 3. R 1, R 3 ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 10/15
14 Example2: Motion Plan Synthesis for 6 Robots 15 i1 i i y i f1 f5 i5 f x f2 i6 f3 f6 Ordering: 1: R 2 2: R 4, R 5, R 6 3. R 1, R 3 Computation Time: Complan: 3hr13m Implan: 27m ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 10/15
15 Properties of Implan Generated trajectories are cost optimal, but may not be time optimal The worst case computational complexity of Implan is the same as Complan ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 11/15
16 Example 3: Motion Planning in a Compact Workspace 25 quadrotors moving in a closed place Specification: collision U reach Workspace Size: 15.2m 16.8m Computation Time: 4hr12m Figure: caption ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 12/15
17 Example 4: Incremental Motion Planning in a Free Workspace 50 quadrotors moving in a free place Specification: collision U reach Workspace Size: 15.2m 16.8m Computation Time: 30m19s ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 13/15
18 Future Work To Extend Implan to arbitrary LTL/MTL properties ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 14/15
19 Thank You!! isaha ExCAPE Annual Meeting 2015 Indranil Saha Incremental Motion Planning for Multi-Robot Systems 15/15
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