174 R. Zlot and A. Stentz timestamping the start and end times of each algorithm. Results are presented in table 1. Experimental results: comparison of solution costs and execution times (results shown are averages of the ratio of solution costs taken over 100 runs). Robots Areas c TT / c FTL c TT / c GR c TT / c OPT t FTL / t TT t GR / t TT t OPT / t TT 2 1 .85 1.03 1.19 .21 3.9 117 4 2 .86 .92 .14 2.7 5 3 .88 1.00 .10 2.8 7 5 .88 1.01 .08 3.4 4 8 .91 1.10 .06 3.1 In terms of solution cost, the task tree algorithm is 10-15% better than the FTL algorithm. One reason for this is that TT allows distributed replanning, so the TT solution is intuitively expected to be no worse than the FTL –inthe worst case no replanning is done by the task tree algorithm and the original tree decomposition is preserved 4 .Inaddition, the task tree algorithm also has an advantage because it allows reallocation through task subcontracting, permitting agents to discard tasks that theymay have been too hasty in purchasing earlier on. It should also be noted that if the solutions are, as we suspect, close to optimal, then a10-15% margin of improvement is significant. We can see this in the 2-robot 1-area case in which we were able to compute the optimal solution. Here the task tree algorithm wasonly 19% worse than optimal, as compared to FTL which wasalmost 40% worse than OPT.The execution time listed for the task tree algorithm ( t TT )isthe time taken to reach the local minimum cost; although FTL appears to run much faster, TT is an anytime algorithm and often reaches alower cost than FTL long before it reaches its local minimum. On average, the task tree algorithm and the GR algorithm produce about the same solution quality; however, the task tree algorithm is faster and does not rely on acentral auctioneer.The execution time for the task tree algorithm shown in table reflects the time taken to reach the locally optimal solution. Though TT found its local optimum three to four times faster than GR,the task tree algorithm produced a feasible solution in an even shorter time and improvedthat solution until it reached equilibrium at the time reflected in the table. The task tree algorithm guides the search quickly through areduced search space without compromising the solution quality,while also allowing for adistributed search. Table 2shows the effects of allowing auction winners to replan abstract tasks that theyhavewon. Task tree auctions were run twice on each of 100 instances. In one run task decomposition wasperformed only once at the beginning by the initial 4 TT almost always performed better that FTL ,but there were afew exceptional cases where FTL did slightly better: since the task tree algorithm is alocal search based on myopic cost estimates, the solution reached can depend on the order the tasks are allocated to each robot. Market-Based Multirobot Coordination Using Task Abstraction 175 auctioneer – tasks were not permitted to be decomposed once the original plan was developed. In the second case, the full task tree algorithm was used, allowing further decompositions after abstract tasks exchanged hands. Table 2 compares the solution costs from these two scenarios. The improvement ranged between 3 and 10% of total cost. Intuitively, we would expect the solution to be more efficient when allowing full decomposition; however, the magnitude of the improvement will depend on the specifics of the application, such as the size of the grid used and how many alternative plans the auctioneers choose to offer in the initial decomposition. Experimental results: comparison of solution quality of TT algorithm with replan- ning vs. the solution quality of TT algorithm without replanning (results shown are averages of the ratio of the solution cost with replanning compared to the solution cost without replan- ning). Robots Areas c replan / c no− replan 2 1 .97 4 2 .96 5 3 .90 7 5 .91 4 8 .97 We have introduced anew method for distributing execution and planning overa team of robots and software agents, which combines ideas from hierarchical plan- ning with amarket-based multirobot coordination architecture. Empirical results in computer simulation showthat task tree auctions can produce cost-efficient solu- tions to difficult optimization problems in atime-efficient manner. In future work we will look at extending the task description language to han- dle richer task constraints and interactions, such as partial order precedence rela- tions and conflicts arising between tasks competing for the same resources. Another interesting issue to explore will be decisions on when decomposition should take place. In some instances it can be costly to decompose abstract tasks, so it may be beneficial to leave the decomposition to the buyers of the task, or until immediately before the task must be executed. This would require the ability to adequately rea- son about the costs and benefits of tasks at an abstract level. We are also working on alternative auction clearing algorithms that will allowthe bidders to use amore expressive bidding language, leaving the burden of selecting which of arobot’sbids to accept to the auctioneer.Additionally,wewould liketoaddress other issues such as further generalization of the tree structures, permitting commitments to be broken and subcontracts to be sold, and howtoefficiently deal with replanning when new information is discovered that affects upcoming plans. We are currently performing further experiments and are in the process of port- ing the system to ateam of 10 ActivMedia Pioneer P2DX robots. The hardware and software infrastructure is in place and first results are expected in the very near future. 176 R. Zlot and A. Stentz This work was sponsored by the U.S. Army Research Laboratory, under contract (contract number DAAD19-01-2- 0012). The views and conclusions contained in this document are those of the au- thors and should not be interpreted as representing the official policies, either ex- pressed or implied, of the Army Research Laboratory or the U. S. Government. The U. S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. The authors also thank Bernardine Dias for helpful contributions and advice. 1. B. J. Clement and E. H. Durfee. Top-down search for coordinating the hierarchical plans or multiple agents. In Proceedings of the Third International Conference on Autonomous Agents (Agents’99), pages 252–259, 1999. 2. M. B. Dias, D. Goldberg, and A. Stentz. Market-based multirobot coordination for com- plex space applications. In The 7th International Symposium on Artificial Intelligence, Robotics and Automation in Space (i-SAIRAS), 2003. 3. M. B. Dias and A. Stentz. 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Distributed robotic mapping of extreme environments. In Proceedings of SPIE: Mobile Robots XV and Telemanipulator and Telepresence Technologies VII, 2000. Market-Based Multirobot Coordination Using Task Abstraction 177 15. R. Zlot and A. Stentz. Multirobot control using task abstraction in a market framework. In Proceedings of the Collaborative Technology Alliances Conference, 2003. 16. R. Zlot, A. Stentz, M. B. Dias, and S. Thayer. Multi-robot exploration controlled by a market economy. In Proceedings of the International Conference on Robotics and Automation, 2002. Decentralised SLAM with Low-Bandwidth Communication for Teams of Vehicles 1 2 1 1 1 2 Abstract. 1Introduction N 2 et al. quadratic 2The Decentralised Architecture ‘information’ 2.1 The Information Filter t i t j ˆ x ( i | j ) P ( i | j ) ˆ y ( i | j ) Y ( i | j ) ˆ y ( i | j ) = P − 1 ( i | j ) ˆ x ( i | j ) , Y ( i | j ) = P − 1 ( i | j ) . additive 2.2 Local Filter Fig. 1. 2.3 Channel Manager et al. 2.4 Channel Filter 3Constant Time Communication all map consistency 3.1 Extracting the Submap to Communicate maximise the information gain M 2 0 ≤ M ≤ N et al. M greatest information gain N 2 G m G m ˆ y ( k | k ) G v G v ˆ y ( k | k ) y ∗ ( k | k ) Y ∗ ( k | k ) y ∗ ( k | k )=G m [ ˆ y ( k | k ) − Y ( k | k ) G T v G v Y ( k | k ) G T v − 1 G v ˆ y ( k | k )] Y ∗ ( k | k )=G m [ Y ( k | k ) − Y ( k | k ) G T v G v Y ( k | k ) G T v − 1 G v Y ( k | k )] × G T m y ∗ ( k | k ) Y ∗ ( k | k ) 3.2 Channel Update t k +1 t k N 2 Y Chan ( k | k )=Y Chan ( k | k − 1) +[Y ∗ ( k | k ) − Y Chan ( k | k − 1)] = Y ∗ ( k | k ) ˆ y Chan ( k | k )= ˆ y Chan ( k | k − 1) +[y ∗ ( k | k ) − ˆ y Chan ( k | k − 1)] = y ∗ ( k | k ) Y ∗ ( k | k ) y ∗ ( k | k ) N 2 [...]... (Eds.): Field and Service Robotics, STAR 24, pp 189–198, 20 06 © Springer-Verlag Berlin Heidelberg 20 06 190 A Morris et al Fig.1 The process of backfilling a domeout with coal flyash [4] 2 Related Methods Current methods for underground void detection include non-intrusive techniques such as ground-penetrating radar (GPR) and microgravity as well as direct methods such as borehole-deployed cameras and human... uncertainty International Journal of Robotics Research, 5(4): 56 68 , 19 86 11 C Thorpe and H Durrant-Whyte Field robots In Proceedings of the 10th International Symposium of Robotics Research (ISRR’01), 2001 12 S Thrun, D Koller, Z Ghahmarani, and H Durrant-Whyte SLAM updates require constant time In Proceedings of the Fifth International Workshop on Algorithmic Foundations of Robotics, Nice, France, 2002 13... 90 100 0 20 30 40 50 60 Communicated Map Size 70 80 90 100 30 20 10 0 Variance 414 40 Feature Error in Y − NoComm 40 60 0 412 60 Feature Error in x − NoComm 40 3 410 50 Time [s] (f) True Vehicle Paths and Map 500 595 40 0 −10 100 [m] [m] 61 0 (g) 0 −5 0 [m] 100 5 1000 61 5 408 90 10 62 0 4 06 80 0 −10 100 Feature Error in Y − CT 1500 True Feature Location CT NSQ NoComm 404 30 40 50 60 70 Vehicle Error in... 10 50 Time [s] 60 70 80 90 100 −10 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 Time [s] 60 70 80 90 10 20 30 70 80 90 100 70 80 90 100 70 80 90 100 60 5 True Feature Location Vehicle Path 0 10 20 30 4 16 418 50 60 0 10 20 30 Variance 0 0 500 [m] (h) 40 50 Time [s] 60 X Variance vs CT Map Size 30 20 10 0 10 20 30 40 50 60 Y Variance vs CT Map Size 70 80 90 100 0 10 −3 x 10 20 30 40 50 60 Phi Variance... information and recover any information discarded through previous conservative CI updates References 1 W Burgard, D Fox, M Moors, R Simmons, and S Thrun Collaborative multi-robot exploration In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) IEEE, 2000 2 S Grime and H.F Durrant-Whyte Data fusion in decentralized sensor networks Control Engineering Practice, 2, No 5:849– 863 ,... Concurrent Mapping and Localization for Autonomous Mobile Robots (W4) ICRA Conference, Washington, DC, 2002 6 P.S Maybeck Stochastic Models, Estimation and Control, Volume 1 Academic Press Inc., New York, 1979 7 E Nettleton Decentralised Architectures for Tracking and Navigation with Multiple Flight Vehicles PhD Thesis, The University of Sydney, 2003 8 E.W Nettleton, P.W Gibbens, and H.F Durrant-Whyte Closed... measurements from the ceiling and floor) Fig .6 Mine map analysis (Left) All three projection plots placed in same map (Right) Calculated warp (X’s mark estimated borehole placement prior to Ferret and arrows point to determined positions) 1 96 A Morris et al Utilizing template-matching techniques [12], column edges and solid landmarks on the mine map were correlated with high-density point clusters To... in realizing, measuring, and mapping abandoned limestone mine sections and domeouts for structural analysis and remediation Furthermore, this study suggests the flexibility of Ferret technology to other application domains such as verification of abandoned coalmines and situational analysis of subterranean hazardous waste disposals Acknowledgements The land owning company and engineering firm in Kansas... developments and had the insight to implement us into their plans and Workhorse Technology, LLC that funded and supported the development of Ferret and mine mapping initiatives at Carnegie Mellon University References 1 2 M Ross and M Roth “All Nine Alive: The Story of the Quecreek Mine Rescue.” Pittsburgh Post-Gazette 04 August 2002 Beck, Barry F and Herring, J.Gayle (eds): Geotechnical and environmental... Autonomous Mapping and Navigation Problems PhD Thesis, University of Sydney, 2001 E Nettleton et al Vehicle Error in x − NSQ 10 20 30 40 50 60 Vehicle Error in y − NSQ 90 100 0 −2 −4 0 10 20 30 40 50 60 70 Vehicle Error in Orientation − NSQ 80 90 Error [rads] −0.1 10 20 30 40 50 Time [s] 20 30 40 50 60 Vehicle Error in y − CT 60 70 80 90 0 10 20 30 10 20 30 40 90 60 70 80 90 30 40 50 60 70 80 90 −10 . voids tobeacquired. In thispaper wediscuss the designof the robotic tool,demonstrateits application in void assessment for prevention and response to subsidence ,and present results from acase study. DAAD1 9-0 1-2 - 0012). The views and conclusions contained in this document are those of the au- thors and should not be interpreted as representing the official policies, either ex- pressed or implied,. richer task constraints and interactions, such as partial order precedence rela- tions and conflicts arising between tasks competing for the same resources. Another interesting issue to explore will