Advertisement

Autonomous Robots

, Volume 42, Issue 4, pp 781–799 | Cite as

Timed abstractions for distributed cooperative manipulation

  • Christos K. Verginis
  • Dimos V. Dimarogonas
Article
Part of the following topical collections:
  1. Special Issue: Online Decision Making in Multi-Robot Coordination

Abstract

This paper addresses the problem of deriving well-defined timed abstractions for the decentralized cooperative manipulation of a single object by N robotic agents. In particular, we propose a distributed model-free control protocol for the trajectory tracking of the cooperatively manipulated object without necessitating feedback of the contact forces/torques or inter-agent communication. Certain prespecified performance functions determine the transient and steady state of the coupled object-agents system. The latter, along with a region partition of the workspace that depends on the physical volume of the object and the agents, allows us to define timed transitions for the coupled system among the derived workspace regions. Therefore, we abstract its motion as a finite transition system and, by employing standard automata-based methodologies, we define high level complex tasks for the object that can be encoded by timed temporal logics. In addition, we use load sharing coefficients to represent potential differences in power capabilities among the agents. Finally, realistic simulation studies verify the validity of the proposed scheme.

Keywords

Timed abstractions Cooperative manipulation Formal verification Robotics Multi-agent systems Robust control 

Supplementary material

10514_2017_9672_MOESM1_ESM.mp4 (118.6 mb)
Supplementary material 1 (mp4 121488 KB)

References

  1. Adzkiya, D., De Schutter, B., & Abate, A. (2013). Finite abstractions of max-plus-linear systems. IEEE Transactions on Automatic Control, 58(12), 3039–3053.MathSciNetCrossRefzbMATHGoogle Scholar
  2. Aksaray, D., Vasile, C.-I., & Belta, C. (2016). Dynamic routing of energy-aware vehicles with temporal logic constraints. Proceedings of the IEEE international conference on robotics and automation (ICRA) (pp. 3141–3146).Google Scholar
  3. Alur, R., & Dill, D. L. (1994). A theory of timed automata. Theoretical computer science, 126(2), 183–235.MathSciNetCrossRefzbMATHGoogle Scholar
  4. Alur, R., Feder, T., & Henzinger, T. A. (1996). The benefits of relaxing punctuality. Journal of the ACM (JACM), 43(1), 116–146.MathSciNetCrossRefzbMATHGoogle Scholar
  5. Baier, C., Katoen, J.-P., et al. (2008). Principles of model checking. Cambridge: MIT Press.zbMATHGoogle Scholar
  6. Bechlioulis, C. P., & Rovithakis, G. A. (2014). A low-complexity global approximation-free control scheme with prescribed performance for unknown pure feedback systems. Automatica, 50(4), 1217–1226.MathSciNetCrossRefzbMATHGoogle Scholar
  7. Belta, C., & Habets, L. C. (2006). Controlling a class of nonlinear systems on rectangles. IEEE Transactions on Automatic Control, 51(11), 1749–1759.MathSciNetCrossRefzbMATHGoogle Scholar
  8. Belta, C., & Kumar, V. (2004). Abstraction and control for groups of robots. IEEE Transactions on robotics, 20(5), 865–875.CrossRefGoogle Scholar
  9. Boskos, D., & Dimarogonas, D. V. (2015). Decentralized abstractions for feedback interconnected multi-agent systems. In Proceedings of the IEEE conference on decision and control (CDC) (pp. 282–287).Google Scholar
  10. Caccavale, F., Chiacchio, P., Marino, A., & Villani, L. (2008). Six-dof impedance control of dual-arm cooperative manipulators. IEEE/ASME Transactions on Mechatronics, 13(5), 576–586.CrossRefGoogle Scholar
  11. Chaimowicz, L., Campos, M. F. M., & Kumar, V. (2003). Hybrid systems modeling of cooperative robots. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), 3, 4086–4091.Google Scholar
  12. Chen, Y., Ding, X. C., Stefanescu, A., & Belta, C. (2012). Formal approach to the deployment of distributed robotic teams. IEEE Transactions on Robotics, 28(1), 158–171.CrossRefGoogle Scholar
  13. Cheng, P., Fink, J., & Kumar, V. (2009). Abstractions and algorithms for cooperative multiple robot planar manipulation. In Robotics: Science and Systems IV, p. 143.Google Scholar
  14. Diaz-Mercado, Y., Jones, A., Belta, C., & Egerstedt, M. (2015). Correct-by-construction control synthesis for multi-robot mixing. In Proceedings of the IEEE conference on decision and control (CDC) (pp. 221–226).Google Scholar
  15. Erhart, S., & Hirche, S. (2013). Adaptive force/velocity control for multi-robot cooperative manipulation under uncertain kinematic parameters. In Proceedings of the IEEE/RSJ international conference on intelligent robots and systems (IROS) (pp. 307–314).Google Scholar
  16. Filippidis, I., & Murray, R. M. (2016). Symbolic construction of gr (1) contracts for systems with full information. In Proceedings of the American control conference (ACC) (pp. 782–789).Google Scholar
  17. Franchi, A., Petitti, A., & Rizzo, A. (2014). Distributed estimation of the inertial parameters of an unknown load via multi-robot manipulation. In IEEE conference on decision and control (CDC) (pp. 6111–6116).Google Scholar
  18. Franchi, A., Petitti, A., & Rizzo, A. (2015). Decentralized parameter estimation and observation for cooperative mobile manipulation of an unknown load using noisy measurements. In IEEE international conference on robotics and automation (ICRA) (pp. 5517–5522).Google Scholar
  19. Guo, M., Tumova, J., & Dimarogonas, D. V. (2014). Cooperative decentralized multi-agent control under local ltl tasks and connectivity constraints. In Proceedings of the IEEE international conference on decision and control (pp. 75–80).Google Scholar
  20. He, K., Lahijanian, M., Kavraki, L. E., and Vardi, M. Y. (2015). Towards manipulation planning with temporal logic specifications. In Proceedings of the IEEE international conference on robotics and automation (ICRA) (pp. 346–352).Google Scholar
  21. Heck, D., Kostic, D., Denasi, A., & Nijmeijer, H. (2013). Internal and external force-based impedance control for cooperative manipulation. In Proceedings of the IEEE European control conference (ECC) (pp. 2299–2304).Google Scholar
  22. Karaman, S., & Frazzoli, E. (2011). Linear temporal logic vehicle routing with applications to multi-uav mission planning. International Journal of Robust and Nonlinear Control, 21(12), 1372–1395.MathSciNetCrossRefzbMATHGoogle Scholar
  23. Kloetzer, M., & Belta, C. (2008). A fully automated framework for control of linear systems from temporal logic specifications. IEEE Transactions on Automatic Control, 53(1), 287–297.MathSciNetCrossRefzbMATHGoogle Scholar
  24. Lionis, G., & Kyriakopoulos, K. J. (2005). Centralized motion planning for a group of micro agents manipulating a rigid object. In Proceedings of the IEEE international symposium on intelligent control, Mediterrean conference on control and automation (pp. 662–667).Google Scholar
  25. Lippiello, V., & Ruggiero, F. (2012). Cartesian impedance control of a uav with a robotic arm. IFAC Proceedings Volumes, 45(22), 704–709.CrossRefGoogle Scholar
  26. Liu, Y.-H., & Arimoto, S. (1998). Decentralized adaptive and nonadaptive position/force controllers for redundant manipulators in cooperations. The International Journal of Robotics Research, 17(3), 232–247.CrossRefGoogle Scholar
  27. Markdahl, J., Karayiannidis, Y., & Hu, X. (2012). Cooperative object path following control by means of mobile manipulators: a switched systems approach. IFAC Proceedings Volumes, 45(22), 773–778.CrossRefGoogle Scholar
  28. Michael, N., Fink, J., & Kumar, V. (2011). Cooperative manipulation and transportation with aerial robots. Autonomous Robots, 30(1), 73–86.CrossRefzbMATHGoogle Scholar
  29. Muthusamy, R., & Kyrki, V. (2014). Decentralized approaches for cooperative grasp planning. In Proceedings of the international conference on control automation robotics & vision (ICARCV) (pp. 693–698).Google Scholar
  30. Nikou, A., Tumova, J., & Dimarogonas, D. V. (2016). Cooperative task planning of multi-agent systems under timed temporal specifications. In Proceedings of the IEEE American control conference (ACC) (pp. 7104–7109).Google Scholar
  31. Ouaknine, J., & Worrell, J. (2005). On the decidability of metric temporal logic. Annual IEEE symposium on logic in computer science (LICS’05) (pp. 188–197).Google Scholar
  32. Palunko, I., Donner, P., Buss, M., & Hirche, S. (2014). Cooperative suspended object manipulation using reinforcement learning and energy-based control. In IEEE/RSJ international conference on intelligent robots and systems (IROS 2014) (pp. 885–891).Google Scholar
  33. Parra-Vega, V., Sanchez, A., Izaguirre, C., Garcia, O., & Ruiz-Sanchez, F. (2013). Toward aerial grasping and manipulation with multiple uavs. Journal of Intelligent & Robotic Systems, 70(1–4), 575–593.CrossRefGoogle Scholar
  34. Petitti, A., Franchi, A., Di Paola, D., & Rizzo, A. (2016). Decentralized motion control for cooperative manipulation with a team of networked mobile manipulators. In Proceedings of the IEEE international conference on robotics and automation (ICRA) (pp. 441–446).Google Scholar
  35. Reissig, G. (2011). Computing abstractions of nonlinear systems. IEEE Transactions on Automatic Control, 56(11), 2583–2598.MathSciNetCrossRefzbMATHGoogle Scholar
  36. Rohmer, E., Singh, S. P., & Freese, M. (2013). V-rep: a versatile and scalable robot simulation framework. In Proceedings of the international conference on intelligent robots and systems (IROS).Google Scholar
  37. Rungger, M., Weber, A., & Reissig, G. (2015). State space grids for low complexity abstractions. In Proceedings of the IEEE conference on decision and control (CDC) (pp. 6139–6146).Google Scholar
  38. Siciliano, B., & Khatib, O. (2008). Springer handbook of robotics. New York: Springer.CrossRefzbMATHGoogle Scholar
  39. Sontag, E. D. (2013). Mathematical control theory: Deterministic finite dimensional systems (Vol. 6). New York: Springer.Google Scholar
  40. Souza, D., & Prabhakar, P. (2007). On the expressiveness of mtl in the pointwise and continuous semantics. International Journal on Software Tools for Technology Transfer, 9(1), 1–4.CrossRefGoogle Scholar
  41. Stroupe, A., Huntsberger, T., Okon, A., & Aghazarian, H. (2005). Precision manipulation with cooperative robots. Multi-Robot Systems. From Swarms to Intelligent Automata, III, 235–248.Google Scholar
  42. Sugar, T. G., & Kumar, V. (2002). Control of cooperating mobile manipulators. IEEE Transactions on robotics and automation, 18(1), 94–103.CrossRefGoogle Scholar
  43. Szewczyk, J., Plumet, F., & Bidaud, P. (2002). Planning and controlling cooperating robots through distributed impedance. Journal of Robotic Systems, 19(6), 283–297.CrossRefzbMATHGoogle Scholar
  44. Tanner, H. G., Loizou, S. G., & Kyriakopoulos, K. J. (2003). Nonholonomic navigation and control of cooperating mobile manipulators. IEEE Transactions on Robotics and Automation, 19(1), 53–64.Google Scholar
  45. Tiwari, A. (2008). Abstractions for hybrid systems. Formal Methods in System Design, 32(1), 57–83.CrossRefzbMATHGoogle Scholar
  46. Tsiamis, A., Tumova, J., Bechlioulis, C. P., Karras, G. C., Dimarogonas, D. V., & Kyriakopoulos, K. J. (2015a). Decentralized leader-follower control under high level goals without explicit communication. In Proceedings of the IEEE/RSJ international conference on intelligent robots and systems (IROS) (pp. 5790–5795).Google Scholar
  47. Tsiamis, A., Verginis, C. K., Bechlioulis, C. P., & Kyriakopoulos, K. J. (2015b). Cooperative manipulation exploiting only implicit communication. In Proceedings of the IEEE/RSJ international conference on intelligent robots and systems (IROS) (pp. 864–869).Google Scholar
  48. Verginis, C. K., & Dimarogonas, D. V. (2016). Distributed cooperative manipulation under timed temporal specifications. American Control Conference (ACC).Google Scholar
  49. Wang, Z., & Schwager, M. (2016). Multi-robot manipulation without communication. Distributed Autonomous Robotic Systems, 112, 135–149.CrossRefGoogle Scholar
  50. Yamashita, A., Arai, T., Ota, J., & Asama, H. (2003). Motion planning of multiple mobile robots for cooperative manipulation and transportation. IEEE Transactions on Robotics and Automation, 19(2), 223–237.CrossRefGoogle Scholar
  51. Zamani, M., Mazo, M., & Abate, A. (2014). Finite abstractions of networked control systems. In Proceedings of the IEEE conference on decision and control (pp. 95–100).Google Scholar
  52. Zhang, Z., & Cowlagi, R. V. (2016). Motion-planning with global temporal logic specifications for multiple nonholonomic robotic vehicles. In Proceedings of the American control conference (ACC) (pp. 7098–7103).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.KTH Royal Institute of TechnologyStockholmSweden

Personalised recommendations