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Ensemble control of spatial variance of microbot systems through sequencing of motion primitives from optimal control trajectories


Spatial variance reduction of microbot systems through ensemble control, i.e., using a global control input, is a challenging task. In this paper, we propose to use a sequence of primary motion maneuvers called motion primitives to perform spatial variance reduction. We extract these primitives from the principal directions of the optimal control trajectories. The primitives efficiently discretize the input space and reduce the dimension of the search space significantly. These enable us to exploit lightweight and adaptable search algorithms like \(A^{*}\) for the task of fast sub-optimal input primitive sequence generation. Furthermore, we propose a primitive-based receding horizon motion planner (PB-RHMP) to increase robustness to process noise and model uncertainty. We validate the proposed methods with several simulated case studies.

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  1. Abbott JJ, Nagy Z, Beyeler F, Nelson BJ (2007) Robotics in the small, part i: microbotics. IEEE Robotics Autom Magaz 14(2):92–103

    Article  Google Scholar 

  2. Becker A, Habibi G, Werfel J, Rubenstein M, McLurkin J (2013) Massive uniform manipulation: Controlling large populations of simple robots with a common input signal. In: IEEE/RSJ International Conference on Intelligent Robots and Systems 520–527.

  3. Cohen BJ, Chitta S, Likhachev M (2010) Search-based planning for manipulation with motion primitives. In: IEEE International Conference on Robotics and Automation 2902–2908.

  4. Diller E, Floyd S, Pawashe C, Sitti M (2012) Control of multiple heterogeneous magnetic microrobots in two dimensions on nonspecialized surfaces. IEEE Trans. Robotics 28(1):172–182.

    Article  Google Scholar 

  5. Ferreira A, Cassier C, Hirai S (2004) Automatic microassembly system assisted by vision servoing and virtual reality. IEEE/ASME Trans. Mechatron. 9(2):321–333

    Article  Google Scholar 

  6. Gauthier M, Regnier S (2011) Robotic Microassembly. John Wiley & Sons

  7. Hansen EA, Zhou R (2007) Anytime heuristic search. J Art Intell Res 28:267–297.

    Article  MathSciNet  MATH  Google Scholar 

  8. Hart P, Nilsson N, Raphael B (1968) A formal basis for the heuristic determination of minimum cost paths. IEEE Trans Syst Sci Cybern 4(2):100–107.

    Article  Google Scholar 

  9. Julius AA, Sakar MS, Steager E, Cheang UK, Kim M, Kumar V, Pappas GJ (2009) Harnessing bacterial power in microscale actuation. In: IEEE International Conference on Robotics and Automation, pp. 1004–1009 . 10.1109/ROBOT.2009.5152631

  10. Kharboutly M, Gauthier M, Chaillet N (2009) Modeling the trajectory of a microparticle in a dielectrophoresis device. J Appl Phys 106(11):114312

    Article  Google Scholar 

  11. Kim DH, Cheang UK, Kőhidai L, Byun D, Kim MJ (2010) Artificial magnetotactic motion control of tetrahymena pyriformis using ferromagnetic nanoparticles: a tool for fabrication of microbiorobots. Appl Phys Lett 10(1063):3497275

    Google Scholar 

  12. Kim PSS, Becker AT, Ou Y, Kim DH, Julius AA, Kim M (2017) Magnetic swarm control of microorganisms. In: Microbiorobotics, second edition edn., pp. 221–243. Elsevier, Boston

  13. Kulić D, Ott C, Lee D, Ishikawa J, Nakamura Y (2012) Incremental learning of full body motion primitives and their sequencing through human motion observation. The Int J Robotics Res 31(3):330–345.

    Article  Google Scholar 

  14. Lewis F, Vrabie D, Syrmos V (2012) Optimal control of discrete-time systems, chap. 2, pp. 19–109. John Wiley & Sons, Ltd .

  15. Liew LA, Bright V, Dunn M, Daily J, Raj R.: Development of sicn ceramic thermal actuators. Technical Digest. IEEE International Conference on Micro Electro-Mechanical Systems 10.1109/memsys.2002.984340

  16. Nelson BJ, Kaliakatsos IK, Abbott JJ (2010) Microrobots for minimally invasive medicine. Ann Rev Biomed Eng 12(1):55–85.

    Article  Google Scholar 

  17. Ou Y, Kim DH, Kim P, Kim MJ, Julius AA (2012) Motion control of magnetized tetrahymena pyriformis cells by a magnetic field with model predictive control. The Int J Robotics Res 32(1):129–140.

    Article  Google Scholar 

  18. Pearson K (1901) On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2(11):559–572.

  19. Pivtoraiko M, Kelly A (2011) Kinodynamic motion planning with state lattice motion primitives. In: 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2172–2179 . 10.1109/IROS.2011.6094900

  20. Qiu F, Zhang L, Tottori S, Marquardt K, Krawczyk K, Franco-Obregón A, Nelson BJ (2012) Bio-inspired microrobots. Mater Today 15(10):463

    Article  Google Scholar 

  21. Sakar MS, Steager EB, Kim DH, Kim MJ, Pappas GJ, Kumar V (2010) Single cell manipulation using ferromagnetic composite microtransporters. Appl Phys Lett 96:043705.

    Article  Google Scholar 

  22. Shahrokhi S, Lin L, Ertel C, Wan M, Becker AT (2018) Steering a swarm of particles using global inputs and swarm statistics. IEEE Trans Robotics 34(1):207–219.

    Article  Google Scholar 

  23. Steager EB, Sakar MS, Kim DH, Kumar V, Pappas GJ, Kim MJ (2011) Electrokinetic and optical control of bacterial microrobots. J Micromech Microeng 21(3):035001.

    Article  Google Scholar 

  24. Stulp F, Theodorou EA, Schaal S (2012) Reinforcement learning with sequences of motion primitives for robust manipulation. IEEE Trans Robotics 28(6):1360–1370.

    Article  Google Scholar 

  25. Suter M, Zhang L, Siringil EC, Peters C, Luehmann T, Ergeneman O, Peyer KE, Nelson BJ, Hierold C (2013) Superparamagnetic microrobots: fabrication by two-photon polymerization and biocompatibility. Biomed Microdev 15(6):997–1003

    Article  Google Scholar 

  26. Truper T, Kortschack A, Jahnisch M, Hulsen H, Fatikow S (2004) Transporting cells with mobile microrobots. In: IEE Proceedings-Nanobiotechnology 151:145–150

  27. Xu T, Yu J, Yan X, Choi H, Zhang L (2015) Magnetic actuation based motion control for microrobots: an overview. Micromachines 6(9):1346–1364

    Article  Google Scholar 

  28. Zilberstein S (1996) Using anytime algorithms in intelligent systems. AI Mag 17(3):73–83

    Google Scholar 

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This work was supported by National Science Foundation (CMMI#1712096, CMMI#1761060, and CNS#1618369).

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Correspondence to Neelanga Thelasingha.

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Thelasingha, N., Julius, A.A. & Kim, M.J. Ensemble control of spatial variance of microbot systems through sequencing of motion primitives from optimal control trajectories. Intel Serv Robotics 15, 215–230 (2022).

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  • Microbot variance control
  • Motion primitives
  • Heuristic-based motion planning
  • Optimal control
  • Graph search
  • Receding horizon planning