Broadcast Feedback of Stochastic Cellular Actuators Inspired by Biological Muscle Control

Abstract

This paper presents a broadcast feedback approach to the distributed stochastic control of an actuator system consisting of many cellular units. This control architecture was inspired by skeletal muscles comprising a vast number of tiny functional units, called sarcomeres. The output of the actuator system is an aggregate e fect of numerous cellular units, each taking a bistable ON—OFF state. A central controller “broadcasts” the error between the aggregate output and a reference input. Rather than ordering the individual units to take specific states, the central controller merely broadcasts the overall error signal to all the cellular units uniformly. In turn each cellular unit makes a stochastic decision with a state transition probability, which is modulated in relation to the broadcasted error. Stochastic properties of both open-loop and closed-loop control systems are analyzed. Stability conditions of the broadcast feedback system are obtained by using a stochastic Lyapunov function. The proposed method is simulated for an artificial cellular actuator, consisting of many segments of smart actuator material. Theoretical results are verified through simulation. It is demonstrated that, even in the absence of deterministic coordination, the ensemble of the cellular units can track a given trajectory stably and robustly.

Keywords

smart actuators broadcast stochastic stability Markov chain cellular control system distributed robot systems muscle

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References

Blom, H. A. and Lygeros, J. , editors (2006). Stochastic Hybrid Systems: Theory and Safety Critical Applications (Lecture Notes in Control and Information Sciences). Springer , 1 edition.

Conway, N.J. and Kim, S.-G. (2004). Large-strain, piezoelectric, in-plane micro-actuator . In 17th IEEE International Conference on Micro Electro Mechanical Systems (IEEE MEMS), pp. 454—457.

Deng, H. and Krstic, M. (1999). Output-feedback stochastic nonlinear stabilization. Automatic Control , IEEE Transactions on, 44(2): 328—333 .

Doob, J.L. (1990). Stochastic Processes (Wiley Classics Library) . Wiley-Interscience , reprint edition.

Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Volume 1. Wiley , 3 edition.

Fu, Y. , Du, H. , Huang, W. , Zhang, S. , and Hu, M. (2004). TiNibased thin films in MEMS applications: a review. Sensors and actuators . A, Physical, 112(2—3): 395—408 .

Hara, S. , Zama, T. , Takashima, W. , and Kaneto, K. (2004). Artificial muscles based on polypyrrole actuators with large strain and stress induced electrically . Polymer journal, 36(3): 151—161 .

Hu, J. , Lygeros, J. , and Sastry, S. (2000). Towards a theory of stochastic hybrid systems . Hybrid Systems: Computation and Control, 1790: 160—173 .

Kitamura, K. and Yanagida, T. (2003). Stochastic properties of actomyosin motor . Biosystems, 71(1—2): 101—110 .

10.

Kostyukov, A.I. (1998). Muscle hysteresis and movement control: a theoretical study . Neuroscience, 83(1): 303—320 .

11.

Kushner, H. (1965). On the Stability of Stochastic Dynamical Systems . Proceedings of the National Academy of Sciences, 53(1): 8—12 .

12.

Kushner, H.J. (1967). Stochastic stability and control (Mathematics in science and engineering). Academic Press .

13.

Madill, D. and Wang, D. (1998). Modeling and L 2-stability of a shape memory alloyposition control system . IEEE Transactions on Control Systems Technology , 6(4): 473— 481 .

14.

Martini, F.H. and Bartholomew, E.F. (2006). Essentials of Anatomy & Physiology (4th Edition). Benjamin Cummings , 4 edition.

15.

Moritz, C.T. , Barry, B.K. , Pascoe, M.A. , and Enoka, R.M. (2005). Discharge rate variability influences the variation in force fluctuations across the working range of a hand muscle . J Neurophysiol, 93(5): 2449—2459 .

16.

Plante, J. and Dubowsky, S. (2006). On the nature of dielectric elastomer actuators and its implications for their design. Smart Structures and Materials 2006: Smart Sensor Monitoring Systems and Applications . Edited by Inaudi, Daniele; Ecke, Wolfgang ; Culshaw, Brian; Peters, Kara J.; Udd, Eric. Proceedings of the SPIE,, 6168: 424—434 .

17.

Selden, B. , Cho, K.-J. , and Asada, H. (2004). Segmented binary control of shape memory alloy actuator systems using the peltier effect . In Proceedings of 2004 IEEE International Conference on Robotics and Automation (ICRA '04), volume 5, pp. 4931—4936.

18.

Shahinpoor, M. , Kim, K. , and Schreyer, H. (2000). Artificial sarcomere and muscle made with conductive polyacrylonitrile(C-PAN) fiber bundles . SPIE's 7 th International Symposium on Smart Structures and Materials and SPIE's 5 th International Symposium on Nondestructive Evaluation and Health Monitoring of Aging Infrastructure, p. 2000.

19.

Srinivasan, A. , McFarland, D. , Canistraro, H. , and Begg, E. (1997). Multiplexing embedded NiTiNOL actuators to obtain increased bandwidth in structural control . Journal of intelligent material systems and structures, 8(3): 202— 214 .

20.

Stanley W. , M. J. (1982). Structure and Function in Man. W B Saunders Co , fifth edition.

21.

Stern, M.D. , Pizarro, G. , and Rs, E. (1997). Local control model of excitation-contraction coupling in skeletal muscle . J Gen Physiol, 110(4): 415—440 .

22.

Tyreman, M.J.A. and Molloy, J.E. (2003). Molecular motors: nature's nanomachines . IEE Proc Nanobiotechnol, 150(3): 95—102 .

23.

Ueda, J. , Odhnar, L. , and Asada, H. (2006a). A broadcast-probability approach to the control of vast dof cellular actuators . In Proceedings of 2006 IEEE International Conference on Robotics and Automation (ICRA '06) , pp. 1456— 1461.

24.

Ueda, J. , Odhner, L. , Kim, S.-G. , and Asada, H. (2006b). Distributed stochastic control of mems-pzt cellular actuators with broadcast feedback . In The First IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob 2006), pp. 272—277.