Robust stabilization in a single-link biomechanical model: a time-domain analysis

In this paper we analyze the robust stabilization of posture in a single-link biomechanical model with force feedback, dual position and velocity feedback, and with delays in all the three feedback loops. The model is physiologically motivated and represents gross approximation of the human neuromusculoskeletal system in the sagittal plane. The feedback paths in the model represent proprioceptive feedback from muscle spindle (MS) and the Golgi tendon organ (GTO), and include the latencies present in the physiological system. Lyapunov functional approach is used to guarantee asymptotic stability with arbitrary feedback delays. The approach leads to linear matrix inequality (LMI)-based delay-independent conditions requiring solution of a set of finite-dimensional algebraic Riccati inequalities. The framework can be extended to Hinfin feedback control synthesis for single and multi-link robotic models with state or feedback delays

[1]  B. E. Maki,et al.  Influence of lateral destabilization on compensatory stepping responses. , 1996, Journal of biomechanics.

[2]  Frans C. T. van der Helm,et al.  Musculoskeletal Systems with Intrinsic and Proprioceptive Feedback , 2000 .

[3]  J. He,et al.  Feedback gains for correcting small perturbations to standing posture , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[4]  M. Mahmoud.  Robust Control and Filtering for Time-Delay Systems , 2000 .

[5]  Hooshang Hemami,et al.  Modeling and control of biological systems with multiple afferent and efferent transmission delays , 2000, J. Field Robotics.

[6]  Y C Pai,et al.  Simulated movement termination for balance recovery: can movement strategies be sought to maintain stability in the presence of slipping or forced sliding? , 1999, Journal of biomechanics.

[7]  Hooshang Hemami,et al.  Point to point motion of skeletal systems with multiple transmission delays , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[8]  V. Kharitonov,et al.  On delay-dependent stability conditions ☆ , 2000 .

[9]  Hooshang Hemami,et al.  Modeling and control of biological systems with multiple afferent and efferent transmission delays , 2000, J. Field Robotics.

[10]  G. Loeb,et al.  Feedback gains for correcting small perturbations to standing posture , 1991 .

[11]  P. Camana,et al.  DETERMINATION OF FEEDBACK FOR HUMAN POSTURE CONTROL WITHOUT PHYSICAL INTERVENTION , 1977 .

[12]  Y. Pai,et al.  Predicted region of stability for balance recovery: motion at the knee joint can improve termination of forward movement. , 2000, Journal of biomechanics.

[13]  V. Kolmanovskii,et al.  On the Liapunov-Krasovskii functionals for stability analysis of linear delay systems , 1999 .

[14]  Hooshang Hemami,et al.  Postural stability of the two-degree-of-freedom biped by general linear feedback , 1976 .

[15]  L. Dugard,et al.  Delay-dependent stability of linear systems with delayed state: an LMI approach , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[16]  Ian E. Brown,et al.  A Reductionist Approach to Creating and Using Neuromusculoskeletal Models , 2000 .

[17]  F. Horak,et al.  Central programming of postural movements: adaptation to altered support-surface configurations. , 1986, Journal of neurophysiology.

[18]  L. Nashner,et al.  The organization of human postural movements: A formal basis and experimental synthesis , 1985, Behavioral and Brain Sciences.

[19]  H. Hemami,et al.  Constrained Inverted Pendulum Model For Evaluating Upright Postural Stability , 1982 .