Energy efficient stability control of a biped based on the concept of Lyapunov exponents
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Date
2012-08, 2012-08, 2011-08
Authors
Sun, Yuming
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Taylor and Francis
Taylor and Francis
Taylor and Francis
Taylor and Francis
Abstract
Balance control is important for biped standing. Due to the time-varying control bounds induced by the foot constraints, and the lack of tools for analyzing stability of highly nonlinear systems, it is extremely difficult to design balance control strategies for a standing biped with a rigorous stability analysis in spite of large efforts. In this thesis, three important issues are fully considered for a standing biped: maintaining the postural stability, minimizing the energy consumption and satisfying the constraints between the biped feet and the ground. Both the theoretical and the experimental studies on the constrained and energy-efficient control are carried out systematically using the genetic algorithm (GA). The stability for the proposed balancing system is thoroughly investigated using the concept of Lyapunov exponents. On the other hand, the controlled standing biped is characterized by high nonlinearity and great complexity. For systems with such features, in general the Lyapunov exponents are hard to be estimated using the model-based method. Meanwhile the biped is supposed to be stabilized at the upright posture, indicating that the system should possess negative Lyapunov exponents only. However the accuracy of negative exponents is usually poor if following the traditional time-series-based methods. As it is nontrivial to examine the system stability for bipedal robots, the numerical accuracy of the estimated Lyapunov exponents is extremely demanding. In this research, two novel approaches are proposed based upon system approximation using different types of Radial-Basis-Function (RBF) networks. Both the proposed methods can estimate the exponents reliably with straightforward algorithms, yet no mathematical model is required in any newly developed method. The efficacies of both methods are demonstrated through a linear quadratic regulator (LQR) balancing system for a standing biped, as well as several other dynamical systems. The thesis as a whole, has set up a framework for developing more sophisticated controllers in more complex movement for robot models with less conservative assumptions. The systematic stability analysis shown in this thesis has a great potential for many other engineering systems.
Description
Keywords
Control of bipeds, Stability analysis, Lyapunov exponents, Nonlinear dynamics
Citation
Sun, Y. and Wu, Q., 2012, A radial-basis-function-network-based method of estimating Lyapunov exponents from a scalar time series for analyzing nonlinear systems stability, Nonlinear Dynamics, 70 (2): 1689-1708.
Sun, Y. and Wu, C. Q., 2012, Stability analysis via the concept of Lyapunov exponents: a case study in optimal controlled biped standing, International Journal of Control, 85 (12): 1952-1966.
Sun, Y., Wang, X., Wu, Q. and Sepehri, N., 2011, On stability analysis via Lyapunov exponents calculated based on Radial Basis Function networks, Internal Journal of Control, 84 (8): 1326-1341.
Sun, Y. and Wu, C. Q., 2012, Stability analysis via the concept of Lyapunov exponents: a case study in optimal controlled biped standing, International Journal of Control, 85 (12): 1952-1966.
Sun, Y., Wang, X., Wu, Q. and Sepehri, N., 2011, On stability analysis via Lyapunov exponents calculated based on Radial Basis Function networks, Internal Journal of Control, 84 (8): 1326-1341.