Balance control for a standing biped and stability analysis using the concept of Lyapunov exponents

The mechanics of balance control essential in biped locomotion has attracted much attention in the past two decades. There are three requirements in designing balance controllers: (1) maintaining the postural stability, (2) improving the energy efficiency of the control systems and (3) satisfying the constraints between the foot-link and the ground.;In spite of the attempts, there has been little success in developing balance controllers which satisfy all three requirements. The lack of a constructive tool for stability analysis is one of the obstacles. Stability analysis based on Lyapunov's stability theory is challenging, due both to the complexity of the system and to its inflexibility to include optimization criterion. It has often been assumed that the constraints between the feet and the ground are always satisfied once the feet contact the ground. However, such constraints have significant effect on control design.;This thesis is concerned with biped balancing in the upright standing posture and the stability analysis of the control systems. The work has been carried out with two objectives: (1) design optimal controllers which can satisfy the constraints between the foot-link and the ground while minimizing the energy cost, and (2) perform stability analysis of the proposed systems using the concept of Lyapunov exponents.;The biped robot is simplified as two inverted pendulums, representing the legs and the trunk. The feet are modeled as a separate link, stationary on level ground. Two optimal controllers are proposed in this thesis. A LQR balance control is first designed to optimize the total energy consumption of torque outputs. A GA-based PD balance control is then proposed to satisfy the constraints between the foot-link and the ground; as well as minimize the energy consumption of torque outputs. The effectiveness of the control laws are tested through computer simulations. Note that, the constraints between the foot-link and the ground are not considered in the design of LQR controller, but their satisfaction is tested through simulations.;Since the biped upright posture is inherently unstable, stability analysis of the control systems is required. The concept of Lyapunov exponents is a powerful tool when analyzing the stability of dynamic systems. However, for complex or unknown systems, deriving system Jacobians is extremely difficult.;A novel approach based on neural networks has been proposed for Jacobian derivation. Neural networks are used to identify the system dynamics, and then numerical Jacobians are derived from the neural model for the calculation of Lyapunov exponents. To increase the modeling accuracy of the biped balance system, Radial Basis Function neural networks (RBFNNs) are employed, providing a capability for nonlinear system identification.;The work contributes significantly to the stability analysis of practical complex or unknown engineering systems in that, a reliable and constructive method for calculating Lyapunov exponents based on neural network identification has been developed.