Stability and control of a two-link inverted pendulum system with application to human trunk movement during walking
The purpose of this study is to contribute to the development of a mathematical model in order to study the control mechanisms of human upper body movement during walking. The upper body, which consists of the pelvis and thorax, is modeled as a chain of inverted pendulums with one degree of rotational freedom each. The base point of the model corresponds to the bony landmark of the sacrum, and can move, two-dimensionally, in a specified way. A control law is developed in order to ensure the stability of the two-link pendulum system about the upright position. The control law is based on Lyapunov's stability theory and contains feedforward and linear feedback components. It is shown that the feedforward element of the controller is essential for the system stability, while the feedback component heavily influences the pattern in which the two-link inverted pendulum system moves about the upright position. Comparing the simulation results with measured results obtained in the Biomechanics Laboratory at the University of Manitoba it is shown that the mathematical model can effectively duplicate the motion patterns of the thorax and pelvis of a human. The results of the comparison make it possible to use the proposed mathematical model as a conceptual model in order to study the involvement of the central nervous system (CNS) in the performance of skilled voluntary motion such as walking.