On Lyapunov´s stability control of two-link base-excited inverted pendulums with applications to human locomotion

Control of a chain of two planar inverted pendulums is studied in this paper. The goal is to keep the pendulums at the upright position in spite of the free base point motion. First a piecewise continuous controller is developed which guarantees the global stability of the system in the sense of Lyapunov. This idealized controller, however, is not desirable from the implementation viewpoint. A continuous control law is then proposed. It is found that the continuous controller only guarantees the stability in a suitable sense. The effectiveness of the developed controllers is tested through computer simulations. The above inverted pendulums are then used to simulate human thorax and pelvic movement during walking. The simulation results are compared with those from gait measurements and found that the above pendulums are capable of producing displacements and torques for the human thorax and the pelvis during normal walking