Occurrence of Complex Behaviors in the Uncontrolled Passive Compass Biped Model

It is widely known that an appropriately built unpowered bipedal robot can walk down an inclined surface with a passive steady gait. The features of such gait are determined by the robot's geometry and inertial properties, as well as the slope angle. The energy needed to keep the biped moving steadily comes from the gravitational potential energy as it descends the inclined surface. The study of such passive natural motions could lead to ideas for managing active walking devices and a better understanding of the human locomotion. The major goal of this study is to further investigate order, chaos and bifurcations and then to demonstrate the complexity of the passive bipedal walk of the compass-gait biped robot by examining different bifurcation diagrams and also by studying the variation of the eigenvalues of the Poincaré map's Jacobian matrix and the variation of the Lyapunov exponents. We reveal also the exhibition of some additional results by changing the inertial and geometrical parameters of the bipedal robot model.