Walking dynamics of a semi-passive compass-like robot with impulse thrust

In this paper, a two-DoF (degree-of-freedom) semi-passive compass-like biped model with nonlinear impulse thrust is considered and investigated. Conditions for the existence and stability of period gaits of the linearized system are obtained. The conditions for flip bifurcation of periodic gait are derived, and bifurcation control is rigorously studied. The results show that impulse thrust and the angle between two legs at the impact can modify the stability of the semi-passive compass-like biped model and lead to chaos through flip bifurcation. It is possible to improve the stability of compass-like biped model by bifurcation control. Period-n gait (n > 2) and chaotic gait are stabilized to period-1 gait or period-2 gait by reducing the angle between the two legs at the impact. Numerical results for periodic gaits, bifurcation diagrams and bifurcation control diagrams are illustrated with an example, and they are in good agreement with the theoretical analysis. The obtained results about period gaits and bifurcation of the linearized system can be used to predict the nonlinear walking pattern.