Exploiting the Passive Dynamics of a Compliant Leg to Develop Gait   Transitions
  In the area of bipedal locomotion, the spring loaded inverted pendulum (SLIP) model has been proposed as a unified framework to explain the dynamics of a wide variety of gaits. In this paper, we present a novel analysis of the mathematical model and its dynamical properties. We use the perspective of hybrid dynamical systems to study the dynamics and define concepts such as partial stability and viability. With this approach, on the one hand, we identified stable and unstable regions of locomotion. On the other hand, we found ways to exploit the unstable regions of locomotion to induce gait transitions at a constant energy regime. Additionally, we show that simple non-constant angle of attack control policies can render the system almost always stable. 
Harold Roberto Martinez Salazar and Juan Pablo Carbajal
cs.RO cs.SY math.OC physics.comp-ph