  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.
