  We present an advanced and novel control method to enable actuated Spring
Loaded Inverted Pendulum model to walk over rough and challenging terrains. The
high-level philosophy is the decoupling of the controls of the vertical and
horizontal states. The vertical state is controlled via Backstepping-Barrier
Function (BBF) based quadratic programs: a combination of control Lyapunov
backstepping and control barrier function, both of which provide inequality
constraints on the inputs. The horizontal state is stabilized via Hybrid-Linear
Inverted Pendulum (H-LIP) based stepping, which has a closed-form formulation.
Therefore, the implementation is computationally-efficient. We evaluate our
method in simulation, which demonstrates the aSLIP walking over various
terrains, including slopes, stairs, and general rough terrains with
uncertainties.
