  We propose a hybrid formulation of the linear inverted pendulum model for
bipedal locomotion, where the foot switches are triggered based on the center
of mass position, removing the need for pre-defined footstep timings. Using a
concept similar to reference spreading, we define nontrivial tracking error
coordinates induced by our hybrid model. These coordinates enjoy desirable
linear flow dynamics and rather elegant jump dynamics perturbed by a suitable
extended class ${\mathcal K}_\infty$ function of the position error. We
stabilize this hybrid error dynamics using a saturated feedback controller,
selecting its gains by solving a convex optimization problem. We prove local
asymptotic stability of the tracking error and provide a certified estimate of
the basin of attraction, comparing it with a numerical estimate obtained from
the integration of the closed-loop dynamics. Simulations on a full-body model
of a real robot show the practical applicability of the proposed framework and
its advantages with respect to a standard model predictive control formulation.
