  In this paper, we propose a novel framework capable of generating various
walking and running gaits for bipedal robots. The main goal is to relax the
fixed center of mass (CoM) height assumption of the linear inverted pendulum
model (LIPM) and generate a wider range of walking and running motions, without
a considerable increase in complexity. To do so, we use the concept of virtual
constraints in the centroidal space which enables generating motions beyond
walking while keeping the complexity at a minimum. By a proper choice of these
virtual constraints, we show that we can generate different types of walking
and running motions. More importantly, enforcing the virtual constraints
through feedback renders the dynamics linear and enables us to design a
feedback control mechanism which adapts the next step location and timing in
face of disturbances, through a simple quadratic program (QP). To show the
effectiveness of this framework, we showcase different walking and running
simulations of the biped robot Bolt in the presence of both environmental
uncertainties and external disturbances.
