  This paper presents a novel method for directly incorporating user-defined
control input saturations into the calculation of a control Lyapunov function
(CLF)-based walking controller for a biped robot. Previous work by the authors
has demonstrated the effectiveness of CLF controllers for stabilizing periodic
gaits for biped walkers, and the current work expands on those results by
providing a more effective means for handling control saturations. The new
approach, based on a convex optimization routine running at a 1 kHz control
update rate, is useful not only for handling torque saturations but also for
incorporating a whole family of user-defined constraints into the online
computation of a CLF controller. The paper concludes with an experimental
implementation of the main results on the bipedal robot MABEL.
