  We are seeking control design paradigms for legged systems that allow
bypassing costly algorithms that depend on heavy on-board computers widely used
in these systems and yet being able to match what they can do by using less
expensive optimization-free frameworks. In this work, we present our
preliminary results in modeling and control design of a quadrupedal robot
called \textit{Husky Carbon}, which under development at Northeastern
University (NU) in Boston. In our approach, we utilized a supervisory
controller and an Explicit Reference Governor (ERG) to enforce ground reaction
force constraints. These constraints are usually enforced using costly
optimizations. However, in this work, the ERG manipulates the state references
applied to the supervisory controller to enforce the ground contact constraints
through an updated law based on Lyapunov stability arguments. As a result, the
approach is much faster to compute than the widely used optimization-based
methods.
