Our research is advancing Lyapunov-funciton based controllers that offer formal guarantees on stability along the three axis of constraints, model uncertainty, and safety-critical constrains. This enables taking a feedback controller that stabilize periodic orbits and enable the following features: - Enforce input constraints such as torque saturation; - Enforce input and state constraints such as unilateral ground contact force constraints and friction constraints; - Enforce safety-critical constraints such as precise footstep placements for walking dynamically on stepping stones or UAV flight while avoiding collisions; and - Do all of the above while also being subject to significant model uncertainty.