  With the goal of moving towards implementation of increasingly dynamic
behaviors on underactuated systems, this paper presents an optimization-based
approach for solving full-body dynamics based controllers on underactuated
bipedal robots. The primary focus of this paper is on the development of an
alternative approach to the implementation of controllers utilizing control
Lyapunov function based quadratic programs. This approach utilizes many of the
desirable aspects from successful inverse dynamics based controllers in the
literature, while also incorporating a variant of control Lyapunov functions
that renders better convergence in the context of tracking outputs. The
principal benefits of this formulation include a greater ability to add costs
which regulate the resulting behavior of the robot. In addition, the model
error-prone inertia matrix is used only once, in a non-inverted form. The
result is a successful demonstration of the controller for walking in
simulation, and applied on hardware in real-time for dynamic crouching.
