Implementing Regularized Predictive Control for Simultaneous RealTime Footstep and Ground Reaction Force Optimization This work presents a successful implementation of a nonlinear optimizationbased Regularized Predictive Control (RPC) for legged locomotion on the MIT Cheetah 3 robot platform. Footstep placements and ground reaction forces at the contact feet are simultaneously solved for over a prediction horizon in realtime. Often in academic literature not enough attention is given to the implementation details that make the theory work in practice and many times it is precisely these details that end up being critical to the success or failure of the theory in real world applications. Nonlinear optimization for realtime legged locomotion control in particular is one of the techniques that has shown promise, but falls short when implemented on hardware systems subjected to computation limits and undesirable local minima. We discuss various algorithms and techniques developed to overcome some of the challenges faced when implementing nonlinear optimizationbased controllers for dynamic legged locomotion.

Online Relative Footstep Optimization for Legged Robots Dynamic Walking Using DiscreteTime Model Predictive Control We present a unified control framework that generates dynamic walking motions for biped and quadruped robots with online relative footstep optimization. The footstep optimization is formulated as a discretetime Model Predictive Control problem which determines future footstep locations. The framework has a hierarchical structure consisting of three layers: footstep planner, trajectory generator and wholebody controller. The footstep planner plans next footstep position based on Linear Inverted Pendulum (LIP) model. Relative footstep optimization is proposed to enable automatic footstep planning without the use of any predefined footstep sequences. The trajectory generator will generate CoM and feet trajectory given the next footstep placement. In order to generalize to quadruped robots, xe2x80x9cvirtual legxe2x80x9d concept has been used to coordinate leg pair movement. The wholebody inverse dynamic controller calculates joint torques to track given Cartesian reference trajectories. To include underactuation into consideration, contact vertices formulation of ground reaction forces (GRFs) has been adopted. Generalized wholebody controller can handle biped robot with line feet as well as quadruped robots with point feet walking with dynamic gaits. Several simulations have been performed to demonstrate the robustness and generality of the proposed framework.