MPC Formulation and Numerical Optimization for Online Synthesis of Athletic Maneuvers with Quadruped Robots

The potential of legged robots lies in their ability to replicate the mobility and agility of humans and animals. Despite notable advancements in recent decades, existing control methods have yet to fully capture the highly dynamic maneuvers observed in nature, such as athletic parkour and jumping. The primary goal of this dissertation is to elevate the dynamic capabilities of quadruped robots to new heights. A major contribution toward this goal is the conceptual development, benchmarking, and successful implementation of a Cascaded-Fidelity Model Predictive Control (CAFE-MPC) framework, which enables a running barrel roll on quadruped robots for the first time. Model Predictive Control (MPC) is a key control technique for legged locomotion, which functions by repeatedly solving Trajectory Optimization (TO) problems. Dynamic behaviors such as a barrel roll involve fast dynamics, demanding a fast udpate rate and reasoning over the whole-body dynamics, posing computational challenges to MPC. This dissertation proposes to address these challenges using two approaches. The first approach is concerned with developing a real-time TO solver. A particular interest herein is on Differential Dynamic Programming (DDP), which naturally has linear computational complexity relative to the prediction horizon. We leverage this favorable property and extend DDP to handle a multiple-shooting formulation and to be applicable to hybrid systems (e.g., legged robots). The second approach seeks to mitigate the computational burden of MPC from a formulation perspective. CAFE-MPC is proposed to relax the planning problem along the prediction horizon, posing a TO problem that is computationally more tractable. In addition, a value-based whole-body controller (VWBC) is formulated for enhanced bandwidth without additional tuning. The DDP-based solver, CAFE-MPC and VWBC synergize to streamline the MPC process, enabling highly dynamic maneuvers like a running barrel roll in experiments with MIT Mini Cheetah.