Tailoring Complexity of Model-Based Controllers for Legged Robots

Abstract

Humanoid robots promise human-like mobility, but must manage complex and often conflicting control objectives. While model-based controllers can address these challenges using online optimization, they have high computational demands. Model predictive control (MPC) provides closed-loop stability with online trajectory optimization, but achieving real-time rates is difficult for high-dimensional systems. To mitigate this limitation, most MPC implementations rely on reduced-order models (ROMs) that simplify planning but fail to capture whole-body constraints like joint limits and self-collisions. Reactive whole-body controllers (WBCs) partially address this limitation by projecting ROM trajectories onto some wholebody constraints, but these are restricted to acceleration-level constraints like friction cones and torque limits. This thesis advances humanoid planning and control through a renewed focus on model fidelity, solution accuracy ans solve times with three key contributions. First, we propose the CBF-WBC, which augments reactive WBCs with position constraints using control barrier functions (CBFs), enabling the MIT Humanoid to avoid selfcollisions with minimal computational overhead. As a result, the robot can reactively deviate from infeasible trajectories from a reduced-order MPC. Despite fast solve times below 100 microseconds, conflicts can arise between the reduced-order MPC and the CBF-WBC. To address this, we enable real-time whole-body MPC using the alternating direction method of multipliers (ADMM) to provide low-accuracy solutions at high feedback rates. The controller is reliably deployed on hardware and enables the MIT Humanoid to walk robustly on rough terrains and plan complex crossed-leg and arm motions that enhance stability when recovering from significant disturbances. While low-accuracy solutions often suffice for real-time control, we found that higher accuracy could still improve closed-loop performance if computational speed allows. Building on this insight, we propose a framework to simultaneously optimize solution accuracy and model complexity to maximize closed-loop performance. Instead of planning with a single model that is too complex or too simple, solve times can be reduced by planning over a sequence of models of reducing complexity. We extract ROMs from whole-body dynamics equations and optimize their horizons, discretization timesteps and solution accuracy using blackbox optimization. The optimizer can sacrifice model complexity for additional ADMM iterations, reducing falls by nine-fold and enabling a 2 m/s walking speed on hardware.