Model Predictive Control vs Whole-Body Control for Locomotion

Model Predictive Control (MPC) excels at handling future constraints and preview dynamics because it continuously solves an online optimization problem over a receding horizon. For example, in the DARPA Robotics Challenge, Atlas used an MPC-based footstep planner to navigate uneven terrain by predicting its center of mass trajectory several steps ahead, achieving a step recovery success rate of over 95% in controlled trials. This predictive capability makes MPC the gold standard for navigating known, structured environments where a reference trajectory is available.

Whole-Body Control (WBC) takes a fundamentally different approach by formulating locomotion as a strict hierarchy of prioritized tasks solved at the joint level in real-time. Instead of optimizing a future trajectory, WBC resolves conflicts between tasks like maintaining balance, tracking a swing foot position, and regulating posture at 1 kHz control loops. This results in superior reactive push recovery; MIT's Cheetah robot demonstrated recovery from unexpected lateral pushes of up to 50 N within 150 ms using a WBC framework, a feat that purely predictive controllers struggle to match without pre-computed trajectories.

The key trade-off: If your priority is navigating complex, pre-mapped terrain with optimal energy efficiency and footstep preview, choose MPC. The computational cost of solving a nonlinear optimization at 50-100 Hz is justified by the quality of the motion plan. If you prioritize robust, reactive stability in the face of unexpected disturbances and unmodeled dynamics, choose WBC. The high-bandwidth, multi-objective task hierarchy provides a safety net that predictive controllers lack when the world model is violated. For many state-of-the-art humanoids, the practical solution is a layered architecture where MPC generates optimal reference trajectories that WBC then robustly tracks while handling real-time perturbations.

Model Predictive Control (MPC) excels at handling future constraints and preview dynamics because it solves a finite-horizon optimal control problem at each time step. For example, an MPC-based humanoid controller can plan footsteps over uneven terrain by optimizing a trajectory that considers the robot's centroidal dynamics and the location of stepping stones 2-3 steps ahead. This predictive capability results in highly anticipatory motion, making it the gold standard for navigating known, structured environments where a reference path is available.

Whole-Body Control (WBC) takes a different approach by solving a reactive, multi-objective optimization problem at the instantaneous joint-torque level. Instead of planning a trajectory, WBC prioritizes a stack of tasks—such as maintaining balance, tracking a hand pose, and regulating posture—while strictly respecting physical constraints like joint limits and friction cones. This results in exceptional robustness to unexpected disturbances. A WBC controller can recover from a sudden shove by instantly reprioritizing all joint torques to maintain the center of mass, a feat that requires complex replanning in a pure MPC framework.

The key trade-off: If your priority is optimal, anticipatory navigation through complex but known environments, choose MPC. Its ability to reason about the future makes it superior for efficient, elegant motion. If you prioritize robust, reactive disturbance recovery and the ability to handle multiple simultaneous, conflicting objectives in real-time, choose WBC. For the most advanced bipedal systems, a hierarchical architecture—using MPC to generate an optimal trajectory for WBC to track—often provides the best of both worlds, combining foresight with reactive stability.