The Surprising Effectiveness of Linear Models for Whole-Body Model-Predictive Control (under construction)

Arun Bishop, Juan Alvarez-Padilla, Sam Schoedel, Ibrahima Sory Sow, Juee Chandrachud, Sheitej Sharma, Will Kraus, Beomyeong Park, Robert J. Griffin, John M. Dolan, and Zachary Manchester

Carnegie Mellon University, Florida Institute for Human and Machine Cognition
Humanoids 2025

Paper Code arXiv

Coming Soon!

TL;DR

When do locomotion controllers require reasoning about nonlinearities? In this work, we show that a whole-body model-predictive controller using a simple linear time-invariant approximation of the whole-body dynamics is able to execute basic locomotion tasks on complex legged robots. The formulation requires no online nonlinear dynamics evaluations or matrix inversions. We demonstrate walking, disturbance rejection, and even navigation to a goal position without a separate footstep planner on a quadrupedal robot. In addition, we demonstrate dynamic walking on a hydraulic humanoid, a robot with significant limb inertia, complex actuator dynamics, and large sim-to-real gap.

Hardware Experiments

Humanoid walking forward with a 0.6 second swing phase and a 0.3 second flight phase (not quasi-static)

Humanoid walking in place for over a minute

Quadruped returning to the initial position without assistance from a footstep planner

Quadruped perturbance recovery while stepping in place

Quadruped jumping

Quadruped stepping over a 24 cm box

The hydraulic humanoid Nadia walking forward over multiple steps using our convex MPC formulation with linear time-invariant dynamics constraints. The gait has a stride length of 30 cm, a swing phase of 0.6 s and a double support phase of 0.3 s.

Top-down view of two perturbations applied to the Unitree Go2 while stepping in place. The robot maintains contact with the ground without slipping and return to its original location.

A Unitree Go2 robot starts from 10 initial conditions with yaw from 5 to 90° and displacements from 0.1 to 1.7 m. Transparent overlays show keyframes starting with 90° yaw and 1.3 m displacement. Our controller is able to return to the initial position without assistance from a footstep planner.

Keyframes of a Unitree Go2 robot stepping onto a 24 cm box. The robot tracks a trajectory with up to 60 degrees joint deviation and 10 degrees pitch deviation from the linearization pose, with the green dashed skeleton showing the linearization pose.

Foot and center-of-mass trajectories across six humanoid walking trials (black) over the desired foot placement positions and center of mass trajectory (blue, dashed). Our controller is able to track the trajectory with minor deviations despite large modeling errors.

Video Presentation

Youtube embed code here

BibTeX

@inproceedings{bishop2025linearwalking,
      title={The Surprising Effectiveness of Linear Models for Whole-Body Model-Predictive Control},
      author={Bishop, Arun and Alvarez-Padilla, Juan and Schoedel, Sam and Sow, Ibrahima S. and Chandrachud, Juee and Sharma, Sheitej and Kraus, Will and Park, Beomyeong and Griffin, Robert J.},
      url = {TBD},
      booktitle = {IEEE International Conference on Humanoid Robots},
      year={2025},
    }