ROAR Lab Columbia Mechanical Engineering

Ground Reaction Force-Aware Model Predictive Control for Underactuated Upright Physical Assistance

Darren Biskup1, Jeonghan Yu1,2,*, Zibo Yu1,*, and Sunil K. Agrawal1,†
1Robotics and Rehabilitation (ROAR) Lab, Columbia University  •  2SUNY Korea
* Equal contribution   † Corresponding author
IEEE Robotics and Automation Letters (RA-L), 2026
Paper link coming! Code YouTube
8-Cable Impedance Perturbation
Baseline: 8-Cable Impedance Control. Reactive response yields higher peak CoM displacement.
4-Cable GRF-MPC Perturbation
This work: 4-Cable GRF-MPC. Proactive force optimization reduces peak excursion by 19.6%.

Motivation & Abstract

Current assistive exoskeletons and rehabilitation robots are fundamentally limited by their inability to predict human volitional joint torques. To guarantee stability, these systems typically pre-compute trajectories that satisfy ZMP stability constraints—then enforce them via stiff reactive tracking. This approach fundamentally treats all deviations from the planned trajectory as disturbances which can counteract human intent.

This paper presents GRF-MPC (Ground Reaction Force-Aware Model Predictive Control), a proactive control framework for underactuated upright physical assistance. By integrating live GRF and center of pressure (CoP) measurements directly into a single-rigid-body centroidal dynamics model, GRF-MPC predicts Center of Mass evolution without estimating internal joint torques or full-body multibody kinematics. At each timestep, a quadratic program optimizes assistive cable tensions over a receding horizon while strictly enforcing tension bounds in under 1 ms, comfortably enabling real-time 100 Hz replanning.

Deployed on the cable-driven Robotic Upright Stand Trainer (RobUST) across nearly 300 human-subject trials, an underactuated 4-cable GRF-MPC was evaluated against a fully actuated 8-cable Cartesian impedance baseline. Operating with half the actuators, GRF-MPC reduced peak planar CoM error during impulse perturbations by 19.6%, lowered dynamic lunge tracking error by 24.1%, required 28.7% less net mechanical work, and permitted a 45.9% larger normalized volitional workspace.

System Architecture

Hardware Schematic
Schematic of the custom cable-driven system highlighting motion tracking and force plate integration.
Centroidal Dynamics MPC Block Diagram
Control block diagram mapping contact GRFs to the human spatial Center of Mass via single rigid body approximation.

Dynamic Tracking (Lunge Task)

8-Cable Impedance Lunge
Baseline: 8-Cable Impedance Control: rigid path enforcement.
4-Cable GRF-MPC Lunge
This work: 4-Cable GRF-MPC: Improved tracking with less robotic effort.

Summary Video

BibTeX

@article{Biskup2026,
    title={Ground Reaction Force-Aware Model Predictive Control for Underactuated Upright Physical Assistance},
    author={Biskup, Darren and Yu, Jeonghan and Yu, Zibo and Agrawal, Sunil K.},
    journal={IEEE Robotics and Automation Letters (RA-L)},
    year={2026},
    publisher={IEEE}
}