Ground Reaction Force-Aware Model Predictive Control for Underactuated Upright Physical Assistance
TL;DR GRF-MPC feeds live force-plate measurements of how a person pushes on the ground into a model-predictive controller that sets the cable tensions of a standing-assistance robot. With 4 cables instead of 8, it cut peak center-of-mass error after a push by 19.6% and lunge tracking error by 24.1% compared with an 8-cable impedance controller, in six healthy participants.
What they do
Robots that support a person standing or moving upright usually track a reference with impedance control: they react to position errors but ignore the forces the person is putting into the ground. GRF-MPC measures those ground reaction forces (GRF) and the center of pressure with force plates and puts them into a centroidal-dynamics model of the person, so a model-predictive controller can plan assistance ahead. It runs on RobUST, a frame-mounted cable-driven trainer pulling on a chest belt, with only 4 cables.
How it works
- Human model. The person is one rigid body: center of mass (CoM) from a Vive tracker on the sacrum, inertia from a cylinder sized by mass, height and shoulder width. Measured GRF and CoP enter as an external force, held constant over the horizon.
- Convex MPC. Linearizing at the current state gives a single QP over cable tensions with hard 10-200 N limits. Horizon 0.5 s, replanned at 100 Hz; the QP solves in under 1 ms.
- Low level. A 1 kHz PID loop tracks the commanded tensions from load cells.
- Baselines. An 8-cable Cartesian impedance controller (8 cables are needed for force closure) and a transparent mode with 10 N per cable.
Results
Six healthy participants, nearly 300 trials:
- 150 N backward pulse while standing: 19.6% lower peak CoM error than impedance, which gave no significant reduction over transparent mode. Settling time was 48.0% shorter than in transparent mode and not significantly different from impedance.
- Lunge with a 20 cm CoM drop: 24.1% lower tracking error than impedance with 28.7% less mechanical work.
- Voluntary leaning: 45.9% more excursion area than impedance allowed.
Limitations
Only healthy young adults were tested. The method needs floor force plates, the rigid-body inertia is coarse, and holding GRF constant over the horizon hurts prediction when contact forces change quickly.
Figures
Abstract
Many rehabilitation robots execute prescribed motions using reactive tracking controllers that do not explicitly incorporate the user's instantaneous human-ground interaction. This paper presents Ground Reaction Force-Aware Model Predictive Control (GRF-MPC), a framework for upright physical assistance. By integrating live GRF and center of pressure (CoP) measurements directly into a human centroidal dynamics model, GRF-MPC formulates a real-time quadratic program (QP) that optimizes assistive forces and moments over a receding horizon. We deployed GRF-MPC on the Robotic Upright Stand Trainer (RobUST) in an underactuated 4-cable configuration and evaluated it against a fully actuated 8-cable Cartesian impedance baseline in nearly 300 trials across six healthy participants. Across tasks spanning impulsive perturbations, lunge trajectories, and voluntary limits of stability, GRF-MPC reduced peak planar center-of-mass (CoM) error by 19.6% during perturbations, lowered trajectory tracking error by 24.1%, required 28.7% less net mechanical work, and permitted a 45.9% greater normalized voluntary excursion area. The underlying QP solves in under 1 ms, comfortably enabling 100 Hz replanning and demonstrating that incorporating live human-ground interaction into predictive control yields stronger, more transparent physical assistance with half the actuators.
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