Graph Neural Model Predictive Control for High-Dimensional Systems
Patrick Benito Eberhard, Luis Pabon, Daniele Gammelli, Hugo Buurmeijer, Amon Lahr, Mark Leone, Andrea Carron, Marco Pavone
AI summary
Problem
Controlling high-dimensional, compliant systems like soft robots requires accurate dynamic models that remain computationally tractable for real-time optimal control, but existing methods struggle with the fidelity-speed trade-off and prohibitive solve times. Integrating expressive relational models like GNNs into MPC remains underexplored due to a lack of sparsity exploitation.
Approach
The system is modeled as a graph with localized interactions, and a GNN learns its dynamics. A tailored condensing algorithm then eliminates state variables from the MPC optimization problem, leveraging the GNN's sparse structure for linear scaling and GPU parallelization.
Key results
- Linear scaling of condensing algorithm with node count
- Closed-loop control of 1,000-node systems at 100 Hz
- 63.6% reduction in trajectory tracking error on hardware
- Effective full-body obstacle avoidance
Why it matters
Enables scalable, real-time optimal control for complex soft and continuum robots, advancing safe manipulation, locomotion, and medical applications.
Abstract
The control of high-dimensional systems, such as soft robots, requires models that faithfully capture complex dynamics while remaining computationally tractable. This work presents a framework that integrates Graph Neural Net- work (GNN)-based dynamics models with structure-exploiting Model Predictive Control to enable real-time control of high- dimensional systems. By representing the system as a graph with localized interactions, the GNN preserves sparsity, while a tailored condensing algorithm eliminates state variables from the control problem, ensuring efficient computation. The complexity of our condensing algorithm scales linearly with the number of system nodes, and leverages Graphics Processing Unit (GPU) parallelization to achieve real-time performance. The proposed approach is validated in simulation and exper- imentally on a physical soft robotic trunk. Results show that our method scales to systems with up to 1,000 nodes at 100 Hz in closed-loop, and demonstrates real-time reference tracking on hardware with sub-centimeter accuracy, outperforming baselines by 63.6%. Finally, we show the capability of our method to achieve effective full-body obstacle avoidance. Website: https://gnn-mpc.github.io/