Graph Neural Model Predictive Control for High-Dimensional Systems
Authors: Patrick Benito Eberhard, Luis Pabon, Daniele Gammelli, Hugo Buurmeijer, Amon Lahr, Mark Leone, Andrea Carron, Marco Pavone
Organizations: Institute for Dynamic Systems and Control, ETH Zürich, Zürich CH-8092, Switzerland · Department of Aeronautics and Astronautics, Stanford University, Stanford, CA · NVIDIA Research
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 Network (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 experimentally 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.
Figures & tables
Fig. 1 : A soft robotic trunk is modeled as a graph with nodes as discrete segments with state xti at time t and edges as physical interactions. A GNN computes the linearized forward dynamics xki , which are condensed into a Quadratic Program (QP) that only depends on the input variables uk . The QP is then solved, and the first input u0 is applied in a receding-horizon fashion.
Model
RMSE [m]
Koopman
(1.16±0.61)×10−3
GNN
(1.38±0.76)×10−3
SSM (Opt.)
(2.88±1.25)×10−3
MLP
(3.59±1.67)×10−3
SSM (Orth.)
(3.67±2.22)×10−3
TABLE I : Average end-effector open-loop RMSE across models, reported as mean ±1σ standard deviation.
Fig. 2 : Scalability of the proposed GNN - MPC framework with respect to the number of subsystems M . The computation times of the relevant stages in Algorithm 1 are shown in log-log scale.
Fig. 3 : Reference tracking of a circle and figure-eight using (a) Koopman Operator modeling, (b) SSM orthogonal reduction and (c) our GNN - MPC approach. The reference is shown in dashed black, while the closed-loop trajectories are shown in red. We additionally provide the MPC plans for each time step in grey.
Fig. 4 : Deflection of the trunk as the obstacle approaches the middle node. The end effector attempts to remain as close as possible to its resting position.
Fig. 5 : Deflection of the trunk as the obstacle approaches the end effector node. The latter moves further away from the obstacle compared to the previous scenario.
New York University, NY 10012, USA · University of California Berkeley, Department of Electrical Engineering and Computer Sciences, Berkeley, CA 94720, USA