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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

TL;DR

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, and shows the capability of the method to achieve effective full-body obstacle avoidance.

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 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.

Graph Neural Model Predictive Control for High-Dimensional Systems

TL;DR

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, and shows the capability of the method to achieve effective full-body obstacle avoidance.

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 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.
Paper Structure (18 sections, 1 theorem, 20 equations, 5 figures, 1 table, 1 algorithm)

This paper contains 18 sections, 1 theorem, 20 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Background
  4. Graph Neural Networks
  5. Condensing in
  6. Problem Formulation
  7. Local System Dynamics
  8. Control Task
  9. Graph Neural Model Predictive Control
  10. Modeling Dynamics with GNNs
  11. Local-Scalable Condensing
  12. - Algorithm
  13. Experimental Results
  14. Setup
  15. Simulation experiments
  16. ...and 3 more sections

Key Result

Theorem 1

Let Assumptions ass:local_dynamics and ass:small_neighborhood hold and consider the in eq:linear_gnn_mpc_ocp_explicit. Then, the condensing procedure in Section subsec:condensing scales linearly in the number of subsystems $M$, i.e. the computation of $\Gamma_u, \Gamma_x, H, g, \tilde{C}, \tilde{d}$

Figures (5)

  • Figure 1: A soft robotic trunk is modeled as a graph with nodes as discrete segments with state $x^i_t$ at time $t$ and edges as physical interactions. A computes the linearized forward dynamics $x^i_k$, which are condensed into a Quadratic Program (QP) that only depends on the input variables $u_k$. The QP is then solved, and the first input $u_0$ is applied in a receding-horizon fashion.
  • Figure 2: Scalability of the proposed - framework with respect to the number of subsystems $M$. The computation times of the relevant stages in Algorithm \ref{['alg:gnn-mpc']} are shown in log-log scale.
  • Figure 3: Reference tracking of a circle and figure-eight using (a) Koopman Operator modeling, (b) orthogonal reduction and (c) our - approach. The reference is shown in dashed black, while the closed-loop trajectories are shown in red. We additionally provide the plans for each time step in grey.
  • Figure 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.
  • Figure 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.

Theorems & Definitions (2)

  • Theorem 1
  • proof