Graph Neural Model Predictive Control for High-Dimensional Systems

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.

Time-Varying Coverage Control: A Distributed Tracker-Planner MPC Framework

Time-varying coverage control addresses the challenge of coordinating multiple agents covering an environment where regions of interest change over time. This problem has broad applications, including the deployment of autonomous taxis and coordination in search and rescue operations. The achievement of effective coverage is complicated by the presence of time-varying density functions, nonlinear agent dynamics, and stringent system and safety constraints. In this paper, we present a distributed multi-agent control framework for time-varying coverage under nonlinear constrained dynamics. Our approach integrates a reference trajectory planner and a tracking model predictive control (MPC) scheme, which operate at different frequencies within a multi-rate framework. For periodic density functions, we demonstrate closed-loop convergence to an optimal configuration of trajectories and provide formal guarantees regarding constraint satisfaction, collision avoidance, and recursive feasibility. Additionally, we propose an efficient algorithm capable of handling nonperiodic density functions, making the approach suitable for practical applications. Finally, we validate our method through hardware experiments using a fleet of four miniature race cars.

Perfecting Periodic Trajectory Tracking: Model Predictive Control with a Periodic Observer ($Π$-MPC)

In Model Predictive Control (MPC), discrepancies between the actual system and the predictive model can lead to substantial tracking errors and significantly degrade performance and reliability. While such discrepancies can be alleviated with more complex models, this often complicates controller design and implementation. By leveraging the fact that many trajectories of interest are periodic, we show that perfect tracking is possible when incorporating a simple observer that estimates and compensates for periodic disturbances. We present the design of the observer and the accompanying tracking MPC scheme, proving that their combination achieves zero tracking error asymptotically, regardless of the complexity of the unmodelled dynamics. We validate the effectiveness of our method, demonstrating asymptotically perfect tracking on a high-dimensional soft robot with nearly 10,000 states and a fivefold reduction in tracking errors compared to a baseline MPC on small-scale autonomous race car experiments.