Distributed Approximate Model Predictive Control for Robot Swarms

Methods

1. Subproject: The aim of this subproject was to develop a centralized MPC for drone swarms and approximate it with a neural network (AMPC). First, we adapted an output tracking MPC by introducing an artificial steady‑state reference and safe flight corridors to ensure collision avoidance and convergence in dynamic multi‑agent environments. Next, we trained neural networks to map system states to control inputs, with a particular focus on addressing the inherent multi‑modality of MPC solutions.

2. Subproject: In the second subproject, we investigated ways to reduce MPC’s computational footprint by computing it only when necessary, particularly for multi-agent systems sharing limited computing resources. The key innovation of our approach is to ensure that only a fixed maximum subset of agents accesses these resources while maintaining high controller performance. For this setup, we developed two approaches. An event-triggered robust MPC guaranteeing stability for nonlinear systems with state disturbances, and an event-triggered distributed MPC that can control quadcopter swarms while guaranteeing collision avoidance.

3. Subproject: In an independent third subproject, we explored neural networks as surrogate models for BO. BO, a popular black-box optimization method, achieves high optimization performance with only a few samples. Typically, BO methods use Gaussian Processes as the internal surrogate model of the objective function to be minimized. In our study, we investigated a specific neural network variant, called variational last layer models, as a replacement for Gaussian Processes.

Results

1. Subproject: In our detailed simulation study, we compared three types of neural network architectures: multilayer perceptrons (MLPs), mixture density networks (MDNs), and conditional variational autoencoders (CVAEs). Our experimental evaluation demonstrated that standard MLPs fail to capture the necessary multi-modality, rendering them incapable of learning safe swarm controllers. Although MDNs are designed to handle multi-modal outputs, they too fell short of producing safe controllers. In contrast, only CVAEs successfully captured the multi-modality, enabling the learning of controllers that safely manage drone swarms, as verified by both simulation and hardware experiments.

2. Subproject: We conducted extensive simulation studies for both approaches, examining the influence of various hyperparameters under different conditions. Our results demonstrated that our event-triggered MPC approaches can significantly reduce required computing power while maintaining high control performance.

3. Subproject: Our simulations showed that variational last layer models perform comparably to, and in some cases even better than, Gaussian Processes on various objective function types.

Discussion

1. Subproject: These results demonstrated that CVAEs are capable of solving the problem of multi-modality in AMPC. Currently, we have only demonstrated this behavior for drone swarm control. In future research, we will investigate AMPC via CVAES for different types of nonlinear systems.

2. Subproject: The proposed event-triggered strategies can increase the resource efficiency of MPC. Future research will focus on applying the developed strategies to different system classes.

3. Subproject: Our results broke the assumption that Gaussian Processes are the best class of surrogate models. Future research will apply neural network surrogate models to different types of BO methods.

Additional Project Information

DFG classification: 407 Systems Engineering
Software: PyTorch, JAX, Casadi, BOTorch
Cluster: CLAIX

Publications

Paul Brunzema, Mikkel Jordahn, John Willes, Sebastian Trimpe, Jasper Snoek, James Harrison. Variational Last Layers for Bayesian Optimization,
Peer-reviewed publication, 2024

Paul Brunzema, Mikkel Jordahn, John Willes, Sebastian Trimpe, Jasper Snoek, James Harrison. Bayesian Optimization via Continual Variational Last Layer Training,
Peer-reviewed publication, 2025

Alexander Gräfe, Sebastian Trimpe. Event-triggered Robust Model Predictive Control under Hard Computation Resource Constraints, Peer-reviewed publication, 2025

Thesis
Nora Wieler. Recycling Information in Event-Triggered Bayesian Optimization for Time-Varying Controller Tuning. Master Thesis, 2024

Lennart Fanter. Exploring Last-Layer Surrogate Models for Model-based Reinforcement Learning. Bachelor Thesis, 2025

Philipp Grünter. Distributed Approximate Model Predictive Control for Drone Swarm
Coordination. Master Thesis, 2024