arXiv subjects

Sebastian Trimpe

Publications and source records attributed to Sebastian Trimpe.

At least 37 records · Page 2Linked to original sources

arXiv2026

Fine-Tuning of Neural Network Approximate MPC without Retraining via Bayesian Optimization

Approximate model-predictive control (AMPC) aims to imitate an MPC's behavior with a neural network, removing the need to solve an expensive optimization problem at runtime. However, during deployment, the parameters of the underlying MPC must usually be fine-tuned. This often renders AMPC impractical as it requires repeatedly generating a new dataset and retraining the neural network. Recent work addresses this problem by adapting AMPC without retraining using approximated sensitivities of the MPC's optimization problem. Currently, this adaption must be done by hand, which is labor-intensive and can be unintuitive for high-dimensional systems. To solve this issue, we propose using Bayesian optimization to tune the parameters of AMPC policies based on experimental data. By combining model-based control with direct and local learning, our approach achieves superior performance to nominal AMPC on hardware, with minimal experimentation. This allows automatic and data-efficient adaptation of AMPC to new system instances and fine-tuning to cost functions that are difficult to directly implement in MPC. We demonstrate the proposed method in hardware experiments for the swing-up maneuver on an inverted cartpole and yaw control of an under-actuated balancing unicycle robot, a challenging control problem.

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arXiv2026

The Mini Wheelbot Dataset: High-Fidelity Data for Robot Learning

The development of robust learning-based control algorithms for unstable systems requires high-quality, real-world data, yet access to specialized robotic hardware remains a significant barrier for many researchers. This paper introduces a comprehensive dynamics dataset for the Mini Wheelbot, an open-source, quasi-symmetric balancing reaction wheel unicycle. The dataset provides 1 kHz synchronized data encompassing all onboard sensor readings, state estimates, ground-truth poses from a motion capture system, and third-person video logs. To ensure data diversity, we include experiments across multiple hardware instances and surfaces using various control paradigms, including pseudo-random binary excitation, nonlinear model predictive control, and reinforcement learning agents. We include several example applications in dynamics model learning, state estimation, and time-series classification to illustrate common robotics algorithms that can be benchmarked on our dataset.

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arXiv2025

A Systems-Theoretic View on the Convergence of Algorithms under Disturbances

Algorithms increasingly operate within complex physical, social, and engineering systems where they are exposed to disturbances, noise, and interconnections with other dynamical systems. This article extends known convergence guarantees of an algorithm operating in isolation (i.e., without disturbances) and systematically derives stability bounds and convergence rates in the presence of such disturbances. By leveraging converse Lyapunov theorems, we derive key inequalities that quantify the impact of disturbances. We further demonstrate how our result can be utilized to assess the effects of disturbances on algorithmic performance in a wide variety of applications, including communication constraints in distributed learning, sensitivity in machine learning generalization, and intentional noise injection for privacy. This underpins the role of our result as a unifying tool for algorithm analysis in the presence of noise, disturbances, and interconnections with other dynamical systems.

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arXiv2025

Local Entropy Search over Descent Sequences for Bayesian Optimization

Searching large and complex design spaces for a global optimum can be infeasible and unnecessary. A practical alternative is to iteratively refine the neighborhood of an initial design using local optimization methods such as gradient descent. We propose local entropy search (LES), a Bayesian optimization paradigm that explicitly targets the solutions reachable by the descent sequences of iterative optimizers. The algorithm propagates the posterior belief over the objective through the optimizer, resulting in a probability distribution over descent sequences. It then selects the next evaluation by maximizing mutual information with that distribution, using a combination of analytic entropy calculations and Monte-Carlo sampling of descent sequences. Empirical results on high-complexity synthetic objectives and benchmark problems show that LES achieves strong sample efficiency compared to existing local and global Bayesian optimization methods.

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arXiv2025

Distributed Event-Based Learning via ADMM

We consider a distributed learning problem, where agents minimize a global objective function by exchanging information over a network. Our approach has two distinct features: (i) It substantially reduces communication by triggering communication only when necessary, and (ii) it is agnostic to the data-distribution among the different agents. We therefore guarantee convergence even if the local data-distributions of the agents are arbitrarily distinct. We analyze the convergence rate of the algorithm both in convex and nonconvex settings and derive accelerated convergence rates for the convex case. We also characterize the effect of communication failures and demonstrate that our algorithm is robust to these. The article concludes by presenting numerical results from distributed learning tasks on the MNIST and CIFAR-10 datasets. The experiments underline communication savings of 35% or more due to the event-based communication strategy, show resilience towards heterogeneous data-distributions, and highlight that our approach outperforms common baselines such as FedAvg, FedProx, SCAFFOLD and FedADMM.

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arXiv2025

The Mini Wheelbot: A Testbed for Learning-based Balancing, Flips, and Articulated Driving

The Mini Wheelbot is a balancing, reaction wheel unicycle robot designed as a testbed for learning-based control. It is an unstable system with highly nonlinear yaw dynamics, non-holonomic driving, and discrete contact switches in a small, powerful, and rugged form factor. The Mini Wheelbot can use its wheels to stand up from any initial orientation - enabling automatic environment resets in repetitive experiments and even challenging half flips. We illustrate the effectiveness of the Mini Wheelbot as a testbed by implementing two popular learning-based control algorithms. First, we showcase Bayesian optimization for tuning the balancing controller. Second, we use imitation learning from an expert nonlinear MPC that uses gyroscopic effects to reorient the robot and can track higher-level velocity and orientation commands. The latter allows the robot to drive around based on user commands - for the first time in this class of robots. The Mini Wheelbot is not only compelling for testing learning-based control algorithms, but it is also just fun to work with, as demonstrated in the video of our experiments.

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arXiv2025

Approximate non-linear model predictive control with safety-augmented neural networks

Model predictive control (MPC) achieves stability and constraint satisfaction for general nonlinear systems, but requires computationally expensive online optimization. This paper studies approximations of such MPC controllers via neural networks (NNs) to achieve fast online evaluation. We propose safety augmentation that yields deterministic guarantees for convergence and constraint satisfaction despite approximation inaccuracies. We approximate the entire input sequence of the MPC with NNs, which allows us to verify online if it is a feasible solution to the MPC problem. We replace the NN solution by a safe candidate based on standard MPC techniques whenever it is infeasible or has worse cost. Our method requires a single evaluation of the NN and forward integration of the input sequence online, which is fast to compute on resource-constrained systems. The proposed control framework is illustrated using two numerical non-linear MPC benchmarks of different complexity, demonstrating computational speedups that are orders of magnitude higher than online optimization. In the examples, we achieve deterministic safety through the safety-augmented NNs, where a naive NN implementation fails.

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arXiv2025

Kernel conditional tests from learning-theoretic bounds

We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals differ with high probability, and include tests of conditional moments or two-sample tests. Our key idea is to transform confidence bounds of a learning method into a test of conditional expectations. We instantiate this principle for kernel ridge regression (KRR) with subgaussian noise. An intermediate data embedding then enables more general tests -- including conditional two-sample tests -- via kernel mean embeddings of distributions. To have guarantees in this setting, we generalize existing pointwise-in-time or time-uniform confidence bounds for KRR to previously-inaccessible yet essential cases such as infinite-dimensional outputs with non-trace-class kernels. These bounds also circumvent the need for independent data, allowing for instance online sampling. To make our tests readily applicable in practice, we introduce bootstrapping schemes leveraging the parametric form of testing thresholds identified in theory to avoid tuning inaccessible parameters. We illustrate the tests on examples, including one in process monitoring and comparison of dynamical systems. Overall, our results establish a comprehensive foundation for conditional testing on functionals, from theoretical guarantees to an algorithmic implementation, and advance the state of the art on confidence bounds for vector-valued least squares estimation.

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arXiv2025

MPX: Mixed Precision Training for JAX

Mixed-precision training has emerged as an indispensable tool for enhancing the efficiency of neural network training in recent years. Concurrently, JAX has grown in popularity as a versatile machine learning toolbox. However, it currently lacks robust support for mixed-precision training. We propose MPX, a mixed-precision training toolbox for JAX that simplifies and accelerates the training of large-scale neural networks while preserving model accuracy. MPX seamlessly integrates with popular toolboxes such as Equinox and Flax, allowing users to convert full-precision pipelines to mixed-precision versions with minimal modifications. By casting both inputs and outputs to half precision, and introducing a dynamic loss-scaling mechanism, MPX alleviates issues like gradient underflow and overflow that commonly arise in half precision computations. Its design inherits critical features from JAX's type-promotion behavior, ensuring that operations take place in the correct precision and allowing for selective enforcement of full precision where needed (e.g., sums, means, or softmax). MPX further provides wrappers for automatic creation and management of mixed-precision gradients and optimizers, enabling straightforward integration into existing JAX training pipelines. MPX's source code, documentation, and usage examples are available at github.com/Data-Science-in-Mechanical-Engineering/mixed_precision_for_JAX .

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arXiv2025

RockNet: Distributed Learning on Ultra-Low-Power Devices

As Machine Learning (ML) becomes integral to Cyber-Physical Systems (CPS), there is growing interest in shifting training from traditional cloud-based to on-device processing (TinyML), for example, due to privacy and latency concerns. However, CPS often comprise ultra-low-power microcontrollers, whose limited compute resources make training challenging. This paper presents RockNet, a new TinyML method tailored for ultra-low-power hardware that achieves state-of-the-art accuracy in timeseries classification, such as fault or malware detection, without requiring offline pretraining. By leveraging that CPS consist of multiple devices, we design a distributed learning method that integrates ML and wireless communication. RockNet leverages all devices for distributed training of specialized compute efficient classifiers that need minimal communication overhead for parallelization. Combined with tailored and efficient wireless multi-hop communication protocols, our approach overcomes the communication bottleneck that often occurs in distributed learning. Hardware experiments on a testbed with 20 ultra-low-power devices demonstrate RockNet's effectiveness. It successfully learns timeseries classification tasks from scratch, surpassing the accuracy of the latest approach for neural network microcontroller training by up to 2x. RockNet's distributed ML architecture reduces memory, latency and energy consumption per device by up to 90 % when scaling from one central device to 20 devices. Our results show that a tight integration of distributed ML, distributed computing, and communication enables, for the first time, training on ultra-low-power hardware with state-of-the-art accuracy.

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arXiv2025

Utilizing Bayesian Optimization for Timetable-Independent Railway Junction Performance Determination

The efficiency of railway infrastructure is significantly influenced by the mix of trains that utilize it, as different service types have competing operational requirements. While freight services might require extended service times, passenger services demand more predictable schedules. Traditional methods for addressing long-term traffic assignment problems often rely on fixed-value capacity limitations, determined based on specific assumptions about traffic composition. This paper introduces a methodology for determining timetable-independent capacity within the traffic rate assignment problem, enabling the calculation of junction capacities under dynamic traffic distributions. We solve the underlying non-linear constrained optimization problem maximizing the traffic throughput using Bayesian optimization (BO). This setting combines a known objective function with expensive- to-compute capacity constraints, motivating an adaption of standard BO problems, where objective functions are usually unknown. We tailor the acquisition process in BO to this specific setting and increase performance by incorporating prior knowledge about the shape of the constraint functions into the Gaussian process surrogate model. Our derived approaches are benchmarked on a railway junction near Paris, significantly outperforming fixed traffic composition models and highlighting the benefits of dynamic capacity allocation.

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arXiv2025

Diffusion-Based Approximate MPC: Fast and Consistent Imitation of Multi-Modal Action Distributions

Approximating model predictive control (MPC) using imitation learning (IL) allows for fast control without solving expensive optimization problems online. However, methods that use neural networks in a simple L2-regression setup fail to approximate multi-modal (set-valued) solution distributions caused by local optima found by the numerical solver or non-convex constraints, such as obstacles, significantly limiting the applicability of approximate MPC in practice. We solve this issue by using diffusion models to accurately represent the complete solution distribution (i.e., all modes) up to kilohertz sampling rates. This work shows that diffusion-based AMPC significantly outperforms L2-regression-based approximate MPC for multi-modal action distributions. In contrast to most earlier work on IL, we also focus on running the diffusion-based controller at a higher rate and in joint space instead of end-effector space. Additionally, we propose the use of gradient guidance during the denoising process to consistently pick the same mode in closed loop to prevent switching between solutions. We propose using the cost and constraint satisfaction of the original MPC problem during parallel sampling of solutions from the diffusion model to pick a better mode online. We evaluate our method on the fast and accurate control of a 7-DoF robot manipulator both in simulation and on hardware deployed at 250 Hz, achieving a speedup of more than 70 times compared to solving the MPC problem online and also outperforming the numerical optimization (used for training) in success ratio.

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arXiv2025

Sailing Towards Zero-Shot State Estimation using Foundation Models Combined with a UKF

State estimation in control and systems engineering traditionally requires extensive manual system identification or data-collection effort. However, transformer-based foundation models in other domains have reduced data requirements by leveraging pre-trained generalist models. Ultimately, developing zero-shot foundation models of system dynamics could drastically reduce manual deployment effort. While recent work shows that transformer-based end-to-end approaches can achieve zero-shot performance on unseen systems, they are limited to sensor models seen during training. We introduce the foundation model unscented Kalman filter (FM-UKF), which combines a transformer-based model of system dynamics with analytically known sensor models via an UKF, enabling generalization across varying dynamics without retraining for new sensor configurations. We evaluate FM-UKF on a new benchmark of container ship models with complex dynamics, demonstrating a competitive accuracy, effort, and robustness trade-off compared to classical methods with approximate system knowledge and to an end-to-end approach. The benchmark and dataset are open sourced to further support future research in zero-shot state estimation via foundation models.

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arXiv2025

DMPC-Swarm: Distributed Model Predictive Control on Nano UAV Swarms

Swarms of unmanned aerial vehicles (UAVs) are increasingly becoming vital to our society, undertaking tasks such as search and rescue, surveillance and delivery. A special variant of Distributed Model Predictive Control (DMPC) has emerged as a promising approach for the safe management of these swarms by combining the scalability of distributed computation with dynamic swarm motion control. In this DMPC method, multiple agents solve local optimization problems with coupled anti-collision constraints, periodically exchanging their solutions. Despite its potential, existing methodologies using this DMPC variant have yet to be deployed on distributed hardware that fully utilize true distributed computation and wireless communication. This is primarily due to the lack of a communication system tailored to meet the unique requirements of mobile swarms and an architecture that supports distributed computation while adhering to the payload constraints of UAVs. We present DMPC-SWARM, a new swarm control methodology that integrates an efficient, stateless low-power wireless communication protocol with a novel DMPC algorithm that provably avoids UAV collisions even under message loss. By utilizing event-triggered and distributed off-board computing, DMPC-SWARM supports nano UAVs, allowing them to benefit from additional computational resources while retaining scalability and fault tolerance. In a detailed theoretical analysis, we prove that DMPC-SWARM guarantees collision avoidance under realistic conditions, including communication delays and message loss. Finally, we present DMPC-SWARM's implementation on a swarm of up to 16 nano-quadcopters, demonstrating the first realization of these DMPC variants with computation distributed on multiple physical devices interconnected by a real wireless mesh networks. A video showcasing DMPC-SWARM is available at http://tiny.cc/DMPCSwarm.

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arXiv2025

Newtonian and Lagrangian Neural Networks: A Comparison Towards Efficient Inverse Dynamics Identification

Accurate inverse dynamics models are essential tools for controlling industrial robots. Recent research combines neural network regression with inverse dynamics formulations of the Newton-Euler and the Euler-Lagrange equations of motion, resulting in so-called Newtonian neural networks and Lagrangian neural networks, respectively. These physics-informed models seek to identify unknowns in the analytical equations from data. Despite their potential, current literature lacks guidance on choosing between Lagrangian and Newtonian networks. In this study, we show that when motor torques are estimated instead of directly measuring joint torques, Lagrangian networks prove less effective compared to Newtonian networks as they do not explicitly model dissipative torques. The performance of these models is compared to neural network regression on data of a MABI MAX 100 industrial robot.

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arXiv2025

Viability of Future Actions: Robust Safety in Reinforcement Learning via Entropy Regularization

Despite the many recent advances in reinforcement learning (RL), the question of learning policies that robustly satisfy state constraints under unknown disturbances remains open. In this paper, we offer a new perspective on achieving robust safety by analyzing the interplay between two well-established techniques in model-free RL: entropy regularization, and constraints penalization. We reveal empirically that entropy regularization in constrained RL inherently biases learning toward maximizing the number of future viable actions, thereby promoting constraints satisfaction robust to action noise. Furthermore, we show that by relaxing strict safety constraints through penalties, the constrained RL problem can be approximated arbitrarily closely by an unconstrained one and thus solved using standard model-free RL. This reformulation preserves both safety and optimality while empirically improving resilience to disturbances. Our results indicate that the connection between entropy regularization and robustness is a promising avenue for further empirical and theoretical investigation, as it enables robust safety in RL through simple reward shaping.

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arXiv2025

CHEQ-ing the Box: Safe Variable Impedance Learning for Robotic Polishing

Robotic systems are increasingly employed for industrial automation, with contact-rich tasks like polishing requiring dexterity and compliant behaviour. These tasks are difficult to model, making classical control challenging. Deep reinforcement learning (RL) offers a promising solution by enabling the learning of models and control policies directly from data. However, its application to real-world problems is limited by data inefficiency and unsafe exploration. Adaptive hybrid RL methods blend classical control and RL adaptively, combining the strengths of both: structure from control and learning from RL. This has led to improvements in data efficiency and exploration safety. However, their potential for hardware applications remains underexplored, with no evaluations on physical systems to date. Such evaluations are critical to fully assess the practicality and effectiveness of these methods in real-world settings. This work presents an experimental demonstration of the hybrid RL algorithm CHEQ for robotic polishing with variable impedance, a task requiring precise force and velocity tracking. In simulation, we show that variable impedance enhances polishing performance. We compare standalone RL with adaptive hybrid RL, demonstrating that CHEQ achieves effective learning while adhering to safety constraints. On hardware, CHEQ achieves effective polishing behaviour, requiring only eight hours of training and incurring just five failures. These results highlight the potential of adaptive hybrid RL for real-world, contact-rich tasks trained directly on hardware.

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arXiv2025

Event-triggered Robust Model Predictive Control under Hard Computation Resource Constraints

Model predictive control (MPC) is capable of controlling nonlinear systems with guaranteed constraint satisfaction and stability. However, MPC requires solving optimization problems online periodically, which often exceeds the local system's computational capabilities. A potential solution is to leverage external processing, such as a central industrial server. Yet, this central computer typically serves multiple systems simultaneously, leading to significant hardware demands due to the need to solve numerous optimization problems concurrently. In this work, we tackle this challenge by developing an event-triggered model predictive control (ET-MPC) that provably stabilizes multiple nonlinear systems under disturbances while solving only optimization problems for a fixed-size subset at any given time. Unlike existing ET-MPC methods, which primarily reduce average computational load yet still require hardware capable of handling all systems simultaneously, our approach reduces the worst-case computational load. This significantly lowers central server hardware requirements by diminishing peak computational demands. We achieve our improvements by leveraging recent advancements in distributed event-triggered linear control and integrating them with a robust MPC that employs constraint tightening.

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