Martin Schuck

Martin Schuck, Marcel P. Rath, Yufei Hua et al.

High-quality, large-scale synthetic data from simulations is becoming a cornerstone for pushing the capabilities of robot algorithms. While aerial robotics simulators have evolved to support specialized needs such as fidelity, differentiability, and swarms independently, a unified platform that can synthesize data across all these domains is missing. In this work, we propose Crazyflow, a simulator designed to push the limits of aerial-robotics algorithm development, from model-based to data-driven methods, gradient-based to sampling-based approaches, and single-agent to multi-agent systems. Compared to existing state-of-the-art drone simulators, it achieves speeds more than an order of magnitude faster for a single drone and can simulate thousands of swarms of 4000 drones each. Real-world experiments show Crazyflow supports both analytical-gradient-based policy learning, achieving sub-centimeter trajectory tracking accuracy without domain randomization, and sampling-based obstacle avoidance at speeds exceeding half a billion steps per second. Breaking the traditional train-then-deploy paradigm, we show that its unprecedented speed even enables in-flight reinforcement learning; we demonstrate this by throwing a physical drone into the air and training a recovery policy from scratch in 0.38 seconds, successfully stabilizing the drone. Crazyflow supports multiple levels of simulation abstraction, is directly compatible with all open-source Crazyflie models, and enables rapid reconfiguration across custom drone platforms and applications by providing a light-weight system identification pipeline. By pushing accuracy, speed, and differentiability simultaneously, Crazyflow serves as an open-source resource for synthetic data generation, with emerging capabilities for large-scale parallelization for online, in-execution learning and optimization, opening the door to novel algorithm development.

Martin Schuck, Jan Brüdigam, Sandra Hirche et al.

Handling orientations of robots and objects is a crucial aspect of many applications. Yet, ever so often, there is a lack of mathematical correctness when dealing with orientations, especially in learning pipelines involving, for example, artificial neural networks. In this paper, we investigate reinforcement learning with orientations and propose a simple modification of the network's input and output that adheres to the Lie group structure of orientations. As a result, we obtain an easy and efficient implementation that is directly usable with existing learning libraries and achieves significantly better performance than other common orientation representations. We briefly introduce Lie theory specifically for orientations in robotics to motivate and outline our approach. Subsequently, a thorough empirical evaluation of different combinations of orientation representations for states and actions demonstrates the superior performance of our proposed approach in different scenarios, including: direct orientation control, end effector orientation control, and pick-and-place tasks.

Martin Schuck, Alexander von Rohr, Angela P. Schoellig

Three-dimensional rigid-body transforms, i.e. rotations and translations, are central to modern differentiable machine learning pipelines in robotics, vision, and simulation. However, numerically robust and mathematically correct implementations, particularly on SO(3), are error-prone due to issues such as axis conventions, normalizations, composition consistency and subtle errors that only appear in edge cases. SciPy's spatial$.$transform module is a rigorously tested Python implementation. However, it historically only supported NumPy, limiting adoption in GPU-accelerated and autodiff-based workflows. We present a complete overhaul of SciPy's spatial$.$transform functionality that makes it compatible with any array library implementing the Python array API, including JAX, PyTorch, and CuPy. The revised implementation preserves the established SciPy interface while enabling GPU/TPU execution, JIT compilation, vectorized batching, and differentiation via native autodiff of the chosen backend. We demonstrate how this foundation supports differentiable scientific computing through two case studies: (i) scalability of 3D transforms and rotations and (ii) a JAX drone simulation that leverages SciPy's Rotation for accurate integration of rotational dynamics. Our contributions have been merged into SciPy main and will ship in the next release, providing a framework-agnostic, production-grade basis for 3D spatial math in differentiable systems and ML.

Martin Schuck, Sherif Samy, Angela P. Schoellig

Many robotic control tasks require policies to act on orientations, yet the geometry of SO(3) makes this nontrivial. Because SO(3) admits no global, smooth, minimal parameterization, common representations such as Euler angles, quaternions, rotation matrices, and Lie algebra coordinates introduce distinct constraints and failure modes. While these trade-offs are well studied for supervised learning, their implications for actions in reinforcement learning remain unclear. We systematically evaluate SO(3) action representations across three standard continuous control algorithms, PPO, SAC, and TD3, under dense and sparse rewards. We compare how representations shape exploration, interact with entropy regularization, and affect training stability through empirical studies and analyze the implications of different projections for obtaining valid rotations from Euclidean network outputs. Across a suite of robotics benchmarks, we quantify the practical impact of these choices and distill simple, implementation-ready guidelines for selecting and using rotation actions. Our results highlight that representation-induced geometry strongly influences exploration and optimization and show that representing actions as tangent vectors in the local frame yields the most reliable results across algorithms.

Martin Schuck, Dinushka Orrin Dahanaggamaarachchi, Ben Sprenger et al.

Drone swarm performances -- synchronized, expressive aerial displays set to music -- have emerged as a captivating application of modern robotics. Yet designing smooth, safe choreographies remains a complex task requiring expert knowledge. We present SwarmGPT, a language-based choreographer that leverages the reasoning power of large language models (LLMs) to streamline drone performance design. The LLM is augmented by a safety filter that ensures deployability by making minimal corrections when safety or feasibility constraints are violated. By decoupling high-level choreographic design from low-level motion planning, our system enables non-experts to iteratively refine choreographies using natural language without worrying about collisions or actuator limits. We validate our approach through simulations with swarms up to 200 drones and real-world experiments with up to 20 drones performing choreographies to diverse types of songs, demonstrating scalable, synchronized, and safe performances. Beyond entertainment, this work offers a blueprint for integrating foundation models into safety-critical swarm robotics applications.

Jan Brüdigam, Martin Schuck, Alexandre Capone et al.

Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications. When using Gaussian process regression to learn unknown systems, a commonly considered approach consists of learning the residual dynamics after applying some generic discretization technique, which might however disregard properties of the underlying physical system. Variational integrators are a less common yet promising approach to discretization, as they retain physical properties of the underlying system, such as energy conservation and satisfaction of explicit kinematic constraints. In this work, we present a novel structure-preserving learning-based modelling approach that combines a variational integrator for the nominal dynamics of a mechanical system and learning residual dynamics with Gaussian process regression. We extend our approach to systems with known kinematic constraints and provide formal bounds on the prediction uncertainty. The simulative evaluation of the proposed method shows desirable energy conservation properties in accordance with general theoretical results and demonstrates exact constraint satisfaction for constrained dynamical systems.