Henrik Krauss

Johannes Kübel, Henrik Krauss, Jinjie Li et al.

Data-driven Model Predictive Control (MPC) has lately been the core research subject in the field of control theory. The combination of an optimal control framework with deep learning paradigms opens up the possibility to accurately track control tasks without the need for complex analytical models. However, the system dynamics are often nuanced and the neural model lacks the potential to understand physical properties such as inertia and conservation of energy. In this work, we propose a novel energy-based regularization loss function which is applied to the training of a neural model that learns the residual dynamics of an omnidirectional aerial robot. Our energy-based regularization encourages the neural network to cause control corrections that stabilize the energy of the system. The residual dynamics are integrated into the MPC framework and improve the positional mean absolute error (MAE) over three real-world experiments by 23% compared to an analytical MPC. We also compare our method to a standard neural MPC implementation without regularization and primarily achieve a significantly increased flight stability implicitly due to the energy regularization and up to 15% lower MAE. Our code is available under: https://github.com/johanneskbl/jsk_aerial_robot/tree/develop/neural_MPC.

Henrik Krauss, Johann Licher, Naoya Takeishi et al.

This work addresses open-loop control of a soft continuum robot (SCR) from video-learned latent dynamics. Visual Oscillator Networks (VONs) from previous work are used, that provide mechanistically interpretable 2D oscillator latents through an attention broadcast decoder (ABCD). Open-loop, single-shooting optimal control is performed in latent space to track image-specified waypoints without camera feedback. An interactive SCR live simulator enables design of static, dynamic, and extrapolated targets and maps them to model-specific latent waypoints. On a two-segment pneumatic SCR, Koopman, MLP, and oscillator dynamics, each with and without ABCD, are evaluated on setpoint and dynamic trajectories. ABCD-based models consistently reduce image-space tracking error. The VON and ABCD-based Koopman models attains the lowest MSEs. Using an ablation study, we demonstrate that several architecture choices and training settings contribute to the open-loop control performance. Simulation stress tests further confirm static holding, stable extrapolated equilibria, and plausible relaxation to the rest state. To the best of our knowledge, this is the first demonstration that interpretable, video-learned latent dynamics enable reliable long-horizon open-loop control of an SCR.

Henrik Krauss, Tim-Lukas Habich, Max Bartholdt et al.

Physics-informed neural networks (PINNs) are trained using physical equations and can also incorporate unmodeled effects by learning from data. PINNs for control (PINCs) of dynamical systems are gaining interest due to their prediction speed compared to classical numerical integration methods for nonlinear state-space models, making them suitable for real-time control applications. We introduce the domain-decoupled physics-informed neural network (DD-PINN) to address current limitations of PINC in handling large and complex nonlinear dynamical systems. The time domain is decoupled from the feed-forward neural network to construct an Ansatz function, allowing for calculation of gradients in closed form. This approach significantly reduces training times, especially for large dynamical systems, compared to PINC, which relies on graph-based automatic differentiation. Additionally, the DD-PINN inherently fulfills the initial condition and supports higher-order excitation inputs, simplifying the training process and enabling improved prediction accuracy. Validation on three systems - a nonlinear mass-spring-damper, a five-mass-chain, and a two-link robot - demonstrates that the DD-PINN achieves significantly shorter training times. In cases where the PINC's prediction diverges, the DD-PINN's prediction remains stable and accurate due to higher physics loss reduction or use of a higher-order excitation input. The DD-PINN allows for fast and accurate learning of large dynamical systems previously out of reach for the PINC.

Henrik Krauss, Takehisa Yairi

We study how different visual information sources contribute to human decision making in dynamic visual environments. Using Atari-HEAD, a large-scale Atari gameplay dataset with synchronized eye-tracking, we introduce a controlled ablation framework as a means to reverse-engineer the contribution of peripheral visual information, explicit gaze information in form of gaze maps, and past-state information from human behavior. We train action-prediction networks under six settings that selectively include or exclude these information sources. Across 20 games, peripheral information shows by far the strongest contribution, with median prediction-accuracy drops in the range of 35.27-43.90% when removed. Gaze information yields smaller drops of 2.11-2.76%, while past-state information shows a broader range of 1.52-15.51%, with the upper end likely more informative due to reduced peripheral-information leakage. To complement aggregate accuracies, we cluster states by true-action probabilities assigned by the different model configurations. This analysis identifies coarse behavioral regimes, including focus-dominated, periphery-dominated, and more contextual decision situations. These results suggest that human decision making in Atari depends strongly on information beyond the current focus of gaze, while the proposed framework provides a way to estimate such information-source contributions from behavior.

Henrik Krauss, Johann Licher, Naoya Takeishi et al.

Data-driven learning of soft continuum robot (SCR) dynamics from high-dimensional observations offers flexibility but often lacks physical interpretability, while model-based approaches require prior knowledge and can be computationally expensive. We bridge this gap by introducing (1) the Attention Broadcast Decoder (ABCD), a plug-and-play module for autoencoder-based latent dynamics learning that generates pixel-accurate attention maps localizing each latent dimension's contribution while filtering static backgrounds. (2) By coupling these attention maps to 2D oscillator networks, we enable direct on-image visualization of learned dynamics (masses, stiffness, and forces) without prior knowledge. We validate our approach on single- and double-segment SCRs, demonstrating that ABCD-based models significantly improve multi-step prediction accuracy: 5.7x error reduction for Koopman operators and 3.5x for oscillator networks on the two-segment robot. The learned oscillator network autonomously discovers a chain structure of oscillators. Unlike standard methods, ABCD models enable smooth latent space extrapolation beyond training data. This fully data-driven approach yields compact, physically interpretable models suitable for control applications.

Johann Licher, Max Bartholdt, Henrik Krauss et al.

Dynamic control of soft continuum robots (SCRs) holds great potential for expanding their applications, but remains a challenging problem due to the high computational demands of accurate dynamic models. While data-driven approaches like Koopman-operator-based methods have been proposed, they typically lack adaptability and cannot capture the full robot shape, limiting their applicability. This work introduces a real-time-capable nonlinear model-predictive control (MPC) framework for SCRs based on a domain-decoupled physics-informed neural network (DD-PINN) with adaptable bending stiffness. The DD-PINN serves as a surrogate for the dynamic Cosserat rod model with a speed-up factor of 44000. It is also used within an unscented Kalman filter for estimating the model states and bending compliance from end-effector position measurements. We implement a nonlinear evolutionary MPC running at 70 Hz on the GPU. In simulation, it demonstrates accurate tracking of dynamic trajectories and setpoint control with end-effector position errors below 3 mm (2.3% of the actuator's length). In real-world experiments, the controller achieves similar accuracy and accelerations up to 3.55 m/s2.

Henrik Krauss, Takehisa Yairi

This study introduces a novel method for revealing human internal attention patterns from gameplay data alone, leveraging offline attention techniques from reinforcement learning (RL). We propose contextualized, task-relevant (CTR) attention networks, which generate attention maps from both human and RL agent gameplay in Atari environments. To evaluate whether the human CTR maps reveal internal attention, we validate our model by quantitative and qualitative comparison to the agent maps as well as to a temporally integrated overt attention (TIOA) model based on human eye-tracking data. Our results show that human CTR maps are more sparse than the agent ones and align better with the TIOA maps. Following a qualitative visual comparison we conclude that they likely capture patterns of internal attention. As a further application, we use these maps to guide RL agents, finding that human internal attention-guided agents achieve slightly improved and more stable learning compared to baselines. This work advances the understanding of human-agent attention differences and provides a new approach for extracting and validating internal attention from behavioral data.