Sebastian Bernhard

Sebastian Bernhard, Jürgen Adamy

This paper considers two different problems in trajectory tracking control for linear systems. First, if the control is not unique which is most input energy efficient. Second, if exact tracking is infeasible which control performs most accurately. These are typical challenges for over-actuated systems and for under-actuated systems, respectively. We formulate both goals as optimal output regulation problems. Then we contribute two new sets of regulator equations to output regulation theory that provide the desired solutions. A thorough study indicates solvability and uniqueness under weak assumptions. E.g., we can always determine the solution of the classical regulator equations that is most input energy efficient. This is of great value if there are infinitely many solutions. We derive our results by a linear quadratic tracking approach and establish a useful link to output regulation theory.

Sebastian Bernhard, Saman Khodaverdian, Jürgen Adamy

In this paper, we address the output synchronization of heterogeneous linear networks. In the literature, all agents are typically required to synchronize exactly to a common trajectory. Here, we introduce optimal stationary synchronization (OSS) instead which permits non-zero steady-state synchronization errors. As a benefit, we are able to relax standard requirements. E.g., agents are allowed to participate in the network even when they usually cannot synchronize exactly. In addition, OSS enables agents to save input-energy by synchronizing within tolerable error-bounds. Our new method combines the synchronization of bounded exosystems with local infinite-time linear quadratic tracking (LQT). This results in an optimal balance of each agent's synchronization error versus its consumed input-energy. Moreover, we extend recent results in LQT such that the derived time-invariant optimal control guarantees that the synchronization error satisfies given strict bounds. All these aspects are demonstrated by an illustrative simulation example with a detailed analysis.

Marius Kästingschäfer, Théo Gieruc, Sebastian Bernhard et al.

Models for egocentric 3D and 4D reconstruction, including few-shot interpolation and extrapolation settings, can benefit from having images from exocentric viewpoints as supervision signals. No existing dataset provides the necessary mixture of complex, dynamic, and multi-view data. To facilitate the development of 3D and 4D reconstruction methods in the autonomous driving context, we propose a Synthetic Ego--Exo Dynamic 4D (SEED4D) data generator and dataset. We present a customizable, easy-to-use data generator for spatio-temporal multi-view data creation. Our open-source data generator allows the creation of synthetic data for camera setups commonly used in the NuScenes, KITTI360, and Waymo datasets. Additionally, SEED4D encompasses two large-scale multi-view synthetic urban scene datasets. Our static (3D) dataset encompasses 212k inward- and outward-facing vehicle images from 2k scenes, while our dynamic (4D) dataset contains 16.8M images from 10k trajectories, each sampled at 100 points in time with egocentric images, exocentric images, and LiDAR data. The datasets and the data generator can be found at https://seed4d.github.io/.

Théo Gieruc, Marius Kästingschäfer, Sebastian Bernhard et al.

Current 3D reconstruction techniques struggle to infer unbounded scenes from a few images faithfully. Specifically, existing methods have high computational demands, require detailed pose information, and cannot reconstruct occluded regions reliably. We introduce 6Img-to-3D, an efficient, scalable transformer-based encoder-renderer method for single-shot image to 3D reconstruction. Our method outputs a 3D-consistent parameterized triplane from only six outward-facing input images for large-scale, unbounded outdoor driving scenarios. We take a step towards resolving existing shortcomings by combining contracted custom cross- and self-attention mechanisms for triplane parameterization, differentiable volume rendering, scene contraction, and image feature projection. We showcase that six surround-view vehicle images from a single timestamp without global pose information are enough to reconstruct 360$^{\circ}$ scenes during inference time, taking 395 ms. Our method allows, for example, rendering third-person images and birds-eye views. Our code is available at https://github.com/continental/6Img-to-3D, and more examples can be found at our website here https://6Img-to-3D.GitHub.io/.

Bojan Derajić, Mohamed-Khalil Bouzidi, Sebastian Bernhard et al.

This paper presents a novel learning-based approach for online estimation of maximal safe sets for local trajectory planning in unknown static environments. The neural representation of a set is used as the terminal set constraint for a model predictive control (MPC) local planner, resulting in improved recursive feasibility and safety. To achieve real-time performance and desired generalization properties, we employ the idea of hypernetworks. We use the Hamilton-Jacobi (HJ) reachability analysis as the source of supervision during the training process, allowing us to consider general nonlinear dynamics and arbitrary constraints. The proposed method is extensively evaluated against relevant baselines in simulations for different environments and robot dynamics. The results show an increase in success rate of up to 52% compared to the best baseline while maintaining comparable execution speed. Additionally, we deploy our proposed method, NTC-MPC, on a physical robot and demonstrate its ability to safely avoid obstacles in scenarios where the baselines fail.

Katharina Winter, Abhishek Vivekanandan, Rupert Polley et al.

Generative AI (GenAI) is rapidly advancing the field of Autonomous Driving (AD), extending beyond traditional applications in text, image, and video generation. We explore how generative models can enhance automotive tasks, such as static map creation, dynamic scenario generation, trajectory forecasting, and vehicle motion planning. By examining multiple generative approaches ranging from Variational Autoencoder (VAEs) over Generative Adversarial Networks (GANs) and Invertible Neural Networks (INNs) to Generative Transformers (GTs) and Diffusion Models (DMs), we highlight and compare their capabilities and limitations for AD-specific applications. Additionally, we discuss hybrid methods integrating conventional techniques with generative approaches, and emphasize their improved adaptability and robustness. We also identify relevant datasets and outline open research questions to guide future developments in GenAI. Finally, we discuss three core challenges: safety, interpretability, and realtime capabilities, and present recommendations for image generation, dynamic scenario generation, and planning.

Bojan Derajić, Mohamed-Khalil Bouzidi, Sebastian Bernhard et al.

In this paper, we propose a hybrid MPC local planner that uses a learning-based approximation of a time-varying safe set, derived from local observations and applied as the MPC terminal constraint. This set can be represented as a zero-superlevel set of the value function computed via Hamilton-Jacobi (HJ) reachability analysis, which is infeasible in real-time. We exploit the property that the HJ value function can be expressed as a difference of the corresponding signed distance function (SDF) and a non-negative residual function. The residual component is modeled as a neural network with non-negative output and subtracted from the computed SDF, resulting in a real-time value function estimate that is at least as safe as the SDF by design. Additionally, we parametrize the neural residual by a hypernetwork to improve real-time performance and generalization properties. The proposed method is compared with three state-of-the-art methods in simulations and hardware experiments, achieving up to 30\% higher success rates compared to the best baseline while requiring a similar computational effort and producing high-quality (low travel-time) solutions.

Eyvaz Najafli, Marius Kästingschäfer, Sebastian Bernhard et al.

Reconstructing unbounded outdoor scenes from sparse outward-facing views poses significant challenges due to minimal view overlap. Previous methods often lack cross-scene understanding and their primitive-centric formulations overload local features to compensate for missing global context, resulting in blurriness in unseen parts of the scene. We propose sshELF, a fast, single-shot pipeline for sparse-view 3D scene reconstruction via hierarchal extrapolation of latent features. Our key insights is that disentangling information extrapolation from primitive decoding allows efficient transfer of structural patterns across training scenes. Our method: (1) learns cross-scene priors to generate intermediate virtual views to extrapolate to unobserved regions, (2) offers a two-stage network design separating virtual view generation from 3D primitive decoding for efficient training and modular model design, and (3) integrates a pre-trained foundation model for joint inference of latent features and texture, improving scene understanding and generalization. sshELF can reconstruct 360 degree scenes from six sparse input views and achieves competitive results on synthetic and real-world datasets. We find that sshELF faithfully reconstructs occluded regions, supports real-time rendering, and provides rich latent features for downstream applications. The code will be released.

Bojan Derajić, Sebastian Bernhard, Wolfgang Hönig

Control barrier functions (CBFs) have been demonstrated as an effective method for safety-critical control of autonomous systems. Although CBFs are simple to deploy, their design remains challenging, motivating the development of learning-based approaches. Yet, issues such as suboptimal safe sets, applicability in partially observable environments, and lack of rigorous safety guarantees persist. In this work, we propose observation-conditioned neural CBFs based on Hamilton-Jacobi (HJ) reachability analysis, which approximately recover the maximal safe sets. We exploit certain mathematical properties of the HJ value function, ensuring that the predicted safe set never intersects with the observed failure set. Moreover, we leverage a hypernetwork-based architecture that is particularly suitable for the design of observation-conditioned safety filters. The proposed method is examined both in simulation and hardware experiments for a ground robot and a quadcopter. The results show improved success rates and generalization to out-of-domain environments compared to the baselines.

Mohamed Parvez Aslam, Bojan Derajic, Mohamed-Khalil Bouzidi et al.

Safe navigation in pedestrian-rich environments remains a key challenge for autonomous robots. This work evaluates the integration of a deep learning-based Social-Implicit (SI) pedestrian trajectory predictor within a Model Predictive Control (MPC) framework on the physical Continental Corriere robot. Tested across varied pedestrian densities, the SI-MPC system is compared to a traditional Constant Velocity (CV) model in both open-loop prediction and closed-loop navigation. Results show that SI improves trajectory prediction - reducing errors by up to 76% in low-density settings - and enhances safety and motion smoothness in crowded scenes. Moreover, real-world deployment reveals discrepancies between open-loop metrics and closed-loop performance, as the SI model yields broader, more cautious predictions. These findings emphasize the importance of system-level evaluation and highlight the SI-MPC framework's promise for safer, more adaptive navigation in dynamic, human-populated environments.