We propose a text-to-IMU (inertial measurement unit) motion-synthesis framework to obtain realistic IMU data by fine-tuning a pretrained diffusion model with an acceleration-based second-order loss (L_acc). L_acc enforces consistency in the discrete second-order temporal differences of the generated motion, thereby aligning the diffusion prior with IMU-specific acceleration patterns. We integrate L_acc into the training objective of an existing diffusion model, finetune the model to obtain an IMU-specific motion prior, and evaluate the model with an existing text-to-IMU framework that comprises surface modelling and virtual sensor simulation. We analysed acceleration signal fidelity and differences between synthetic motion representation and actual IMU recordings. As a downstream application, we evaluated Human Activity Recognition (HAR) and compared the classification performance using data of our method with the earlier diffusion model and two additional diffusion model baselines. When we augmented the earlier diffusion model objective with L_acc and continued training, L_acc decreased by 12.7% relative to the original model. The improvements were considerably larger in high-dynamic activities (i.e., running, jumping) compared to low-dynamic activities~(i.e., sitting, standing). In a low-dimensional embedding, the synthetic IMU data produced by our refined model shifts closer to the distribution of real IMU recordings. HAR classification trained exclusively on our refined synthetic IMU data improved performance by 8.7% compared to the earlier diffusion model and by 7.6% over the best-performing comparison diffusion model. We conclude that acceleration-aware diffusion refinement provides an effective approach to align motion generation and IMU synthesis and highlights how flexible deep learning pipelines are for specialising generic text-to-motion priors to sensor-specific tasks.

In the era of mega-constellations, the need for accurate and publicly available information has become fundamental for satellite operators to guarantee the safety of spacecrafts and the Low Earth Orbit (LEO) space environment. This study critically evaluates the accuracy and reliability of publicly available ephemeris data for a LEO mega-constellation - Starlink. The goal of this work is twofold: (i) compare and analyze the quality of the data against high-precision numerical propagation. By analyzing two months of real orbital data for approximately 1500 Starlink satellites, we identify discrepancies between high precision numerical algorithms and the published ephemerides, recognizing the use of simplified dynamics at fixed thresholds, planned maneuvers, and limitations in uncertainty propagations. Furthermore, we compare data obtained from multiple sources to track and analyze deorbiting satellites over the same period. Empirically, we extract the acceleration profile of satellites during deorbiting and provide insights relating to the effects of non-conservative forces during reentry. For non-deorbiting satellites, the position Root Mean Square Error (RMSE) was approximately 300 m, while for deorbiting satellites it increased to about 600 m. Through this in-depth analysis, we highlight potential limitations in publicly available data for accurate and robust Space Situational Awareness (SSA), and importantly, we propose a data-driven model of satellite decay in mega-constellations. Keywords: Starlink, Low Earth Orbit, Physics-Informed Machine Learning, Space Situational Awareness, Satellite Decay 1. Introduction As the number of active satellites in Low Earth Orbit (LEO) continues to grow, ensuring their safe operation has become a complex challenge. Accurate trajectory prediction and collision avoidance are now essential, as overcrowding in LEO has significantly raised the likelihood of orbital collisions [1]. Such events not only threaten the functionality of space assets but also contribute to the accumulation of debris, increasing the risk of chain reaction scenarios like the Kessler syndrome [2].

-- Accurate prediction of surrounding road users' trajectories is essential for safe and efficient autonomous driving. While deep learning models have improved performance, challenges remain in preventing off-road predictions and ensuring kinematic feasibility. Existing methods incorporate road-awareness modules and enforce kinematic constraints but lack plausibility guarantees and often introduce trade-offs in complexity and flexibility. This paper proposes a novel framework that formulates trajectory prediction as a constrained regression guided by permissible driving directions and their boundaries. Using the agent's current state and an HD map, our approach defines the valid boundaries and ensures on-road predictions by training the network to learn superimposed paths between left and right boundary polylines. T o guarantee feasibility, the model predicts acceleration profiles that determine the vehicle's travel distance along these paths while adhering to kinematic constraints. We evaluate our approach on the Argoverse-2 dataset against the HPTR baseline. Our approach shows a slight decrease in benchmark metrics compared to HPTR but notably improves final displacement error and eliminates infeasible trajectories. Moreover, the proposed approach has a superior generalization to less prevalent maneuvers and unseen out-of-distribution scenarios, reducing the off-road rate under adversarial attacks from 66% to just 1%.

Prior flow matching methods in robotics have primarily learned velocity fields to morph one distribution of trajectories into another. In this work, we extend flow matching to capture second-order trajectory dynamics, incorporating acceleration effects either explicitly in the model or implicitly through the learning objective. Unlike diffusion models, which rely on a noisy forward process and iterative denoising steps, flow matching trains a continuous transformation (flow) that directly maps a simple prior distribution to the target trajectory distribution without any denoising procedure. By modeling trajectories with second-order dynamics, our approach ensures that generated robot motions are smooth and physically executable, avoiding the jerky or dynamically infeasible trajectories that first-order models might produce. We empirically demonstrate that this second-order conditional flow matching yields superior performance on motion planning benchmarks, achieving smoother trajectories and higher success rates than baseline planners. These findings highlight the advantage of learning acceleration-aware motion fields, as our method outperforms existing motion planning methods in terms of trajectory quality and planning success.

The whole-body center of mass (CoM) plays an important role in quantifying human movement. Prediction of future CoM trajectory, modeled as a point mass under influence of external forces, can be a surrogate for inferring intent. Given the current CoM position and velocity, predicting the future CoM position by forward integration requires a forecast of CoM accelerations during the prediction horizon. However, it is unclear how assumptions about the acceleration, prediction horizon length, and information from ground reaction forces (GRFs), which provide the instantaneous acceleration, affect the prediction. We study these factors by analyzing data of 10 healthy young adults performing 14 non-cyclic activities. We assume that the acceleration during a horizon will be 1) zero, 2) remain constant, or 3) converge to zero as a cubic trajectory, and perform predictions for horizons of 125 to 625 milliseconds. We quantify the prediction performance by comparing the position error and accuracy of identifying the main direction of displacement against trajectories obtained from a whole-body marker set. For all the assumed accelerations profiles, position errors grow quadratically with horizon length ($R^2 > 0.930$) while the accuracy of the predicted direction decreases linearly ($R^2>0.615$). Post-hoc tests reveal that the constant and cubic profiles, which utilize the GRFs, outperform the zero-acceleration assumption in position error ($p<0.001$, Cohen's $d>3.23$) and accuracy ($p<0.034$, Cohen's $d>1.44)$ at horizons of 125 and 250$\,ms$. The results provide evidence for benefits of incorporating GRFs into predictions and point to 250$\,ms$ as a threshold for horizon length in predictive applications.

Motion prediction is a key factor towards the full deployment of autonomous vehicles. It is fundamental in order to ensure safety while navigating through highly interactive and complex scenarios. Lack of visibility due to an obstructed view or sensor range poses a great safety issue for autonomous vehicles. The inclusion of occlusion in interaction-aware approaches is not very well explored in the literature. In this work, the MultIAMP framework, which produces multimodal probabilistic outputs from the integration of a Dynamic Bayesian Network and Markov chains, is extended to tackle occlusions. The framework is evaluated with a state-of-the-art motion planner in two realistic use cases.

The Space Domain Awareness (SDA) community routinely tracks satellites in orbit by fitting an orbital state to observations made by the Space Surveillance Network (SSN). In order to fit such orbits, an accurate model of the forces that are acting on the satellite is required. Over the past several decades, high-quality, physics-based models have been developed for satellite state estimation and propagation. These models are exceedingly good at estimating and propagating orbital states for non-maneuvering satellites; however, there are several classes of anomalous accelerations that a satellite might experience which are not well-modeled, such as satellites that use low-thrust electric propulsion to modify their orbit. Physics-Informed Neural Networks (PINNs) are a valuable tool for these classes of satellites as they combine physics models with Deep Neural Networks (DNNs), which are highly expressive and versatile function approximators. By combining a physics model with a DNN, the machine learning model need not learn astrodynamics, which results in more efficient and effective utilization of machine learning resources. This paper details the application of PINNs to estimate the orbital state and a continuous, low-amplitude anomalous acceleration profile for satellites. The PINN is trained to learn the unknown acceleration by minimizing the mean square error of observations. We evaluate the performance of pure physics models with PINNs in terms of their observation residuals and their propagation accuracy beyond the fit span of the observations. For a two-day simulation of a GEO satellite using an unmodeled acceleration profile on the order of $10^{-8} \text{ km/s}^2$, the PINN outperformed the best-fit physics model by orders of magnitude for both observation residuals (123 arcsec vs 1.00 arcsec) as well as propagation accuracy (3860 km vs 164 km after five days).

A critical element in the development and deployment of AVs is the design of car-following (CF) controllers capable of producing desirable performance in real-world settings. Ideally, a CF control system would effectively and safely handle the longitudinal maneuvers of the vehicle at every encounter it faces. However, designing and training such a controller requires enormous data, testing, and experimentation that covers all possible driving scenarios/encounters. In other words, it requires us to have a perfect understanding of the environment these AVs would be operating under. Clearly, this is very challenging and, possibly, unattainable. AVs are likely to encounter unseen scenarios and be exposed to exogenous and endogenous uncertainties in the physical world. The sources of exogenous and endogenous uncertainties are vast and roughly classified into (Macfarlane and Stroila, 2016; Yao et al., 2020; Katrakazas et al., 2015): (i) vehicular and system dynamics (e.g., vehicle condition, road gradient, aerodynamic drag force, external loads, transmission, brake, the performance of the engine, etc.), (ii) environmental conditions (snow, dust, wind, wet conditions, etc.), and (iii) situational detection (e.g., sensor/measurement errors, radar errors, vehicle speed fluctuations, vehicle localization, communication latency, etc.). All these types of uncertainties can hinder desirable performance (e.g., stability). Yet, a major challenge lies in the complexity of integrating these uncertainties into the control system and the design of the AV.

Analysis of runner's data will often examine gait variables with reference to one or more gait events. Two such representative events are the initial contact and toe off events. These correspond respectively to the moments in time when the foot makes the initial contact with the ground and when the foot leaves the ground again. These variables are traditionally measured with a force plate or motion capture system in a lab setting. However, thanks to recent evolutions in wearable technology, the use of accelerometers has become commonplace for prolonged outdoor measurements. Previous research has developed heuristic methods to identify the initial contact and toe off timings based on minima, maxima and thresholds in the acceleration profiles. A significant flaw of these heuristic-based methods is that they are tailored to very specific acceleration profiles, providing no guidelines on how to handle deviant profiles. Therefore, we frame the problem as a structured prediction task and propose a machine learning approach for determining initial foot contact and toe off events from 3D tibial acceleration profiles. With mean absolute errors of 2 ms and 4 ms for respectively the initial contact and toe-off events, our method significantly outperforms the existing heuristic approaches.