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Trajectories are fundamental to winning in alpine skiing. Tools enabling the analysis of such curves can enhance the training activity and enrich broadcasting content. In this paper, we propose SkiTraVis, an algorithm to visualize the sequence of points traversed by a skier during its performance. SkiTraVis works on monocular videos and constitutes a pipeline of a visual tracker to model the skier's motion and of a frame correspondence module to estimate the camera's motion. The separation of the two motions enables the visualization of the trajectory according to the moving camera's perspective. We performed experiments on videos of real-world professional competitions to quantify the visualization error, the computational efficiency, as well as the applicability. Overall, the results achieved demonstrate the potential of our solution for broadcasting media enhancement and coach assistance.

We introduce a method for generating realistic pedestrian trajectories and full-body animations that can be controlled to meet user-defined goals. We draw on recent advances in guided diffusion modeling to achieve test-time controllability of trajectories, which is normally only associated with rule-based systems. Our guided diffusion model allows users to constrain trajectories through target waypoints, speed, and specified social groups while accounting for the surrounding environment context. This trajectory diffusion model is integrated with a novel physics-based humanoid controller to form a closed-loop, full-body pedestrian animation system capable of placing large crowds in a simulated environment with varying terrains. We further propose utilizing the value function learned during RL training of the animation controller to guide diffusion to produce trajectories better suited for particular scenarios such as collision avoidance and traversing uneven terrain. Video results are available on the project page at //nv-tlabs.github.io/trace-pace .

The dynamics of systems of many degrees of freedom evolving on multiple scales are often modeled in terms of stochastic differential equations. Usually the structural form of these equations is unknown and the only manifestation of the system's dynamics are observations at discrete points in time. Despite their widespread use, accurately inferring these systems from sparse-in-time observations remains challenging. Conventional inference methods either focus on the temporal structure of observations, neglecting the geometry of the system's invariant density, or use geometric approximations of the invariant density, which are limited to conservative driving forces. To address these limitations, here, we introduce a novel approach that reconciles these two perspectives. We propose a path augmentation scheme that employs data-driven control to account for the geometry of the invariant system's density. Non-parametric inference on the augmented paths, enables efficient identification of the underlying deterministic forces of systems observed at low sampling rates.

We devise a theoretical framework and a numerical method to infer trajectories of a stochastic process from samples of its temporal marginals. This problem arises in the analysis of single cell RNA-sequencing data, which provide high dimensional measurements of cell states but cannot track the trajectories of the cells over time. We prove that for a class of stochastic processes it is possible to recover the ground truth trajectories from limited samples of the temporal marginals at each time-point, and provide an efficient algorithm to do so in practice. The method we develop, Global Waddington-OT (gWOT), boils down to a smooth convex optimization problem posed globally over all time-points involving entropy-regularized optimal transport. We demonstrate that this problem can be solved efficiently in practice and yields good reconstructions, as we show on several synthetic and real datasets.

The dynamic scheduling of ultra-reliable and low-latency traffic (URLLC) in the uplink can significantly enhance the efficiency of coexisting services, such as enhanced mobile broadband (eMBB) devices, by only allocating resources when necessary. The main challenge is posed by the uncertainty in the process of URLLC packet generation, which mandates the use of predictors for URLLC traffic in the coming frames. In practice, such prediction may overestimate or underestimate the amount of URLLC data to be generated, yielding either an excessive or an insufficient amount of resources to be pre-emptively allocated for URLLC packets. In this paper, we introduce a novel scheduler for URLLC packets that provides formal guarantees on reliability and latency irrespective of the quality of the URLLC traffic predictor. The proposed method leverages recent advances in online conformal prediction (CP), and follows the principle of dynamically adjusting the amount of allocated resources so as to meet reliability and latency requirements set by the designer.

Verification plays an essential role in the formal analysis of safety-critical systems. Most current verification methods have specific requirements when working on Deep Neural Networks (DNNs). They either target one particular network category, e.g., Feedforward Neural Networks (FNNs), or networks with specific activation functions, e.g., RdLU. In this paper, we develop a model-agnostic verification framework, called DeepAgn, and show that it can be applied to FNNs, Recurrent Neural Networks (RNNs), or a mixture of both. Under the assumption of Lipschitz continuity, DeepAgn analyses the reachability of DNNs based on a novel optimisation scheme with a global convergence guarantee. It does not require access to the network's internal structures, such as layers and parameters. Through reachability analysis, DeepAgn can tackle several well-known robustness problems, including computing the maximum safe radius for a given input, and generating the ground-truth adversarial examples. We also empirically demonstrate DeepAgn's superior capability and efficiency in handling a broader class of deep neural networks, including both FNNs, and RNNs with very deep layers and millions of neurons, than other state-of-the-art verification approaches.

Trajectory planning for multiple robots in shared environments is a challenging problem especially when there is limited communication available or no central entity. In this article, we present Real-time planning using Linear Spatial Separations, or RLSS: a real-time decentralized trajectory planning algorithm for cooperative multi-robot teams in static environments. The algorithm requires relatively few robot capabilities, namely sensing the positions of robots and obstacles without higher-order derivatives and the ability of distinguishing robots from obstacles. There is no communication requirement and the robots' dynamic limits are taken into account. RLSS generates and solves convex quadratic optimization problems that are kinematically feasible and guarantees collision avoidance if the resulting problems are feasible. We demonstrate the algorithm's performance in real-time in simulations and on physical robots. We compare RLSS to two state-of-the-art planners and show empirically that RLSS does avoid deadlocks and collisions in forest-like and maze-like environments, significantly improving prior work, which result in collisions and deadlocks in such environments.

In order to perform highly dynamic and agile maneuvers, legged robots typically spend time in underactuated domains (e.g. with feet off the ground) where the system has limited command of its acceleration and a constrained amount of time before transitioning to a new domain (e.g. foot touchdown). Meanwhile, these transitions can have instantaneous, unbounded effects on perturbations. These properties make it difficult for local feedback controllers to effectively recover from disturbances as the system evolves through underactuated domains and hybrid impact events. To address this, we utilize the fundamental solution matrix that characterizes the evolution of perturbations through a hybrid trajectory and its 2-norm, which represents the worst-case growth of perturbations. In this paper, the worst-case perturbation analysis is used to explicitly reason about the tracking performance of a hybrid trajectory and is incorporated in an iLQR framework to optimize a trajectory while taking into account the closed-loop convergence of the trajectory under an LQR tracking controller. The generated convergent trajectories are able to recover more effectively from perturbations, are more robust to large disturbances, and use less feedback control effort than trajectories generated with traditional optimization methods.

Mobile manipulator systems are comprised of a mobile platform with one or more manipulators and are of great interest in a number of applications such as indoor warehouses, mining, construction, forestry etc. We present an approach for computing actuator commands for such systems so that they can follow desired end-effector and platform trajectories without the violation of the nonholonomic constraints of the system in an indoor warehouse environment. We work with the Fetch robot which consists of a 7-DOF manipulator with a differential drive mobile base to validate our method. The major contributions of our project are, writing the dynamics of the system, Trajectory planning for the manipulator and the mobile base, state machine for the pick and place task and the inverse kinematics of the manipulator. Our results indicate that we are able to successfully implement trajectory control on the mobile base and the manipulator of the Fetch robot.

Recent advances in sensor and mobile devices have enabled an unprecedented increase in the availability and collection of urban trajectory data, thus increasing the demand for more efficient ways to manage and analyze the data being produced. In this survey, we comprehensively review recent research trends in trajectory data management, ranging from trajectory pre-processing, storage, common trajectory analytic tools, such as querying spatial-only and spatial-textual trajectory data, and trajectory clustering. We also explore four closely related analytical tasks commonly used with trajectory data in interactive or real-time processing. Deep trajectory learning is also reviewed for the first time. Finally, we outline the essential qualities that a trajectory management system should possess in order to maximize flexibility.