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Data-driven models of robot motion constructed using principles from Geometric Mechanics have been shown to produce useful predictions of robot motion for a variety of robots. For robots with a useful number of DoF, these geometric…
Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a…
In this paper, a distributed stochastic gradient (SG) algorithm is proposed where the estimators are aimed to collectively estimate an unknown time-invariant parameter from a set of noisy measurements obtained by distributed sensors. The…
This paper introduces a novel motion planning algorithm for stochastic scenarios. We extend the concept of a navigation function to such scenarios. Our main idea is to consider both the Gaussian distribution probabilities of the players'…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
Effective collective decision-making in swarm robotics often requires balancing exploration, communication and individual uncertainty estimation, especially in hazardous environments where direct measurements are limited or costly. We…
Recent 3D Gaussian Splatting (3DGS) techniques for Visual Simultaneous Localization and Mapping (SLAM) have significantly progressed in tracking and high-fidelity mapping. However, their sequential optimization framework and sensitivity to…
We consider nonlinear stochastic systems that arise in path planning and control of mobile robots. As is typical of almost all nonlinear stochastic systems, the optimally solving problem is intractable. We provide a design approach which…
This paper tackles the problem of missing data imputation for noisy and non-Gaussian data. A classical imputation method, the Expectation Maximization (EM) algorithm for Gaussian mixture models, has shown interesting properties when…
Accurate platform localization is an integral component of most robotic systems. As these robotic systems become more ubiquitous, it is necessary to develop robust state estimation algorithms that are able to withstand novel and…
This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…
A key ingredient to achieving intelligent behavior is physical understanding that equips robots with the ability to reason about the effects of their actions in a dynamic environment. Several methods have been proposed to learn dynamics…
Accurate prediction of future agent trajectories is a critical challenge for ensuring safe and efficient autonomous navigation, particularly in complex urban environments characterized by multiple plausible future scenarios. In this paper,…
We present a mathematical model to predict pedestrian motion over a finite horizon, intended for use in collision avoidance algorithms for autonomous driving. The model is based on a road map structure, and assumes a rational pedestrian…
In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…
This letter presents a continuous probabilistic modeling methodology for spatial point cloud data using finite Gaussian Mixture Models (GMMs) where the number of components are adapted based on the scene complexity. Few hierarchical and…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
Perception algorithms that provide estimates of their uncertainty are crucial to the development of autonomous robots that can operate in challenging and uncontrolled environments. Such perception algorithms provide the means for having…
RecentadvancesinDistributedComputinghighlightmodelsandalgo- rithms for autonomous swarms of mobile robots that self-organize and cooperate to solve global objectives. The overwhelming majority of works so far considers handmade algorithms…
Many systems such as autonomous vehicles and quadrotors are subject to parametric uncertainties and external disturbances. These uncertainties can lead to undesired performance degradation and safety issues. Therefore, it is important to…