Related papers: Forecasting Continuous Non-Conservative Dynamical …

Tracking and forecasting the rotation of objects is fundamental in computer vision and robotics, yet SO(3) extrapolation remains challenging as (1) sensor observations can be noisy and sparse, (2) motion patterns can be governed by complex…

This paper revisits the problem of continuous-time structure from motion, and introduces a number of extensions that improve convergence and efficiency. The formulation with a $\mathcal{C}^2$-continuous spline for the trajectory naturally…

Many robotic control tasks require policies to act on orientations, yet the geometry of SO(3) makes this nontrivial. Because SO(3) admits no global, smooth, minimal parameterization, common representations such as Euler angles, quaternions,…

In this article, a brief description of Discrete Mechanics and Variational Integrators which preserve the symplectic structure of the flow will be provided and a Newton-Raphson algorithm that can be used to solve implicit equations on the…

Learning about the three-dimensional world from two-dimensional images is a fundamental problem in computer vision. An ideal neural network architecture for such tasks would leverage the fact that objects can be rotated and translated in…

Single image pose estimation is a fundamental problem in many vision and robotics tasks, and existing deep learning approaches suffer by not completely modeling and handling: i) uncertainty about the predictions, and ii) symmetric objects…

3D human motion prediction is a research area of high significance and a challenge in computer vision. It is useful for the design of many applications including robotics and autonomous driving. Traditionally, autogregressive models have…

In many real-world settings, image observations of freely rotating 3D rigid bodies, such as satellites, may be available when low-dimensional measurements are not. However, the high-dimensionality of image data precludes the use of…

The number of resident space objects is rising at an alarming rate. Mega-constellations and breakup events are proliferating in most orbital regimes, and safe navigation is becoming increasingly problematic. It is important to be able to…

We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all…

Learning to predict reliable characteristic orientations of 3D point clouds is an important yet challenging problem, as different point clouds of the same class may have largely varying appearances. In this work, we introduce a novel method…

In real-world robotics applications, accurate models of robot dynamics are critical for safe and stable control in rapidly changing operational conditions. This motivates the use of machine learning techniques to approximate robot dynamics…

This work proposes a nonlinear stochastic filter evolved on the Special Orthogonal Group SO(3) as a solution to the attitude filtering problem. One of the most common potential functions for nonlinear deterministic attitude observers is…

Learning complex trajectories from demonstrations in robotic tasks has been effectively addressed through the utilization of Dynamical Systems (DS). State-of-the-art DS learning methods ensure stability of the generated trajectories;…

This paper analyzes the robustness of recent 3D shape descriptors to SO(3) rotations, something that is fundamental to shape modeling. Specifically, we formulate the task of rotated 3D object instance detection. To do so, we consider a…

Dynamical Systems (DS) are an effective and powerful means of shaping high-level policies for robotics control. They provide robust and reactive control while ensuring the stability of the driving vector field. The increasing complexity of…

This paper contributes towards the development of motion tracking algorithms for time-critical applications, proposing an infrastructure for solving dynamically the inverse kinematics of highly articulate systems such as humans. We present…

Accurately modelling the dynamics of complex systems and discovering their governing differential equations are critical tasks for accelerating scientific discovery. Using noisy, synthetic data from two damped oscillatory systems, we…

A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model…

Successful control of a rigid-body rotating in three dimensional space requires accurate estimation of its attitude. The attitude dynamics are highly nonlinear and are posed on the Special Orthogonal Group $SO(3)$. In addition, measurements…