Related papers: Learning Stable Vector Fields on Lie Groups

Stable dynamical systems are a flexible tool to plan robotic motions in real-time. In the robotic literature, dynamical system motions are typically planned without considering possible limitations in the robot's workspace. This work…

A novel Neural Network architecture is proposed using the mathematically and physically rich idea of vector fields as hidden layers to perform nonlinear transformations in the data. The data points are interpreted as particles moving along…

This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the…

Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued…

Accurate gravity field models are essential for safe proximity operations around small bodies. State-of-the-art techniques use spherical harmonics or high-fidelity polyhedron shape models. Unfortunately, these techniques can become…

This paper presents a novel control protocol for distance and orientation formation control of rigid bodies, whose sensing graph is a static and undirected tree, in the special Euclidean group SE(3). The proposed control laws are…

Vision-Language-Action (VLA) models offer a compelling framework for tackling complex robotic manipulation tasks, but they are often expensive to train. In this paper, we propose a novel VLA approach that leverages the competitive…

Inverse kinematics is a fundamental technique for motion and positioning control in robotics, typically applied to end-effectors. In this paper, we extend the concept of inverse kinematics to guiding vector fields for path following in…

This paper presents a generic motion model to capture mobile robots' dynamic behaviors (translation and rotation). The model is based on statistical models driven by white random processes and is formulated into a full state estimation…

Robots need to be able to adapt to unexpected changes in the environment such that they can autonomously succeed in their tasks. However, hand-designing feedback models for adaptation is tedious, if at all possible, making data-driven…

Robots are increasingly being deployed not only in workplaces but also in households. Effectively execute of manipulation tasks by robots relies on variable impedance control with contact forces. Furthermore, robots should possess adaptive…

Model generalization of the underlying dynamics is critical for achieving data efficiency when learning for robot control. This paper proposes a novel approach for learning dynamics leveraging the symmetry in the underlying robotic system,…

Force fields developed with machine learning methods in tandem with quantum mechanics are beginning to find merit, given their (i) low cost, (ii) accuracy, and (iii) versatility. Recently, we proposed one such approach, wherein, the…

Two novel nonlinear pose (i.e, attitude and position) filters developed directly on the Special Euclidean Group SE(3)able to guarantee prescribed characteristics of transient and steady-state performance are proposed. The position error and…

Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been…

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 paper presents a novel nonlinear pose filter evolved directly on the Special Euclidean Group SE(3) with guaranteed characteristics of transient and steady-state performance. The above-mention characteristics can be achieved by trapping…

Classical mathematical techniques such as discrete integration, gradient descent optimization, and state estimation (exemplified by the Runge-Kutta method, Gauss-Newton minimization, and extended Kalman filter or EKF, respectively), rely on…

We introduce an approach based on moving frames for polygon recognition and symmetry detection. We present detailed algorithms for recognition of polygons modulo the special Euclidean, Euclidean, equi-affine, skewed-affine and similarity…

Most prior research in deep imitation learning has predominantly utilized fixed cameras for image input, which constrains task performance to the predefined field of view. However, enabling a robot to actively maneuver its neck can…