Related papers: Rigidity Theory in SE(2) for Unscaled Relative Pos…
A key limitation of current multi-robot systems is a lack of relative localization, particularly in environments without GPS or motion capture systems. This article presents a centralized method for relatively localizing a 2D swarm using…
Category theory plays a special character in mathematics - it unifies distinct branches under the same formalism. Despite this integrative power in math, it also seems to provide the proper foundations to the experimental physicist. In this…
Compared with traditional rigid-body robots, soft robots not only exhibit unprecedented adaptation and flexibility but also present novel challenges in their modeling and control because of their infinite degrees of freedom. Most of the…
Accurately modeling soft robots in simulation is computationally expensive and commonly falls short of representing the real world. This well-known discrepancy, known as the sim-to-real gap, can have several causes, such as coarsely…
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…
Scalable frames are frames with the property that the frame vectors can be rescaled resulting in tight frames. However, if a frame is not scalable, one has to aim for an approximate procedure. For this, in this paper we introduce three…
We present a novel framework for the probabilistic modelling of random fourth order material tensor fields, with a focus on tensors that are physically symmetric and positive definite (SPD), of which the elasticity tensor is a prime…
Accurate state estimation for flexible robotic systems poses significant challenges, particularly for platforms with dynamically deforming structures that invalidate rigid-body assumptions. This paper addresses this problem and enables the…
Precisely tracking uncertainties is crucial for robots to successfully and safely operate in unstructured and dynamic environments. We present a probabilistic framework to precisely keep track of uncertainties throughout the entire…
Accurate robot kinematics is essential for precise tool placement in articulated robots, but non-geometric factors can introduce configuration-dependent model discrepancies. This paper presents a configuration-dependent kinematic…
We analyse a second-order SPDE model in multiple space dimensions and develop estimators for the parameters of this model based on discrete observations of a solution in time and space on a bounded domain. While parameter estimation for one…
The non-commutative nature of 3D rotations poses well-known challenges in generalizing planar problems to three-dimensional ones, even more so in contact-rich tasks where haptic information (i.e., forces/torques) is involved. In this sense,…
In this work, we utilize discrete geometric mechanics to derive a 2nd-order variational integrator so as to simulate rigid body dynamics. The developed integrator is to simulate the motion of a free rigid body and a quad-rotor. We…
A rigid motion in $\mathbb{R}^d$ consists of a proper rotation and a translation, and it can be represented as a matrix in $\mathbb{R}^{(d+1)\times (d+1)}$. The problem of rigid motion synchronization aims to estimate a collection of rigid…
A natural problem in combinatorial rigidity theory concerns the determination of the rigidity or flexibility of bar-joint frameworks in $\mathbb{R}^d$ that admit some non-trivial symmetry. When $d=2$ there is a large literature on this…
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…
Radio-based methods such as Ultra-Wideband (UWB) and RAdio Detection And Ranging (radar), which have traditionally seen limited adoption in robotics, are experiencing a boost in popularity thanks to their robustness to harsh environmental…
We introduce and analyze a model for self-reconfigurable robots made up of unit-cube modules. Compared to past models, our model aims to newly capture two important practical aspects of real-world robots. First, modules often do not occupy…
It is well-understood that different algorithms, training processes, and corpora produce different word embeddings. However, less is known about the relation between different embedding spaces, i.e. how far different sets of embeddings…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…