Related papers: Special Orthogonal Group SO(3), Euler Angles, Angl…
Strapdown inertial navigation research involves the parameterization and computation of the attitude, velocity and position of a rigid body in a chosen reference frame. The community has long devoted to finding the most concise and…
Euler proved that every rotation of a 3-dimensional body can be realized as a sequence of three rotations around two given axes. If we allow sequences of an arbitrary length, such a decomposition will not be unique. In this paper we solve…
The orthogonal projection of a 4-cube onto a uniform random 3-subspace in R^4 is a convex 3-polyhedron P with 14 vertices almost surely. Three numerical characteristics of P -- volume, surface area and mean width -- are studied. These…
Many robotic systems allow independent control of position and orientation (pose), including omnidirectional aerial vehicles, underwater robots, and manipulator end-effectors. In many applications, these systems must follow a continuous…
Previous work on predicting or generating 3D human pose sequences regresses either joint rotations or joint positions. The former strategy is prone to error accumulation along the kinematic chain, as well as discontinuities when using Euler…
In this paper, we provide some careful analysis of certain pathological behavior of Euler angles and unit quaternions encountered in previous works related to rotation representation in neural networks. In particular, we show that for…
We compare three approaches to posing the index 3 set of differential algebraic equations (DAEs) associated with the constrained multibody dynamics problem formulated in absolute coordinates. The first approach works directly with the…
Determining the 3D orientations of an object in an image, known as single-image pose estimation, is a crucial task in 3D vision applications. Existing methods typically learn 3D rotations parametrized in the spatial domain using Euler…
This paper considers the problem of nonlinear attitude estimation for a rigid body system using intermittent and multi-rate inertial vector measurements as well as continuous (high-rate) angular velocity measurements. Two types of hybrid…
The mechanics of an oriented point (point with "spin") based on 3D and 4D Frenet equations is considered. In such mechanics there is an opportunity to describe formally any physical trajectory of a particle with own rotation. We use…
Two novel robust nonlinear stochastic full pose (i.e, attitude and position) estimators on the Special Euclidean Group SE(3) are proposed using the available uncertain measurements. The resulting estimators utilize the basic structure of…
This paper proposes to use the three vectors in a rotation matrix as the representation in head pose estimation and develops a new neural network based on the characteristic of such representation. We address two potential issues existed in…
We give a simple and self contained introduction to quaternions and their practical usage in dynamics. The rigid body dynamics are presented in full details. In the appendix, some more exotic relations are given that allow to write more…
This paper primarily focuses on evaluating and benchmarking the robustness of visual representations in the context of object assembly tasks. Specifically, it investigates the alignment and insertion of objects with geometrical extrusions…
Starting from the defining transformations of complex matrices for the SO(4) group, we construct the fundamental representation and the tensor and spinor representations of the group SO(4). Given the commutation relations for the…
This paper presents a geometric control framework on the Lie group SO(3) for 3D source-seeking by robots with first-order attitude dynamics and constant translational speed. By working directly on SO(3), the approach avoids Euler-angle…
We consider a category-level perception problem, where one is given 3D sensor data picturing an object of a given category (e.g. a car), and has to reconstruct the pose and shape of the object despite intra-class variability (i.e. different…
6D pose estimation of rigid objects from RGB-D images is crucial for object grasping and manipulation in robotics. Although RGB channels and the depth (D) channel are often complementary, providing respectively the appearance and geometry…
Just like the well-established Euler angles representation, fused angles are a convenient parameterisation for rotations in three-dimensional Euclidean space. They were developed in the context of balancing bodies, most specifically walking…
The left and right invariant vector fields are calculated in an ``Euler angle'' type parameterization for the group manifold of SU(3), referred to here as Euler coordinates. The corresponding left and right invariant one-forms are then…