This paper proposesa new class of unit quaternion curves in SO(3). A general method is developed that transforms a curve in R3 (defined as a weighted sum of basis functions) into its unit quaternion analogue in SO(3). Applying the method to well-known spline curves (such as Bézier, Hermite, and B-spline curves), we are able to construct various unit quaternion curves which share many important ...

We address the synthesis of serial chain spatial mechanisms with revolute joints in which the rotations about the joints are coupled via cables and pulleys. Such coupled serial chain mechanisms o er a middle ground between the more versatile and compact serial chains and the simpler closed chains by combining some of the advantages of both types of systems. In particular, we focus on the synthe...

Formulation of proper and efficient algorithms for robot kinematics is essential for the analysis and design of serial manipulators. Kinematic modeling of manipulators is most often performed in Cartesian space. However, due to disadvantages of most widely used mathematical constructs for description of orientation such as Euler angles and rotational matrices, a need for unambiguous, compact, s...

In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular admissibility condition. We present several ...

Quaternion-valued signals along with quaternion Fourier transforms (QFT) provide an effective framework for vector-valued signal and image processing. However, the sampling theory of quaternion valued signals has not been well developed. In this paper, we present the generalized sampling expansions associated with QFT by using the generalized translation and convolution. We show that a σ-bandli...

Quaternion models have been developed for both direction of arrival estimation and beamforming based on crossed-dipole arrays in the past. However, for almost all the models, especially for adaptive beamforming, the desired signal is still complex-valued and one example is the quaternion-Capon beamformer. However, since the complex-valued desired signal only has two components, while there are ...

The field of deep learning has seen significant advancement in recent years. However, much of the existing work has been focused on real-valued numbers. Recent work has shown that a deep learning system using the complex numbers can be deeper for a fixed parameter budget compared to its real-valued counterpart. In this work, we explore the benefits of generalizing one step further into the hype...