A Hardware-Efficient Approach to Computing the Rotation Matrix from a Quaternion

TL;DR

This paper introduces a hardware-efficient method for computing rotation matrices from quaternions by replacing multiplications with squarings, reducing power consumption and circuit complexity in VLSI implementations.

Contribution

It presents a novel VLSI-oriented approach using Logan's identity to eliminate multiplications in quaternion to rotation matrix conversion.

Findings

Reduces hardware complexity and power consumption

Eliminates multiplications by replacing them with squarings

Uses Logan's identity for efficient computation

Abstract

In this paper, we have proposed a novel VLSI-oriented approach to computing the rotation matrix entries from the quaternion coefficients. The advantage of this approach is the complete elimination of multiplications and replacing them by less costly squarings. Our approach uses Logan's identity, which proposes to replace the calculation of the product of two numbers on summing the squares via the Binomial Theorem. Replacing multiplications by squarings implies reducing power consumption as well as decreases hardware circuit complexity.