Introduction

This book presents a unified mathematical treatment of diverse problems in the

general domain of robotics and associated fields using Clifford or geometric alge-

bra. By addressing a wide spectrum of problems in a common language, it offers

both fresh insights and new solutions that are useful to scientists and engineers

working in areas related with robotics.

Overview

It introduces non-specialists to Clifford and geometric algebra, and provides ex-

amples to help readers learn how to compute using geometric entities and geomet-

ric formulations. It also includes an in-depth study of applications of Lie group

theory, Lie algebra, spinors and versors and the algebra of incidence using the

universal geometric algebra generated by reciprocal null cones.

Applications and Topics Covered

Featuring a detailed study of kinematics, differential kinematics and dynamics

using geometric algebra, the book also develops Euler Lagrange and Hamiltoni-

ans equations for dynamics using conformal geometric algebra, and the recursive

Newton-Euler using screw theory in the motor algebra framework. Further, it

comprehensively explores robot modeling and nonlinear controllers, and discusses

several applications in computer vision, graphics, neurocomputing, quantum com-

puting, robotics and control engineering using the geometric algebra framework.

Additional Content

The book also includes over 200 exercises and tips for the development of future

computer software packages for extensive calculations in geometric algebra, and a

entire section focusing on how to write the subroutines in C++, Matlab and Maple

to carry out efficient geometric computations in the geometric algebra framework.

Lastly, it shows how program code can be optimized for real-time computations.

Target Audience

An essential resource for applied physicists, computer scientists, AI researchers,

roboticists and mechanical and electrical engineers, the book clarifies and demon-

strates the importance of geometric computing for building autonomous systems

to advance cognitive systems research.