Geometric Algebra Applications Vol. II

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.

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.

Featuring a detailed study of kinematics, differential kinematics and dynamics

using geometric algebra, the book also develops Euler Lagrangeand 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.

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.

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.

Offers in a compact and complete way the theory and methods to apply Geometric Algebra to Robotics Introduces the basics of geometric algebra to specialists and non- specialists in a gentle and comprehensive manner using examples and abundant figures and simulation results Step by step using examples encourages readers to learn how to model, design algorithms for modern applications in the area of robotics

Zusammenfassung
"The book is intended for students and scientists and should be of interest to practicing and research engineers as well of the PhD students in the field of robot modeling and control." (Clementina Mladenova, zbMATH 1471.93001, 2021)

Inhalt
Geometric Algebra for Modeling in Robotic Physics.- Introduction to Geometric Algebra.- Lie Algebras, Lie Groups and Algebra of Incidence.- 2D, 3D and 4D Geometric Algebras.- Kinematics of the 2D and 3D Spaces.- Conformal Geometric Algebra.- Programming Issues.- Rigid Motion Interpolation.- Robot Kinematics.- Robot Dynamics.- Control of Robot Manipulators.- Robot Neurocontrol.- Robot Control and Tracking.- Rigid Motion Estimation Using Line Observations.- Tracker Endoscope Calibration and Body-Sensors Calibration.- Tracking, Grasping and Object Manipulation.- 3D Maps, Navigation and Relocalization.- Quadrotor.- Modeling and Registration of Medical Data.- Geometric Computing for Minimal Invasive Surgery.