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Geometric Algebra Applications Vol. II

Robot Modelling and Control

  • Eduardo¬†Bayro-Corrochano
Book
  • 2.3k Downloads

Table of contents

  1. Front Matter
    Pages i-xxix
  2. Eduardo Bayro-Corrochano
    Pages 1-17
  3. Fundamentals of Geometric Algebra

    1. Front Matter
      Pages 19-19
    2. Eduardo Bayro-Corrochano
      Pages 21-54
    3. Eduardo Bayro-Corrochano
      Pages 55-123
    4. Eduardo Bayro-Corrochano
      Pages 125-152
    5. Eduardo Bayro-Corrochano
      Pages 153-179
    6. Eduardo Bayro-Corrochano
      Pages 181-217
    7. Eduardo Bayro-Corrochano
      Pages 243-252
  4. Interpolation, Kinematics, and Dynamics

    1. Front Matter
      Pages 253-253
    2. Eduardo Bayro-Corrochano
      Pages 255-267
    3. Eduardo Bayro-Corrochano
      Pages 269-295
    4. Eduardo Bayro-Corrochano
      Pages 297-357
  5. Robot Control

    1. Front Matter
      Pages 359-359
    2. Eduardo Bayro-Corrochano
      Pages 361-377
    3. Eduardo Bayro-Corrochano
      Pages 379-412
    4. Eduardo Bayro-Corrochano
      Pages 413-427
  6. Applications I: Robot Vision, Quadrotor

    1. Front Matter
      Pages 429-429
    2. Eduardo Bayro-Corrochano
      Pages 431-462
    3. Eduardo Bayro-Corrochano
      Pages 463-476
    4. Eduardo Bayro-Corrochano
      Pages 477-505
    5. Eduardo Bayro-Corrochano
      Pages 507-530
    6. Eduardo Bayro-Corrochano
      Pages 531-543
  7. Applications II: Medical Robotics

    1. Front Matter
      Pages 545-545
    2. Eduardo Bayro-Corrochano
      Pages 547-563
    3. Eduardo Bayro-Corrochano
      Pages 565-583
  8. Back Matter
    Pages 585-600

About this book

Introduction

The goal of Geometric Algebra Applications Vol. II: Robot Modeling and Control is to present a unified mathematical treatment of diverse problems in the general domain of robotics and associated fields using Clifford, or geometric algebra. By treating a wide spectrum of problems in a common language, this Volume II offers both new insights and new solutions that should be useful to scientists, and engineers working in different areas related with robotics.

Topics and features

-Introduces a no specialists to Clifford, or geometric, algebra and by examples encourages the reader to learn to compute using geometric entities and geometric formulations.

-A study in depth for 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.

-Includes a thorough study of kinematics, differential kinematics and dynamics using geometric algebra. The Euler Lagrange and Hamiltonians equations for dynamics are developed using conformal geometric algebra and the recursive Newton-Euler using screw theory in the motor algebra framework. A thorough study of robot modeling and nonlinear controllers.

-Thorough discussion of several applications in computer vision, graphics, neurocomputing, quantum computing, robotics and control engineering using the geometric algebra framework.

-209 exercises and hints for the development of future computer software packages for extensive calculations in geometric algebra. A entire section is dedicated to explain how one should write the subroutines in C++, Matlab and Maple to carry out efficient geometric computations in the geometric algebra framework. Furthermore it is shown how program code can be optimized for real time computations.

-The book is an essential resource for applied physicists, computer scientists, AI researchers, roboticists and mechanical and electrical engineers, it clarifies and demonstrates the importance of geometric computing for building autonomous systems and push forward advances in cognitive systems research.

Keywords

Cognitive Robotics Geometric Algebra Humanoids Medical Robotics Robotics

Authors and affiliations

  • Eduardo¬†Bayro-Corrochano
    • 1
  1. 1.Electrical Engineering and Computer Science DepartmentCINVESTAVGuadalajaraMexico

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