Geometry And Robotics
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Geometric Fundamentals of Robotics
Author: J.M. Selig
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-12-13
Geometric Fundamentals of Robotics provides an elegant introduction to the geometric concepts that are important to applications in robotics. This second edition is still unique in providing a deep understanding of the subject: rather than focusing on computational results in kinematics and robotics, it includes significant state-of-the-art material that reflects important advances in the field, connecting robotics back to mathematical fundamentals in group theory and geometry. Geometric Fundamentals of Robotics serves a wide audience of graduate students as well as researchers in a variety of areas, notably mechanical engineering, computer science, and applied mathematics. It is also an invaluable reference text.
Algebraic Geometry for Robotics and Control Theory
Author: Laura Menini
language: en
Publisher: World Scientific Publishing Europe Limited
Release Date: 2021-09-28
Algebraic geometry notions -- Implementations in Macaulay2 -- The inverse kinematics of robot arms -- Observer design -- Immersions of polynomial systems into linear ones up to an output injection -- Solving systems of equations and inequalities -- Motion planning for mobile robots -- Computation of the largest f-invariant set contained in an affine variety -- Boolean networks -- Multi-objective optimization -- Distance to internal instability of LTI systems under structured perturbations -- Decomposition in sum of squares.
Geometrical Methods in Robotics
Author: J. M. Selig
language: en
Publisher: Springer Science & Business Media
Release Date: 1996
Subsequent chapters develop the structure of Lie groups and how these relate to planar kinematics, line geometry, representation theory, and other topics. Having provided the conceptual framework, the author then demonstrates the power and elegance of these methods to robotics, notably to the statics and dynamics of robots, to the problems of gripping solid objects, to the numbers of postures of robots, and to screw systems.