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In this chapter we will consider two applications of concepts and techniques from algebraic geometry in areas of computer science. First, continuing a theme introduced in several examples in Chapter 1, we will develop a systematic approach that uses affine varieties to describe the space of possible configurations of mechanical linkages such as robot “arms.” We will use this approach to solve the forward and inverse kinematic problems of robotics for certain types of robots.

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Robotics and Automatic Geometric Theorem Proving

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  • 发表日期：

    2025年

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  • David A. Cox,
  • John Little,
  • Donal O’Shea

摘要

In this chapter we will consider two applications of concepts and techniques from algebraic geometry in areas of computer science. First, continuing a theme introduced in several examples in Chapter 1, we will develop a systematic approach that uses affine varieties to describe the space of possible configurations of mechanical linkages such as robot “arms.” We will use this approach to solve the forward and inverse kinematic problems of robotics for certain types of robots.