Topological and Algebraic Invariants to Classify Types of Singularities of Maps relevant to...
summary
Classifies kinematic singularities into passable vs impassable types and shows when steering via the null space (SVD / Moore‑Penrose pseudoinverse) can recover exact control. Uses relative homology to count and measure singular components for minimally redundant systems (four CMGs) and notes six CMGs can push singularities to boundaries. Lifts trigonometric kinematic maps to real algebraic varieties, applies Thom‑Boardman stratification (Martin Helmer and Vidit Nanda) for finite computations via Macaulay2, and demonstrates a working 3,000‑kg simulator that points and holds. algebraic lifting and stratification
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chapters (10)
- 0:00Introduction
- 0:43Singularities in spacecraft pointing
- 3:12Kinematic maps and Jacobian rank
- 7:10Passable vs impassable singularities
- 10:19Classifying singularities by fiber topology
- 14:51Fibers and critical values
- 17:39Algebraic maps and stratification
- 20:49Existence of kinematic singularities
- 21:55Precision pointing demo
- 22:36Q&A
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