The Geometry of Flight: A Geometric Reading of Guidance, Navigation, and Control (Geometric Intelligence)

A new book in the Davis-Geometric series. A geometric reading of Guidance, Navigation, and Control, written backwards from a patent-pending flight-control architecture.Twenty-seven years in aerospace, intelligence, and cybersecurity. Then a layoff, a job at Olive Garden, and a stranger at table six whose husband turned out to be a rocket scientist. He asked if I'd ever heard of GNC. I hadn't.A few weeks later: a recognition. Guidance, Navigation, and Control is geometric to the bone. Configuration manifolds as fiber bundles. Attitude on the three-sphere as the double cover of SO(3). Trajectories as geodesics. The Bode sensitivity integral as a Gauss–Bonnet-style obstruction on the frequency line. The Kalman filter as natural-gradient estimation on the Fisher manifold. The entire classical stack — Bode, LQR, H∞, Kalman, Lyapunov, MRAC, SLAM, guidance — re-derived as fiber-bundle calculations on a small set of geometric primitives.This book is that derivation, written backwards from ICARUS — the flight-control architecture the Davis-Geometric framework was built to produce.What's insideThe Bra Strap Principle and the Davis Field Equation, the framework's two foundational resultsThe classical control stack — Bode, LQR, H∞ — re-derived as geometric obstructions on the controller bundleKalman filtering on the Fisher manifold; Lyapunov methods; MRAC and the matching condition; the Curvature Floor conjectureInertial navigation, GNSS/INS fusion, and SLAM as bundle composition, with loop closure as the Bra Strap Principle made operationalThe ICARUS architecture in full: GIGI (the fiber-bundle database), DHOOM (the wire format), the curvature-gated controller, the non-actuating sentinelGuidance as geodesic computation on a cost manifold, with the classical laws (waypoint following, proportional navigation, terminal energy management, minimum-time and minimum-fuel) as cost-functional instances of one machinerySix runnable Python labs covering bundle storage, closed-loop simulation, MRAC with persistency-of-excitation monitoring, GNSS/INS + SLAM fusion, the end-to-end ICARUS run, and guidance with obstaclesSix appendices — notation index, framework glossary, primers on sub-Riemannian geometry, Fisher information, and Pontryagin's Minimum Principle, plus an end-to-end worked example walking one millisecond of an X4 quadcopter control cycle through every layer of the frameworkWritten forAerospace and controls engineers who want the geometric reading of the field they work inMathematicians and applied geometers who want to see the bundle structure GNC has been hidingStudents of either field looking for the book that translates between themAnyone curious how a self-taught researcher built a flight-control architecture from differential geometry and a fiber-bundle databaseBee Rosa Davis is a Trinidadian-American applied-mathematics researcher and aerospace systems builder. Previously: NASA Mission Systems Engineer, NSA, DISA, founding engineer at Pandora, principal adversarial-intelligence researcher at IBM X-Force Red. Holds an MS in Digital Forensics, Counterintelligence, and Cybersecurity from Brown University; an MA in Communication from the University of the Pacific; and a BA in Logic and Analytics from Morehouse College, where she was a Martin Luther King Jr. Scholar.ICARUS, GIGI, and DHOOM are covered by US provisional patents (64/045,891, 64/045,889, 64/008,940). The architecture's defensive commitments are explicit and architectural: the sentinel module is non-actuating by construction.The Geometry of Flight is the fifth book in the Davis-Geometric series. Nearly 600 pages, with fifteen figures, six labs, six appendices, and a unified references chapter. Read more