[Announcement] Theoretical Framework Refinement: Shift to Partial Stability & Architecture-Level Robustness #2
Description
Major Update on Theoretical Framework
I'll transitioning the mathematical proof of the Trajecto framework from an ideal global stability model to a realistic, architecture-oriented partial stability model.
1. Why the Change?
- Reality Check: We acknowledge that in a pure IMU setup without GPS, the absolute position state is Rank Deficient (unobservable). Claiming global asymptotic stability for position was physically inaccurate.
- Focus on Usability: For 3D handwriting tasks, preserving the relative shape (geometry) is more critical than preventing absolute global drift.
2. Current Status of Mathematical Proof (v1.0)
Validated: We have strictly proven the Partial Stability of the observable states (velocity, attitude) and the Linearity of position drift. This mathematically guarantees the system's robustness for handwriting tasks.
Limitation: Due to the hardware rank-deficiency (no GPS), global asymptotic stability for absolute position is physically unattainable. Therefore, our proof focuses on Shape Consistency rather than absolute localization.
Future Roadmap: We plan to extend this analysis using Itô Calculus (SDE) in future versions to model stochastic noise properties more deeply.
3. Documentation
The updated proof has been uploaded to docs/Proof_of_HybridModel.pdf. This document represents the definitive theoretical basis for the current v1.0 release.
Note: This issue will be pinned to serve as a reference for the project's theoretical background.