A Cyber-Physical Sovereign Architecture for Autonomous Grid-Inspection Humanoids: Real-Time Kinematic Optimization, LMI-Synthesized H∞ Control, and Immutable Zero-Trust Sandboxing (Phase II)

Abstract

Autonomous humanoid robotics deployed in high-voltage transmission grid inspection require deterministic stability guarantees and cryptographic resilience against physical, cyber, and adversarial sensor intrusion. Most existing architectures decouple software security from physical control theory, introducing vulnerabilities where software exploitation or sensor spoofing causes catastrophic mechanical cascade failures. This paper establishes the mathematical foundation and systems architecture for Phase II of the ZARQA Grid Inspection Humanoid Core (zarqa_gih_kinematics_core.py). We establish proofs of asymptotic stability and disturbance attenuation for an underactuated 7-Degree-of-Freedom (7-DOF) humanoid manipulator and balance controller operating on high-voltage transmission towers. Specifically, we prove: 1. Kinematic Singularity Resilience: Global convergence of a hybrid Active-Set Sequential Least Squares Programming (SLSQP) and Damped Least-Squares (DLS) inverse kinematics algorithm bounded by minimum singular value damping. 2. Disturbance Attenuation: Lyapunov-based dissipation inequalities for Linear Matrix Inequality (LMI) synthesized controllers under continuous wind loads and structural tower vibrations. 3. False Data Injection Attack (FDIA) Resilience: Cartesian residual boundedness that mathematically guarantees detection of adversarial encoder injection before actuator saturation occurs. The control engine is embedded inside an immutable, zero-trust Blue-Green Linux sandboxing architecture with TPM 2.0 cryptographic attestation and POSIX atomic symlink deployment, achieving full compliance with IEC 63439 and IEC 62443 industrial automation standards.