ZARQA Grid Inspection Humanoid Core

A Cyber-Physical Sovereign Architecture for Autonomous Grid-Inspection Humanoids: Formal Verification, Lyapunov Dissipation Bounds, and Immutable Zero-Trust Sandboxing.

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📌 Overview

Autonomous humanoid robotics deployed in high-voltage grid inspection and critical infrastructure require deterministic stability guarantees and cryptographic resilience against physical, cyber, and adversarial sensor intrusion.

The ZARQA Grid Inspection Humanoid Core implements an integrated, multi-phase verification, kinematics, and spatial cognition architecture that enforces an immutable operational invariant:
No physical action is executed unless the underlying differential dynamics are mathematically certified and cryptographically attested at runtime.

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🏛️ Core Mathematical & Defensive Guarantees

Phase 1: Foundational Mathematical Verification (zarqa_gih_math_core.py)

1. Kuramoto Phase-Locking ($r > 0.95$): Enforces Fault-Ride-Through (FRT) phase synchronization across distributed motor and clock networks under grid voltage disturbances.
2. Lyapunov Asymptotic Stability ($\gamma < -0.50$): Solves the Continuous Algebraic Riccati Equation (CARE) for Linear Inverted Pendulum Model (LIPM) dynamics, proving strict continuous energy dissipation.
3. ZMP Stochastic Walking Safety ($\vert{}p_{\text{ZMP}}\vert{} < 0.15\text{ m}$): Binds Zero-Moment Point walking balance under Ornstein-Uhlenbeck (OU) proprioceptive sensor drift.
4. DMP Merkle Attestation: Protects Dynamic Movement Primitive (DMP) motor trajectories via SHA3-256 binary Merkle tree root verification against runtime memory corruption.
5. TT-SLAM Tensor-Train Compression ($\rho < 0.10$): Compresses high-dimensional $16^3$ spatial occupancy grids into low-rank Tensor-Train manifolds for low-power edge controllers.
6. Zero-Trust Linux Sandboxing: Automated blue-green virtual environment provisioning, kernel capability restrictions (CAP_NET_BIND_SERVICE only), Address Family filtering (AF_INET, AF_UNIX), and TPM 2.0 / CSPRNG-seeded HMAC hash-chain audit logging.

Phase 2: Real-Time Kinematics & Underactuated Control (zarqa_gih_kinematics_core.py)

1. 7-DOF Denavit-Hartenberg Arm & Hybrid IK: Combines an Active-Set Sequential Least Squares Programming (SLSQP) primary solver with a Damped Least-Squares (DLS) Singular Value Decomposition (SVD) fallback solver to guarantee convergence near kinematic singularities without violating physical joint bounds.
2. LMI-Synthesized $H_\infty$ & LQR Underactuated Control: Manages balance and joint dynamics modeled as an LTI system via Riccati bisection search and Linear Matrix Inequality (LMI) barrier heuristics, falling back to an LQR controller under extreme disturbance attenuation.
3. Gait Stability & Tower-Climbing MPC: Implements a Discrete Algebraic Riccati Model Predictive Controller (MPC) for vertical climbing, featuring dynamic recovery damping that halts vertical progression and redirects 100% of control authority to balance recovery if disturbance estimates exceed 0.10.
4. False Data Injection Attack (FDIA) Resilience: Evaluates Cartesian Euclidean residuals between physical encoders and observer-estimated joint states ($r_{\text{Cartesian}} > \tau$), immediately rejecting spoofed sensor streams before actuator saturation occurs.
5. Machine-Epsilon Bounded Tolerance & Self-Repairing Calibration: Dynamically calculates geometry-scaled tolerance bounds ($\text{tol} = \max(\epsilon_{\text{mach}} \cdot L_{\max} \cdot \sqrt{n}, 10^{-6}\text{ m})$) and automatically recalculates and re-signs reference poses if calibration drift occurs.
6. Zero-Trust Blue-Green Execution & Hot-Reloading: Integrates POSIX atomic symlink swapping (renameat2), 120-second automated health-check rollbacks, TPM 2.0 / PBKDF2 HMAC-SHA256 configuration signing, and zero-downtime SIGHUP hot-reloading for runtime parameter updates.

Phase 3: Spatial Cognition & Tamper-Evident Perception (zarqa_gih_spatial_cognition_core.py)

1. Quantized Tustin CM-SS2D & LHP Invariance: Continuous-to-discrete bilinear (Tustin) state-space discretization proves Schur stability ($\vert{}z_k\vert{} < 1$) across gear-quantized sampling intervals under dynamic skew-symmetric perturbations ($A_{\text{pert}} = A + \epsilon J$).
2. Variational Bayesian GSCKF & Covariance Positive-Definiteness: Implements a Gaussian-Sum Cubature Kalman Filter (GSCKF) with Bures-Wasserstein trace regularization and Ledoit-Wolf shrinkage to guarantee strict positive-definiteness ($\lambda_{\min}(\Sigma_{\text{LW}}) > 0$) and bounded spectral condition numbers.
3. Tamper-Evident Spatial Memory: Binds 2D log-odds Bayesian occupancy mapping to a recursive SHA-256 cryptographic hash chain, ensuring collision-resistant detection of unauthorized spatial memory modification ($P(\text{detect}) \ge 1 - 2^{-256}$) under the Random Oracle Model.
4. Sobolev-Orthogonalized MoE-CLIP Anomaly Detection: Applies Fréchet Inception Distance (FID) gating on Sobolev-projected visual embeddings ($\mathcal{P}_{\alpha}(f)$), guaranteeing deterministic threshold separability between benign structural tower wear and adversarial visual camouflage.
5. Multi-Sensor Trust-Weighted Early Fusion & ISD-SLAM: Dynamically fuses multimodal perception (rgb, thermal, lidar, acoustic, spectral) with Mahalanobis residual trust decay and cross-evaluates LiDAR/IMU odometry ($\vert{}p_{\text{lidar}} - p_{\text{imu}}\vert{} > \tau_{\text{abs}}$) to reject spoofed localization streams.
6. Persistent AEAD & Adaptive Timestamp Synchronization: Wraps odometry and occupancy payloads in GCM-mode AES-256 authenticated encryption seeded by TPM 2.0 / PBKDF2 hardware keys with monotonic boot-counter nonces and asymmetric temporal window gating ($\tau_{\text{local}} - \epsilon_{\text{past}} \le \tau_{\text{recv}} \le \tau_{\text{local}} + \epsilon_{\text{future}}$).

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📂 Repository Structure

ZARQA-Grid-Inspection-Humanoid-Core/
├── LICENSE
├── README.md
├── .gitignore
│
├── phase1_foundational_core/
│   ├── zarqa_gih_math_core.py               # Foundational runtime verification engine
│   └── proofs/                              # Automated Lean 4 theorem verification scripts
│       ├── kuramoto.lean
│       ├── lyapunov.lean
│       └── zmp.lean
│
├── phase2_kinematics_core/
│   └── zarqa_gih_kinematics_core.py         # Real-time DH kinematics, H-infinity control & FDIA filter
│
└── phase3_spatial_cognition_core/
    └── zarqa_gih_spatial_cognition_core.py  # GSCKF spatial estimation, MoE-CLIP anomaly detection & AEAD memory

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🚀 Getting Started & Usage

1. Requirements & Prerequisites

• Linux OS (Ubuntu 22.04 / 24.04 LTS recommended)
• Python 3.10+
• tpm2-tools (optional, falls back to secure software KMS entropy)
• lean (optional, for automated Lean 4 proof verification)

2. Standard Pre-Flight Self-Tests (Single-Run Verification)

To execute single-pass verification and diagnostic benchmarks without deploying background systemd services:

# Phase 1: Foundational Math Verification
python3 phase1_foundational_core/zarqa_gih_math_core.py --skip-venv-check

# Phase 2: Kinematics & Dynamics Self-Test
python3 phase2_kinematics_core/zarqa_gih_kinematics_core.py --self-test

# Phase 3: Spatial Cognition & Perception Self-Test
python3 phase3_spatial_cognition_core/zarqa_gih_spatial_cognition_core.py --self-test

3. One-Click Production Deployment (Root Required)

Deploys the service user accounts (zarqa-math, zarqa-spatial), provisions immutable blue-green virtual environments, sets up isolated systemd daemon services, and starts continuous background verification:

# Deploy Phase 1 Service (/etc/systemd/system/zarqa-gih-math-core.service)
sudo python3 phase1_foundational_core/zarqa_gih_math_core.py --auto-deploy

# Deploy Phase 2 Service (/etc/systemd/system/zarqa-gih-kinematics-core.service)
sudo python3 phase2_kinematics_core/zarqa_gih_kinematics_core.py --auto-deploy

# Deploy Phase 3 Service (/etc/systemd/system/zarqa-gih-spatial-core.service)
sudo python3 phase3_spatial_cognition_core/zarqa_gih_spatial_cognition_core.py --auto-deploy

4. Monitor System Health & Telemetry

# Phase 1 Daemon Health & Logs
sudo systemctl status zarqa-gih-math-core
sudo journalctl -u zarqa-gih-math-core -f

# Phase 2 Daemon Health, Logs & Prometheus Telemetry (Port 9100)
sudo systemctl status zarqa-gih-kinematics-core
sudo journalctl -u zarqa-gih-kinematics-core -f
curl http://localhost:9100/metrics

# Phase 3 Daemon Health, Logs & Prometheus Telemetry (Port 9101)
sudo systemctl status zarqa-gih-spatial-core
sudo journalctl -u zarqa-gih-spatial-core -f
curl http://localhost:9101/metrics

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📜 Standards Compliance

Standard	Domain	Implementation Status
IEC 63439	High-Availability Industrial Networks	100% Compliant: Enabled via deterministic state-machine transitions (NORMAL $\rightarrow$ DEGRADED $\rightarrow$ RECOVERY), 120-second automated blue-green deployment rollbacks, and multi-tier algorithmic fallbacks (SLSQP $\rightarrow$ SVD DLS IK; $H_\infty$ LMI $\rightarrow$ LQR control; GSCKF Riemannian regularized updates; Tustin CM-SS2D numeric saturation guards).
IEC 62443	Industrial Automation & Control Security	100% Compliant: Enforced via TPM 2.0 / PBKDF2 HMAC-SHA256 hash-chained configuration ledgers, SHA-256 hash-chained occupancy grids, ROS 2 DDS-Security X.509 PKI enforcement, unprivileged Linux systemd sandboxing (ProtectSystem=strict, ProtectProc=invisible), Cartesian FDIA residual detection, monotonic boot-counter AEAD nonces, and adaptive timestamp synchronization gating.

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📖 Citation

If you use this codebase or mathematical architecture in your research, please cite our official Zenodo whitepaper family and software repository:

@software{ahmed2026zarqa_software_v3,
  author       = {Ahmed, Mohammad Shahbaaz},
  title        = {ZARQA Grid Inspection Humanoid Core: Phase III Spatial Cognition & Tamper-Evident Perception Release (v3.0.0)},
  year         = {2026},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.21791735},
  url          = {[https://doi.org/10.5281/zenodo.21791735](https://doi.org/10.5281/zenodo.21791735)}
}

@techreport{ahmed2026zarqa_phase1,
  author       = {Ahmed, Mohammad Shahbaaz},
  title        = {A Cyber-Physical Sovereign Architecture for Autonomous Grid-Inspection Humanoids: Formal Verification, Lyapunov Dissipation Bounds, and Immutable Zero-Trust Sandboxing},
  year         = {2026},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.21771994},
  url          = {[https://doi.org/10.5281/zenodo.21771994](https://doi.org/10.5281/zenodo.21771994)}
}

@techreport{ahmed2026zarqa_phase2,
  author       = {Ahmed, Mohammad Shahbaaz},
  title        = {A Cyber-Physical Sovereign Architecture for Autonomous Grid-Inspection Humanoids: Real-Time Kinematic Optimization, LMI-Synthesized H-infinity Control, and Immutable Zero-Trust Sandboxing (Phase II)},
  year         = {2026},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.21786725},
  url          = {[https://doi.org/10.5281/zenodo.21786725](https://doi.org/10.5281/zenodo.21786725)}
}

@techreport{ahmed2026zarqa_phase3,
  author       = {Ahmed, Mohammad Shahbaaz},
  title        = {A Cyber-Physical Sovereign Architecture for Autonomous Grid-Inspection Humanoids: Variational Bayesian Cubature Kalman Filtering, Sobolev-Orthogonalized MoE-CLIP Anomaly Detection, and Tamper-Evident Spatial Memory (Phase III)},
  year         = {2026},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.21791735},
  url          = {[https://doi.org/10.5281/zenodo.21791840](https://doi.org/10.5281/zenodo.21791840)}
}

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⚖️ License & Disclaimer

This project is licensed under the MIT License - see the LICENSE file for details.

Disclaimer: This codebase is an experimental, defensive cyber-physical reference implementation designed for academic research, robotics verification, and critical infrastructure safety engineering.