---
language:
- en
license: mit
tags:
- robotics
- embodied-ai
- mujoco
- humanoid
- reinforcement-learning
- evolutionary-strategies
- pcei
- mamba
- bitnet
- fastkan
pipeline_tag: robotics
---

# PCEI-Robotics: Embodied 18-Meter Ninja Warrior Humanoid Controller

[![GitHub: MtnMCG/PCEI](https://img.shields.io/badge/GitHub-Repository-blue.svg?logo=github)](https://github.com/MtnMCG/PCEI)
[![Architecture: Mamba SSM + FastKAN + BitNet](https://img.shields.io/badge/Architecture-Mamba%20SSM%20%2B%20FastKAN%20%2B%20BitNet-red.svg)](https://github.com/MtnMCG/PCEI)
[![Traversal: 18.00m Touchdown](https://img.shields.io/badge/Traversal-18.00m%20Stage%202%20Touchdown-green.svg)](https://github.com/MtnMCG/PCEI)

> **Official Weights, Physics Models, and Simulation Environments for the PCEI (Physically Constrained Emergent Intelligence) Embodied Humanoid Agent conquering the 18-meter American Ninja Warrior obstacle course in real-time MuJoCo continuous physics at 40 FPS.**
> 
> Master GitHub Repository: [https://github.com/MtnMCG/PCEI](https://github.com/MtnMCG/PCEI)

---

## 🏃 Autonomous 18-Meter Obstacle Traversal Demonstration

Inside an American Ninja Warrior MuJoCo humanoid simulation, without dense Transformer attention or sample-inefficient deep RL, the PCEI agent autonomously accelerates down the high-momentum Sprint Runway (Stage 0), bounds across the angled 45° Quad Steps (Stage 1), and touches down cleanly at **18.00 meters** on the Stage 2 Balance Beam platform:

![PCEI 18m Ninja Warrior Course Run](best_run_18m_ninja.gif)

*▶️ [Watch High-Definition MP4 Video](best_run_18m_ninja.mp4)*

---

## 📊 Run Telemetry & Benchmarks

| Metric / Dimension | Measured Performance | Architectural Context |
| :--- | :--- | :--- |
| **Course Traversal Distance** | **18.00 meters** (Stage 2 Touchdown) | Cleared Stage 0 (0–8 m) & Stage 1 Quad Steps (8–18 m) |
| **Trajectory Duration** | **284 execution frames (7.1 s)** | Real-time continuous physics evaluation at 40 FPS |
| **Peak Sprint Velocity ($v_x$)** | **4.06 m/s (14.6 km/h)** | Dynamic acceleration across runway into 45° angled platforms |
| **Total Environment Training Steps** | **17.4M steps** | Traversal achieved 3×–5× faster than standard MLP / RL baselines |
| **Simulated Training Episodes** | **213,000+ episodes** | Sampled across 16 parallel MuJoCo vector environments |
| **Evolutionary Generations** | **110 generations** | Darwinian Pioneer-Anchor Partitioning (70% Anchors : 30% Pioneers) |
| **BitNet Codon Point Mutations** | **143,646 mutations** ($\\mu = 0.0025$) | Discrete ternary synaptic adaptation without catastrophic forgetting |
| **Start-Line Balance Retention** | **100.0%** (0 fall rate at origin) | Pioneer-Anchor duality prevented start-line forgetting |
| **Observation & Motor Dim** | **572-dim Input → 21-dim Torque** | 3D solid-state LiDAR + proprioception driving 21 continuous joint actuators |
| **Neural Backbone Engine** | **Mamba SSM + FastKAN + BitNet** | Constant `O(1)` recurrent state space + cubic B-spline non-linear torque manifold |

---

## 🧠 Architectural Foundation

Standard monolithic Transformer architectures fail at high-frequency continuous control due to quadratic latency scaling ($\\mathcal{O}(L^2)$) and unbounded memory buffers. The PCEI robotic controller unifies three core principles:

1. **Selective State-Space Recurrence (Mamba SSM)**: Linear $\\mathcal{O}(L)$ compute with constant $\\mathcal{O}(1)$ memory buffer, updating continuous proprioceptive and LiDAR representations at 40 FPS without latency spikes.
2. **FastKAN Cubic B-Spline Torque Manifolds**: Non-linear spline basis functions (`FastKANMixer`) placed in residual branches enable smooth, biologically plausible motor activations that prevent actuator jerk and joint instability.
3. **Discrete 1.58-Bit Ternary Synaptic Gating**: Weight quantization constrained to `{-1, 0, +1}`, providing homeostatic metabolic efficiency and biological zero-inhibition.

---

## 🛠️ Reproduction & Local Execution

To inspect the agent or run local rollouts in MuJoCo:

```bash
# Clone the master PCEI repository
git clone https://github.com/MtnMCG/PCEI.git
cd PCEI/pcei_framework

# Create virtual environment and install dependencies
python3 -m venv venv
source venv/bin/activate
pip install -r requirements.txt
pip install mujoco gymnasium

# Run interactive MuJoCo humanoid evaluation
python3 embodied_pcei/src/ninja_env.py --checkpoint checkpoints/pcei_ninja_best.pt
```

---

## 📜 Full Scientific Documentation & Compendium

Complete specifications, mathematical proofs, and ablation studies are available in the master repository:
- Master Codebase & Research Papers: [https://github.com/MtnMCG/PCEI](https://github.com/MtnMCG/PCEI)
- [Research Paper IX: FastKAN Spline Manifolds & Mamba Motor Control](https://github.com/MtnMCG/PCEI/blob/main/pcei_framework/docs/RESEARCH_PAPER_09_FASTKAN_SPLINE_MANIFOLDS_AND_MAMBA_MOTOR_CONTROL.md)
- [Research Paper XI: Darwinian Pioneer-Anchor Population Partitioning](https://github.com/MtnMCG/PCEI/blob/main/pcei_framework/docs/RESEARCH_PAPER_11_DARWINIAN_PIONEER_ANCHOR_POPULATION_PARTITIONING.md)

---

## 🖋️ Citation

```bibtex
@article{ramirez2026pcei,
  title   = {Physically Constrained Emergent Intelligence: Subverting Transformer Hyperscaling via Linear State Spaces, Ternary Synaptic Gating, and Latent Dreaming},
  author  = {Ramirez, Emerson and Antigravity Assistant},
  journal = {PCEI Theoretical Research Compendium},
  year    = {2026},
  url     = {https://github.com/MtnMCG/PCEI}
}
```