Update visuals of docs

Author: mstoelzle

docs/404.md

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+---
+hide:
+  - navigation
+  - toc
+---
+
+# 🤖 404 - Page Not Found
+
+<div class="doc-summary">
+  <strong>Oops! The page you're looking for doesn't exist.</strong> But don't worry, we can help you get back on track with your soft robotics journey!
+</div>
+
+---
+
+## 🧭 Navigation Help
+
+<div class="feature-grid">
+  <div class="feature-card">
+    <h3><span class="icon">🏠</span> [Home](index.md)</h3>
+    <p>Go back to the main page and start fresh</p>
+  </div>
+  
+  <div class="feature-card">
+    <h3><span class="icon">🚀</span> [Quick Start](user-guide/quick-start.md)</h3>
+    <p>Jump into hands-on tutorials and examples</p>
+  </div>
+  
+  <div class="feature-card">
+    <h3><span class="icon">📚</span> [API Reference](api/systems.md)</h3>
+    <p>Browse the complete API documentation</p>
+  </div>
+  
+  <div class="feature-card">
+    <h3><span class="icon">📖</span> [Examples](user-guide/examples.md)</h3>
+    <p>Explore comprehensive examples and use cases</p>
+  </div>
+</div>
+
+---
+
+## 🔍 Popular Resources
+
+!!! tip "Most Visited Pages"
+    
+    - **[Installation Guide](installation.md)** - Get JSRM up and running
+    - **[Planar PCS Systems](api/planar-pcs.md)** - Continuum soft robot documentation  
+    - **[Contributing Guidelines](development/contributing.md)** - Join our community
+    - **[System Factory Pattern](user-guide/quick-start.md#core-concepts)** - Learn the basics
+
+---
+
+## 🆘 Still Lost?
+
+!!! question "Need help finding something specific?"
+
+    === "🔍 Search"
+        Use the search box at the top of the page to find what you're looking for.
+    
+    === "📧 Contact"
+        Reach out to us at [[email protected]](mailto:[email protected])
+    
+    === "🐛 Report Issue"
+        If you think this is a broken link, please [report it on GitHub](https://github.com/tud-phi/jax-soft-robot-modelling/issues/new)
+
+---
+
+<div style="text-align: center; margin: 2rem 0;">
+  <p style="font-size: 1.2rem; color: var(--md-primary-fg-color);">
+    🤖 <strong>Happy Coding with JSRM!</strong>
+  </p>
+</div>

docs/includes/mkdocs.md

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+*[JAX]: Just After eXecution - A library for high-performance machine learning research
+*[PCS]: Piecewise Constant Strain
+*[HSA]: Handed Shearing Auxetics  
+*[SE(2)]: Special Euclidean group in 2D
+*[SE(3)]: Special Euclidean group in 3D
+*[DOF]: Degrees of Freedom
+*[JIT]: Just-In-Time compilation
+*[API]: Application Programming Interface
+*[GPU]: Graphics Processing Unit
+*[TPU]: Tensor Processing Unit
+*[CPU]: Central Processing Unit
+*[JSRM]: JAX Soft Robot Modelling

docs/index.md

@@ -1,53 +1,176 @@
-# JAX Soft Robot Modelling
+# 🤖 JAX Soft Robot Modelling
 
-Welcome to the documentation for JAX Soft Robot Modelling (JSRM)!
+<div class="doc-summary">
+  <strong>Welcome to JAX Soft Robot Modelling (JSRM)!</strong> A cutting-edge library for fast, parallelizable, and differentiable simulations of soft robots using JAX and symbolic mathematics.
+</div>
 
-## Overview
+---
+
+## 🎯 Overview
+
+This repository contains symbolic derivations of the kinematics and dynamics of various soft robots using **SymPy**.
+The symbolic expressions are then implemented in **JAX** and can be used for fast, parallelizable, and differentiable simulations.
 
-This repository contains symbolic derivations of the kinematics and dynamics of various soft robots using Sympy.
-The symbolic expressions are then implemented in JAX and can be used for fast, parallelizable, and differentiable simulations.
+<div class="feature-grid">
+  <div class="feature-card">
+    <h3><span class="icon">⚡</span> JAX-Powered</h3>
+    <p>Leverage JAX for lightning-fast computations with automatic differentiation and JIT compilation</p>
+  </div>
+  
+  <div class="feature-card">
+    <h3><span class="icon">🧮</span> Symbolic Foundation</h3>
+    <p>Mathematically rigorous models derived from first principles using symbolic computation</p>
+  </div>
+  
+  <div class="feature-card">
+    <h3><span class="icon">🔧</span> Modular Design</h3>
+    <p>Extensible architecture that makes it easy to add new robot types and configurations</p>
+  </div>
+  
+  <div class="feature-card">
+    <h3><span class="icon">📊</span> Differentiable</h3>
+    <p>Full gradient support for optimization, control, and machine learning applications</p>
+  </div>
+  
+  <div class="feature-card">
+    <h3><span class="icon">🚀</span> High Performance</h3>
+    <p>Parallelizable computations that scale efficiently across multiple devices</p>
+  </div>
+  
+  <div class="feature-card">
+    <h3><span class="icon">🔬</span> Research-Ready</h3>
+    <p>Validated implementations used in peer-reviewed robotics research</p>
+  </div>
+</div>
+
+---
+
+## 🤖 Supported Robot Types
+
+We focus on planar settings and have implemented the following soft robot architectures:
+
+!!! note "🦾 **N-link Pendulum**"
+    Classical articulated robot perfect for benchmarking and comparison studies
+
+!!! tip "🌊 **Planar Piecewise Constant Strain (PCS)**"
+    Advanced continuum soft robot with constant strain segments for precise modeling
+
+!!! info "🔗 **Planar Handed Shearing Auxetics (HSA)**"
+    Novel soft robot with auxetic properties for unique deformation characteristics
+
+---
+
+## ✨ Key Features
+
+=== "🚀 Performance"
+
+    - **JAX Backend**: Ultra-fast computations with automatic vectorization
+    - **JIT Compilation**: Optimized machine code generation for maximum speed  
+    - **GPU/TPU Support**: Seamless acceleration on modern hardware
+    - **Parallel Processing**: Scale across multiple devices effortlessly
+
+=== "🧠 Intelligence"
+
+    - **Automatic Differentiation**: Full gradient support for all operations
+    - **Symbolic Derivation**: Mathematically rigorous kinematic and dynamic models
+    - **Optimization Ready**: Perfect for control and learning applications
+    - **Numerical Stability**: Robust implementations that handle edge cases
+
+=== "🔧 Usability"
+
+    - **Clean API**: Intuitive interfaces that are easy to learn and use
+    - **Comprehensive Documentation**: Detailed guides, examples, and API reference
+    - **Extensible Design**: Add new robot types and configurations with ease
+    - **Research Proven**: Validated in real-world robotics applications
+
+---
+
+## 🚀 Quick Start
+
+Get up and running in minutes:
+
+=== "Installation"
+
+    ```bash
+    pip install jsrm
+    ```
+
+=== "Basic Usage"
+
+    ```python
+    import jax.numpy as jnp
+    from jsrm.systems import PlanarPCS
+    
+    # Create a planar PCS robot
+    robot = PlanarPCS(num_segments=3, params=params)
+    
+    # Compute forward kinematics
+    q = jnp.array([0.1, 0.2, 0.3])  # Configuration
+    chi = robot.forward_kinematics(q, s=1.0)  # End-effector pose
+    ```
+
+=== "Advanced Features"
+
+    ```python
+    # Compute Jacobians for control
+    J = robot.jacobian(q, s=1.0)
+    
+    # Dynamic simulation
+    B, C, G, K, D, A = robot.dynamical_matrices(q, qd)
+    
+    # Differentiable operations
+    loss_fn = lambda q: jnp.sum(robot.forward_kinematics(q, s=1.0)**2)
+    grad_fn = jax.grad(loss_fn)
+    ```
+
+---
+
+## 📚 Quick Links
+
+<div class="feature-grid">
+  <div class="feature-card">
+    <h3><span class="icon">📦</span> [Installation Guide](installation.md)</h3>
+    <p>Get JSRM installed and configured on your system</p>
+  </div>
+  
+  <div class="feature-card">
+    <h3><span class="icon">🚀</span> [Quick Start](user-guide/quick-start.md)</h3>
+    <p>Jump right in with hands-on tutorials and examples</p>
+  </div>
+  
+  <div class="feature-card">
+    <h3><span class="icon">📖</span> [Examples](user-guide/examples.md)</h3>
+    <p>Explore comprehensive examples and use cases</p>
+  </div>
+  
+  <div class="feature-card">
+    <h3><span class="icon">📋</span> [API Reference](api/systems.md)</h3>
+    <p>Complete documentation of all classes and functions</p>
+  </div>
+</div>
 
-## Supported Robot Types
-
-So far, we have focused on planar settings and implemented the following soft robots:
-
-- **N-link pendulum** - Classical articulated robot for benchmarking
-- **Planar Piecewise Constant Strain (PCS) continuum soft robot** - Continuum robot with constant strain segments
-- **Planar Handed Shearing Auxetics (HSA) robot** - Soft robot with auxetic properties
-
-## Key Features
-
-- **JAX-based**: Fast, parallelizable, and differentiable computations
-- **Symbolic derivations**: Mathematically rigorous kinematic and dynamic models
-- **Multiple robot types**: Support for various soft robot architectures
-- **Extensible**: Easy to add new robot types and configurations
-
-## Quick Links
-
-- [Installation Guide](installation.md)
-- [Quick Start](user-guide/quick-start.md)
-- [Examples](user-guide/examples.md)
-- [API Reference](api/systems.md)
-
-## Citation
-
-This simulator is part of the publication **An Experimental Study of Model-based Control
-for Planar Handed Shearing Auxetics Robots** presented at the _18th International Symposium on Experimental Robotics_. 
-
-If you use our software in your research, please cite:
-
-```bibtex
-@inproceedings{stolzle2023experimental,
-  title={An experimental study of model-based control for planar handed shearing auxetics robots},
-  author={St{\"o}lzle, Maximilian and Rus, Daniela and Della Santina, Cosimo},
-  booktitle={International Symposium on Experimental Robotics},
-  pages={153--167},
-  year={2023},
-  organization={Springer}
-}
-```
-
-## Contributing
+---
+
+## 📄 Citation
+
+This simulator is part of the publication **"An Experimental Study of Model-based Control for Planar Handed Shearing Auxetics Robots"** presented at the *18th International Symposium on Experimental Robotics*.
+
+!!! quote "If you use our software in your research, please cite:"
+
+    ```bibtex
+    @inproceedings{stolzle2023experimental,
+      title={An experimental study of model-based control for planar handed shearing auxetics robots},
+      author={St{\"o}lzle, Maximilian and Rus, Daniela and Della Santina, Cosimo},
+      booktitle={International Symposium on Experimental Robotics},
+      pages={153--167},
+      year={2023},
+      organization={Springer}
+    }
+    ```
+
+---
+
+## 🤝 Contributing
 
 We welcome contributions! Please see our [Contributing Guide](development/contributing.md) for details on how to get started.