We have it under Control
====================================

**Theme:** *We Have It Under Control* — this week focuses on the art and science of 
**robot control**, where mathematical feedback transforms chaotic systems 
into stable and predictable motion.

.. image:: _static/arm.gif
   :alt: Example GIF
   :align: center


Focus
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- Understand the role of control in robotics.
- Learn the difference between **open-loop** and **closed-loop** systems.
- Explore **feedback control** and why it is essential for robots.
- Implement **PID controllers** to track positions and trajectories.

Learning Flow
-------------

1. **Theory**
   - What is control and why do robots need it?
   - Open-loop vs closed-loop systems.
   - Feedback and error correction.
   - Control laws: proportional (P), proportional-derivative (PD), 
     and proportional-integral-derivative (PID).
   - Stability and performance in control systems.

2. **Practical / Code**
   - Implement a simple **PD controller** in Python.
   - Extend to a **PID controller** for improved performance.
   - Test the controller on a simulated joint or mobile robot.
   - Visualize errors converging to zero over time.

3. **Simulation**
   - Use **Gazebo** or **PyBullet** to simulate a robotic arm or mobile robot.
   - Apply your controller to track a reference trajectory.
   - Observe how feedback stabilizes the robot’s behavior.

4. **Assignment**
   - Implement and test a PID controller.
   - Compare open-loop vs closed-loop performance.
   - Document results with plots of error vs time.
   - Push code and README to GitHub, showing:
     
     - Your controller implementation
     - Plots and results
     - Explanation of stability improvements

Takeaway
--------

By the end of this week, students will understand how control transforms 
**commands into reliable motion**. They will learn that without feedback, 
robots drift and fail, but with control, robots execute tasks precisely.  

This week gives students the tools to **tame dynamics and guide robots** — 
proving once and for all that *we have it under control*.