From Code to Motion: Simulating and Deploying Robots

🧠 What is Adaptive Control?

Adaptive Control is a control strategy that automatically adjusts its parameters in real-time to handle systems with uncertain, unknown, or time-varying dynamics. It's especially useful when system parameters (like mass, friction, or payload) are not fixed or perfectly known.

📐 General Idea

Adaptive control augments a normal feedback controller with an online learning mechanism that updates control parameters based on system performance.

    u(t) = θ(t)T · φ(x, t)
    θ̇(t) = adaptation law (based on error)
  

• u(t): control input
• θ(t): adjustable parameters
• φ(x, t): known basis functions (like measurements)

🤖 Why Adaptive Control in Robotics?

• Robots often experience changing dynamics (e.g., carrying different payloads)
• Exact models are rarely available
• Can reduce need for precise tuning
• Useful in environments with

🔄 Key Components of Adaptive Control

1. Control Law: Defines how control input is computed using current parameter estimates.
2. Adaptation Law: Algorithm to update the estimated parameters (e.g., gradient descent, Lyapunov-based).
3. Reference Model: (in MRAC) defines the desired system behavior to track.

📚 Types of Adaptive Control

• Model Reference Adaptive Control (MRAC): Tracks the output of a reference model.
• Self-Tuning Regulators (STR): Identifies system parameters and redesigns the controller accordingly.
• Gain Scheduling: Adjusts controller gains based on operating conditions (predefined rule-based adaptation).

✅ Advantages

• Robust to parameter uncertainties and changes
• Enables stable control in unpredictable environments
• Improves long-term system performance and safety

🚫 Limitations

• More complex to design and analyze
• Can be sensitive to measurement noise
• May require persistent excitation to ensure convergence

📍 Example in Robotics

A robotic arm with unknown payload mass: As the load changes, the controller adjusts torque commands automatically to maintain precise motion without re-tuning.

📌 Summary

• Adaptive control adjusts itself to unknown or changing dynamics
• Crucial in robotics where modeling uncertainty is common
• Works well for tasks with high variability like human-robot interaction, aerial drones, and manipulators