🛡️ What is Robust Control?
Robust Control is a control strategy that ensures system performance and stability even when there is uncertainty or variation in the system model. It is particularly useful in real-world robotics where perfect models are rarely available.
🎯 Core Idea
Design a controller that works well enough for all models within a known set of possible uncertainties — instead of relying on an exact model.
🔍 Why is Robust Control Important in Robotics?
- Robot models have parameter uncertainty (e.g., mass, friction, payload)
- Unpredictable external disturbances (e.g., wind, terrain variation, noise)
- Sensor and actuator inaccuracies
- It avoids performance degradation in the face of real-world unpredictability
📐 Mathematical Formulation
Consider a system:
ẋ = (A + ΔA)x + (B + ΔB)u
where ΔA and ΔB represent structured or unstructured model uncertainties.
The goal is to design a controller u = Kx that stabilizes the system for all admissible uncertainties.
🧰 Common Robust Control Methods
- H∞ Control: Minimizes the worst-case gain from disturbance to output.
- μ-Synthesis: Handles structured uncertainty using the structured singular value.
- Sliding Mode Control (SMC): Forces system trajectories to "slide" along a stable manifold despite disturbances.
- Lyapunov Robustness: Designs controllers with guaranteed bounds on error despite parameter variations.
✅ Advantages
- Ensures performance and stability under uncertainty
- Often doesn't require exact model identification
- Suitable for high-precision and safety-critical robotic systems
🚫 Challenges
- Can be overly conservative (sacrifices performance)
- Mathematically complex (e.g., solving LMIs or Riccati equations)
- Design trade-off between robustness and performance
🤖 Examples in Robotics
- Designing a drone controller that remains stable despite wind gusts
- Controlling a robotic manipulator with unknown payloads
- Ground robots navigating rough terrain without precise traction models
📌 Robust Control vs Adaptive Control
- Robust Control: Assumes uncertainty is bounded but doesn't change much over time
- Adaptive Control: Assumes system can adapt or learn unknown parameters online
📦 Summary
- Robust control provides performance guarantees in the presence of model uncertainty
- Essential in safety-critical or unpredictable environments (e.g., space, underwater, disaster zones)
- Often used with or in comparison to adaptive and nonlinear control techniques