3.4 Adaptive and robust control techniques

Adaptive control techniques in robotics dynamically adjust parameters to handle changing conditions. These methods use real-time data to update control strategies, enabling robots to maintain performance despite uncertainties in their environment or internal dynamics.

Robust control, on the other hand, focuses on maintaining stability and performance in the face of uncertainties. This approach uses techniques like H∞ control and sliding mode control to ensure consistent robot behavior across various operating conditions.

Adaptive Control Techniques

Principles of adaptive control

• Adaptive control adjusts parameters in real-time responding to changes in system dynamics or environment
• Key components include parameter estimator evaluates system behavior, controller design implements control strategy, adaptation mechanism updates parameters
• Types: Model Reference Adaptive Control (MRAC) uses reference model, Self-Tuning Regulators (STR) estimate plant parameters
• Applications: handles varying payloads in robotic arms, compensates for joint wear in industrial robots, adapts to different terrains for mobile robots

Design of adaptive controllers

• Design steps: 1. Identify uncertain parameters (mass, inertia) 2. Choose adaptation law (gradient descent, least squares) 3. Select control law (Certainty Equivalence, Lyapunov-based)
• Adaptation laws: gradient descent method minimizes error, least squares estimation fits model to data
• Control laws: Certainty Equivalence (CE) principle assumes estimated parameters are true, Lyapunov-based design ensures stability
• Stability considerations: persistent excitation ensures parameter convergence, robustness to unmodeled dynamics prevents instability
• Implementation: considers computational requirements (processing power), integrates sensor feedback (encoders, IMUs)

Robust Control Techniques

Concepts of robust control

• Robust control maintains stability and performance despite uncertainties in robotic systems
• Uncertainties: parametric (mass variations), unmodeled dynamics (flexibilities), external disturbances (wind, friction)
• Importance: ensures consistent performance across operating conditions improves safety and reliability reduces need for precise system modeling
• Key concepts: worst-case analysis considers extreme scenarios, small-gain theorem ensures stability, $H_∞$ control minimizes worst-case error

Application of robust control techniques

• $H_∞$ control minimizes the $H_∞$ norm of closed-loop transfer function optimizing worst-case performance
• $μ$-synthesis addresses structured uncertainties providing more refined robustness
• Loop-shaping: sensitivity function shaping improves disturbance rejection, complementary sensitivity function shaping enhances noise attenuation
• Sliding mode control: variable structure control switches between control laws, chattering reduction techniques (boundary layer) smooth control signal
• Disturbance observers estimate and compensate for external disturbances (friction, wind loads)
• Robustness analysis: Nyquist stability criterion assesses closed-loop stability, structured singular value (μ) analyzes robustness to structured uncertainties
• Performance trade-offs: balance robustness vs nominal performance consider bandwidth limitations in actuators