3.3 Force control and impedance control

Force and impedance control are crucial for robots interacting with their environment. These techniques allow robots to apply precise forces and adapt to different surfaces, making them safer and more versatile in tasks like assembly and human collaboration.

Control laws for force and impedance use feedback to achieve desired behavior. Force control aims for specific forces, while impedance control regulates the relationship between motion and force. Implementation requires sensors, real-time processing, and careful tuning to ensure stability and performance.

Force Control and Impedance Control in Robotics

Concepts of force and impedance control

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• Force control manipulates forces and torques applied by robot enabling safe and precise environmental interaction (assembly tasks)
• Impedance control regulates dynamic relationship between robot's motion and interaction forces allowing desired mechanical impedance behavior (human-robot collaboration)
• Force control achieves desired force/torque while impedance control aims for desired dynamic behavior
• Applications include assembly tasks, surface finishing, and human-robot collaboration

Derivation of control laws

• Force control law: $u = K_p(F_d - F_a) + K_i \int (F_d - F_a) dt$
  • $F_d$: desired force
  • $F_a$: actual force
  • $K_p$: proportional gain adjusts response speed
  • $K_i$: integral gain eliminates steady-state error
• Impedance control law: $M_d \ddot{x} + B_d \dot{x} + K_d x = F$
  • $M_d$: desired inertia affects acceleration response
  • $B_d$: desired damping influences velocity behavior
  • $K_d$: desired stiffness determines position compliance
  • $x$: position error
  • $F$: interaction force
• Robotic manipulator dynamics: $M(q)\ddot{q} + C(q,\dot{q})\dot{q} + G(q) = \tau + J^T(q)F$
  • $q$: joint positions
  • $M(q)$: inertia matrix represents mass distribution
  • $C(q,\dot{q})$: Coriolis and centrifugal terms account for velocity-dependent forces
  • $G(q)$: gravity vector compensates for gravitational effects
  • $\tau$: joint torques
  • $J(q)$: Jacobian matrix maps joint to Cartesian velocities

Implementation of control algorithms

• Force control implementation:
  1. Measure actual force using force/torque sensor
  2. Calculate force error
  3. Apply control law to generate joint torques
  4. Use inverse dynamics to compensate for robot's natural dynamics
• Impedance control implementation:
  1. Measure position and force
  2. Calculate desired acceleration based on impedance model
  3. Use inverse dynamics to generate joint torques
• Sensor integration incorporates force/torque sensors, joint encoders, and tactile sensors for accurate feedback
• Control loop requires high-frequency updates (1 kHz or higher) and real-time operating system for precise control
• Stability considerations involve gain tuning and robustness to uncertainties to prevent instability

Robot-environment interaction analysis

• Contact modeling considers rigid contact, compliant contact, and friction models (Coulomb, viscous) for accurate interaction simulation
• Performance metrics evaluate force tracking error, position tracking error, settling time, and overshoot to assess control quality
• Stability analysis employs Lyapunov stability theory and small-gain theorem to ensure system stability
• Environmental uncertainty addressed through stiffness estimation and adaptive control techniques for robust performance
• Task-specific analysis examines peg-in-hole assembly, surface following, and cooperative manipulation to optimize control strategies