Question

What is the difference between impedance and admittance controller?

Answer 1

Impedance and admittance controllers are both types of controllers used in systems like robotics, haptic interfaces, and force control systems. They define how a system responds to forces or motions applied to it, but they do so in different ways. Let me break it down simply:

1. Impedance Controller:

   - Definition: Impedance is the relationship between force and motion (displacement) in a mechanical system. An impedance controller manages how a system's position or velocity responds when forces are applied.
   - How It Works: It controls the relationship between force and motion by defining the system’s "stiffness" (resistance to motion), "damping" (resistance to velocity), and "inertia" (resistance to acceleration).
   - Key Focus: Impedance controllers focus on how much motion occurs for a given force. It’s like setting how rigid or flexible the system is when it gets pushed.
   - Application: You'd use an impedance controller when you want to control a system's behavior based on external forces while maintaining specific motion characteristics (e.g., in robotic arm movements where you need to control how hard or soft the arm moves when pushing against an object).

   Mathematically: Impedance \( Z \) is typically defined as \( Z = F / \dot{x} \) (Force / Velocity).

2. Admittance Controller:

   - Definition: Admittance is the inverse of impedance, and it defines how the system moves in response to an applied force.
   - How It Works: An admittance controller controls the system's motion based on the force applied. It takes a force as input and determines the resulting displacement, considering the system's “mass,” “damping,” and “stiffness.”
   - Key Focus: Admittance controllers are focused on how much motion happens for a given force input. It’s like controlling how much the system moves when a force is applied to it.
   - Application: Admittance controllers are often used when you want to make sure the system's motion is directly based on the force applied to it, such as in a robotic hand where the motion changes in response to force, like when pressing an object gently.

   Mathematically: Admittance \( Y \) is defined as \( Y = \dot{x} / F \) (Velocity / Force).

Key Differences:

| Feature                | Impedance Controller                          | Admittance Controller                          |
|------------------------|-----------------------------------------------|-----------------------------------------------|
| Focus              | How force affects motion (position, velocity) | How motion (position, velocity) responds to force |
| Input              | Force (applied to the system)                 | Force (applied to the system)                 |
| Output             | Position or velocity of the system            | Position or velocity of the system            |
| Control Type       | Control the resistance to motion            | Control the response to force               |
| Application Example| Robotic arms where you control stiffness/rigidity | Robotic systems where you want to feel softness or compliance |

In simpler terms:

1. Impedance controller is like controlling how "hard" or "soft" the system feels when something pushes it.
   

1. Admittance controller is like controlling how much the system moves when something pushes it.
   

In practice:

1. Impedance is used more when you're concerned with how the system's motion "resists" forces (like a spring or a damper).
   

1. Admittance is more about making the system "compliant" or reactive to forces, like a soft-touch interface.
   

Both controllers are used to make systems respond intelligently to physical interaction, but they do so with different goals.