Impedance Control

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Impedance control is an advanced robot control technique that regulates the dynamic interaction between a robot and its environment. It allows a robot to move in a compliant and safe manner when contacting objects or people. Impedance control has become an essential component of modern robotics and is widely used in industrial and service applications.

In this article, we will provide an overview of impedance control, its working principles, applications, and recent advances. We will also discuss the challenges of implementing impedance control and ways to address them.

What is Impedance Control?

Impedance control aims to regulate the impedance of a robot, which characterizes its dynamic behavior when interacting with the environment. The impedance determines how the robot reacts to external forces.

Specifically, a robot’s impedance is defined along directions of motion by:

  • Mass – resistance to acceleration
  • Damping – resistance to velocity
  • Stiffness – resistance to displacement

By adjusting these parameters, we can vary the robot’s responsiveness to forces. Low impedance results in compliant behavior, while high impedance leads to stiff behavior.

Impedance control works by controlling the relationship between displacement and force. The goal is to achieve a target impedance behavior when the robot contacts objects or humans. This is accomplished using feedback control to modulate torque inputs so that the desired impedance is attained.

Key Features

Some key features of impedance control include:

  • Safety – Compliant, low impedance allows safe human-robot interaction and collision detection.
  • Stability – Well-tuned impedance parameters ensure stable dynamic behavior.
  • Robustness – Provides disturbance rejection against unmodeled forces.
  • Versatility – Impedance can be designed to match task requirements.

By facilitating safe and dynamic interaction between robots and their environment, impedance control enables advanced applications such as assembly, collaborative robotics, and physical human-robot interaction.

Brief History

The concept of impedance control was first introduced in the 1970s by Neville Hogan at MIT. He proposed the idea of controlling a robot’s dynamic interaction with its environment in his seminal paper Impedance Control: An Approach to Manipulation.

In the 1980s and 1990s, impedance control gained traction in research on the interaction control problem. Notable work was done by Kremer, Burdet, Salisbury, Mason and others to develop theoretical foundations and applications.

The field greatly expanded in the late 1990s and 2000s with the rise of human-friendly robotics. Impedance control proved essential to enabling safe and seamless physical human-robot collaboration. This drove extensive research to address implementation challenges.

Today, impedance control is a mature technique implemented in most advanced industrial and service robots. Ongoing research aims to further improve performance, robustness and ease of tuning.

How Impedance Control Works

The goal of impedance control is to attain desired dynamic behavior between the robot end-effector and the environment. This is achieved by controlling the relationship between displacement and force.

1. Defining Target Impedance

First, we define the target impedance parameters (mass, damping and stiffness) along each direction of motion. Together these characterize the desired behavior.

For example, low stiffness means compliant motion in that direction. High damping provides shock absorption. The parameters can be set arbitrarily to match task requirements.

2. Measuring Displacement and Force

Next, we need to measure the displacement and force between the end-effector and environment.

  • Displacement is obtained from the motion sensors of the robot (encoders, IMU, etc).
  • Force is measured using a force-torque sensor at the end-effector.

3. Generating Torque Inputs

The controller uses the displacement and force information to compute required torque inputs that will attain the target impedance.

The general control law is:Copy code

τ = M(θ)θ̈ + C(θ, θ̇)θ̇ + g(θ) + JT(θ)F


  • τ is the vector of joint torque inputs
  • M is the inertia matrix
  • C accounts for coriolis/centrifugal effects
  • g is gravitational torque
  • JT maps cartesian end-effector forces F to joint-space

By modulating the torque inputs, the relationship between displacement and force is regulated to match the desired impedance behavior.

4. Feedback Control

Impedance control relies on feedback control to continually update the torque inputs based on measured displacement and force. This allows dynamic adjustment against disturbances and unmodeled effects.

Advanced control techniques (e.g. sliding mode control) are often used to ensure accurate and robust impedance regulation.

Applications of Impedance Control

Impedance control is a powerful technique that enables a wide range of robotics applications:

Industrial Assembly

Compliant control allows gentle part mating and insertion for robotic assembly. Low impedance also helps absorb positioning errors.


Dynamic force regulation is essential for robotic grinding, deburring and polishing. Impedance control prevents excessive forces.

Collaborative Robotics

Safe physical interaction between humans and robots requires very low impedance. This allows collision detection and safeguarding.

Physical Therapy

Controlled compliant behavior is important for rehabilitation robots to interact safely with patients.

Mobile Manipulation

Impedance control allows mobile robots to modulate forces when navigating constrained spaces or manipulating objects.

Assistive Devices

Prosthetic limbs and exoskeletons use impedance control to naturally conform to human motion.

For any application involving physical interaction between a robot and its environment, impedance control can critically enhance performance, safety and versatility.

Design Considerations

Several important factors must be considered when designing and implementing an impedance controller:

1. Performance Objectives

The target impedance parameters should be chosen to optimize the desired performance. Key criteria include safety, stability, precision, and disturbance rejection. The impedance can be tuned to balance these as needed.

2. Actuator Capabilities

The robot actuators must be capable of providing the dynamic forces and speeds required by the target impedance. High fidelity force control is essential.

3. Control Stability

Stability is affected by the impedance parameters, actuator limits, and contact dynamics. Stability analysis and control design should ensure robustness.

4. Sensing Resolution

Accurate measurement of displacement and force is critical for impedance regulation. Sensor resolution and noise directly impact control performance.

5. Modeling Fidelity

Impedance control relies on faithful models of robot dynamics. Insufficiently modeled effects will degrade control accuracy.

By considering these factors, a well-designed impedance controller can be developed that is optimized for the particular application.

Advanced Control Techniques

While basic impedance control is conceptually straightforward, there are many advanced techniques that improve performance and robustness:

Adaptive Impedance Control

The impedance parameters are continually adjusted based on force measurements to enhance compliance and stability.

Variable Impedance Control

Time-varying or state-dependent impedance allows greater flexibility to handle changing tasks.

Robust Impedance Control

Robustness against uncertainties and disturbances is enhanced using control techniques like sliding mode control.

Model-Free Impedance Control

Reliance on dynamics models is reduced by using model-free reinforcement learning methods.

Shared Impedance Control

For human-in-the-loop applications, impedance is shared between human and robot.

Multi-Priority Impedance Control

Concurrent low- and high-impedance objectives are met by partitioning directions.

By leveraging such advanced methods, the performance and applicability of impedance control can be expanded. This is an active ongoing research area.


Despite its advantages, impedance control also poses some practical challenges:

Modeling Complexity

The dynamics models required for fidelity impedance control can be highly complex for real robots. This complicates control design.

Stability Issues

The coupled stability between controller, actuators, and contact environment can be difficult to ensure under all conditions.

Noise Sensitivity

Sensor noise in force/torque measurements directly impacts control performance and can cause instability.

High Cost

Quality force-torque sensors and high-bandwidth actuators required for impedance control can be extremely costly.

Tuning Difficulty

Determining optimal impedance parameters requires extensive modeling and experimentation. Automated methods are lacking.

While these remain active research problems, various methods exist to help address the challenges. Control theorists continue working to improve the robustness and applicability of impedance control.

Future Outlook

Impedance control has cemented itself as an essential capability for advanced robotics. Looking forward, research is focused on further extending its performance and ease of implementation.

Key trends include:

  • Simplified modeling – Using model-free learning and other data-driven methods to reduce modeling dependence.
  • Human-aware control – Ensuring safe and intuitive physical human-robot interaction across applications.
  • High-speed manipulation – Enabling dynamic impedance behavior for high-speed robot operation.
  • Modular robots – Implementing impedance control on decentralized, modular robot systems.
  • Medical rehabilitation – Advancing assistive robotics for personalized healthcare using impedance control.
  • Haptic feedback – Better conveying impedance via haptic interfaces for teleoperation.

As robots become more ubiquitous across industrial and social domains, impedance control will remain indispensable in allowing their safe and seamless integration. Continued innovation in this field is critical for unlocking the full potential of robotics.


In summary, impedance control is a vital technique that enables robots to interact dynamically and safely with their environment. By regulating the relationship between motion and forces, it facilitates compliant and robust behavior.

Impedance control has evolved from academic research into an essential feature of most modern robot systems. Ongoing advances aim to improve performance, address implementation challenges, and expand applications.

This versatile tool will continue enabling robots to achieve extraordinary tasks working alongside humans. Impedance control represents a crucial bridge between robotic capability and the diversity of the real world.

Frequently Asked Questions

What are the key components needed for impedance control?

The key components needed are:

  • High-fidelity torque-controlled actuators
  • Accurate force/torque sensing
  • Precise position and velocity sensing
  • A dynamic model of the robot
  • A control algorithm to modulate motor torques

Together these allow the relationship between motion and force to be regulated.

How does impedance control differ from position or force control?

Unlike position control, impedance control does not aim to achieve precise trajectory tracking. Rather, it regulates dynamic behavior.

It differs from force control in that the interact force is controlled indirectly by controlling position and torque, not force directly.

Impedance control focuses on the holistic dynamic interaction, not isolated position or force.

What makes impedance control challenging to implement?

Key challenges include:

  • The need for high-fidelity sensing and actuation
  • Modeling complex real-world contact dynamics
  • The coupled stability between controller, mechanics, and environment
  • Tuning optimal impedance parameters
  • Handling noise and disturbances

Substantial modeling, analysis, and testing is required for robust real-world implementation.

How can stability be ensured in impedance control?

Stability can be promoted by:

  • Carefully choosing impedance parameters using stability criteria
  • Incorporating damping in the target impedance
  • Using advanced control techniques (e.g. sliding mode control)
  • Adding saturation limits on torque and motion
  • Experimentally validating stability across expected operating conditions

Modeling and analysis is key to guarantee stability.

What are some examples of robots using impedance control?

Some examples include:

  • Industrial co-bots like Baxter and Sawyer
  • Space robot arms like Canadarm
  • Robotic prosthetic limbs
  • Exoskeletons and rehabilitation devices
  • Legged robots like Atlas and Spot
  • Snake robots
  • Robotic manipulators handling delicate tasks

Impedance control is widely used where safe and dexterous environmental interaction is needed.