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Admittance control is a fundamental control strategy in robotics and mechatronics that governs how a system interacts with its environment. It is designed to make a system respond to external forces by producing a corresponding motion, such as a change in velocity or position, based on a predefined dynamic relationship. This compliance-oriented approach stands in contrast to impedance control, where the system generates a force in response to an imposed motion. Admittance control’s ability to yield to external forces makes it particularly valuable in applications requiring adaptability and safety, such as human-robot collaboration, industrial assembly, and haptic interfaces.

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Understanding Admittance Control

At its core, admittance control defines how a system moves in response to an applied force. It is often implemented through a two-loop control structure. The outer loop measures the interaction forces—typically using force or torque sensors—and calculates the desired motion based on a specified admittance model. This model incorporates virtual parameters like mass, damping, and stiffness to shape the system’s dynamic response.

Once the desired motion is determined, the inner loop ensures the system accurately follows the computed trajectory using position or velocity control. This force-to-motion approach is especially suited for robots with precise motion control, allowing them to adjust smoothly to external forces rather than trying to generate counteracting forces directly.

The Admittance control can be split into 3 stages. Outer loop (for measuring the external force/torque), calculation of the admittance model and the inner loop. Let’s dive into each stages hereunder.

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‍1. Force/Torque Measurement (Outer Loop)

For the outer loop there are 2 methods that could be used.

a) Current Estimation:

Current estimation is the process of determining the actual electric current flowing through a system, either by direct measurement or mathematical models. It is commonly used in motor control, battery management, and power electronics to monitor and control current without expensive sensors. By using voltage readings and system models, current can be accurately estimated even without direct measurement.

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b) Using a force/torque sensor:

A force/torque sensor mounted on the robot’s end-effector or relevant joint continuously measures the forces and torques arising from interaction with the environment. These readings can directly be fed into the outer loop of the control system.

For example, Acrome provides a force/torque sensor option for its Stewart Platform products, as can be seen in the image below. Having a direct sensor measurement simplifies the calculations of the force/torque set points.

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2. Calculation of the Admittance Model

The measured force/torque data is input into a predefined admittance model (e.g., Mx¨+Dx˙+Kx=F), where: 

• M: virtual mass (inertia),
  
• D: damping coefficient,
  
• K: stiffness coefficient,
  
• F: external force,
  
• x: position (motion)

The output of this model determines how the system should move, typically in terms of velocity or position.

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3. Inner Loop – Motion Execution

In the inner control loop, the robot’s actuators use position or velocity controllers to follow the calculated motion. Instead of counteracting the external force directly, the robot complies with it and adjusts its movement accordingly.

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Applications of Admittance Control

Industrial Robotics

In manufacturing and assembly, robots often need to interact with objects and surfaces in a flexible yet precise manner. Admittance control allows robots to adapt their movement based on physical contact, reducing the risk of jamming or misalignment and improving the efficiency of automated processes.

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Human-Robot Interaction in Tesla’s Optimus

In collaborative environments, safety and adaptability are essential. Tesla’s humanoid robot, Optimus, embodies these principles by integrating advanced AI and real-time sensor feedback to interact safely and intuitively with humans. Drawing from Tesla’s Full Self-Driving (FSD) technology, Optimus can perceive its surroundings, predict human motion, and respond accordingly.

One of the key elements in making human-robot interaction seamless is admittance control—a feature Tesla is expected to incorporate into Optimus. This control method allows the robot to sense and react to external forces applied by humans, enabling it to yield or adjust its motion dynamically. For instance, if a human gently pushes Optimus aside while passing through a narrow space, the robot can safely and compliantly give way without resistance or loss of balance.

This kind of responsive behavior is critical in environments where robots and humans share tasks—such as in homes, factories, or healthcare settings. By continuously adjusting its posture and actions based on physical feedback, Optimus minimizes the risk of injury and promotes

trust and collaboration. Tesla’s focus on combining AI perception, motion planning, and human-safe control mechanisms positions Optimus as a powerful example of the future of human-robot collaboration.

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Haptic Interfaces

In virtual reality and teleoperation systems, admittance control helps create realistic force feedback. For instance, when using a haptic device, a user might feel the sensation of touching a virtual wall or holding an object. By translating applied forces into controlled movements, admittance control makes digital interactions feel more natural and immersive.

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Rehabilitation Robotics

Rehabilitation robots use admittance control to assist patients in physical therapy by adjusting the level of support based on the patient’s movements. This ensures that assistance is provided only when necessary, encouraging active participation and aiding in the recovery process.

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Legged Robotics

In legged robots, admittance control helps adjust how the legs respond to different terrains, allowing robots to walk more naturally on uneven surfaces. This improves stability and adaptability in dynamic environments, making it valuable for applications like search-and-rescue or exploration.

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Advantages and Challenges

Admittance control offers several benefits, making it a widely used approach. It allows for better interaction with rigid environments, preventing excessive forces that could cause damage [3]. It is also relatively easy to implement on systems with strong motion control capabilities, and the parameters can be adjusted to fine-tune the interaction dynamics.

However, there are also challenges. The approach relies heavily on accurate force sensing, which can be costly and prone to noise, affecting system performance [3]. Stability is another concern—if the system does not respond quickly enough, it can lead to oscillations or instability. To address these limitations, some systems combine admittance control with impedance control, leveraging the strengths of both approaches.

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Challenges Due to Orientation-Dependent Force/Torque Sensor Readings in Admittance Control

In admittance control architectures, Force/Torque (F/T) sensors play a crucial role in detecting the external forces applied by the human or the environment. However, these sensors can introduce significant challenges, especially due to their sensitivity to changes in orientation. Since F/T sensors measure forces in their local coordinate frame, any change in the orientation of the robot end-effector may result in a shift of the perceived direction and magnitude of the applied forces. This issue becomes particularly problematic when the center of mass of the attached tool is not aligned with the sensor’s coordinate system, causing gravity-induced forces to project differently depending on the tool’s orientation.

Such effects may lead to misleading force readings, where the sensor interprets gravitational components as user-applied forces. For example, during a drilling task, as the orientation of the robot arm changes, the weight of the drill may create additional force components in unintended axes, potentially degrading the control performance. As highlighted in [4], filtering the raw force measurements and accounting for orientation-dependent effects are essential for stable and transparent human-robot interaction. Proper compensation or transformation of sensor data is therefore necessary to ensure that the control system accurately interprets external inputs and maintains safe and intuitive behavior​. 

Conclusion

Admittance control is a powerful and flexible method that enhances how robots interact with their environment. Whether in manufacturing, healthcare, or human-robot collaboration, its ability to adapt to external forces makes it a critical tool in modern robotics. While challenges like force sensing and stability remain, continuous advancements are refining its implementation, ensuring its continued relevance in future robotic applications. By blending precision with adaptability, admittance control plays a key role in shaping the next generation of interactive robotic systems.

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Resources:

[1] Y. Aydin, O. Tokatli, V. Patoglu, and C. Basdogan, “Stable Physical Human-Robot Interaction Using Fractional Order Admittance Control,” in IEEE Transactions on Haptics, vol. 11, no. 3, pp. 464-475, 1 July-Sept. 2018, doi: 10.1109/TOH.2018.2810871.

[2] “Optimus (robot),” Wikipedia: The Free Encyclopedia, https://en.wikipedia.org/wiki/Optimus_(robot) (accessed Apr. 20, 2025).

[3] A. Q. Keemink, H. van der Kooij, and A. H. Stienen, “Admittance control for physical human–robot interaction,” The International Journal of Robotics Research, vol. 37, no. 11, pp. 1421–1444, Sep. 2018, doi: 10.1177/0278364918768950.

[4] A. Madani, P. P. Niaz, B. Guler, Y. Aydin and C. Basdogan, “Robot-Assisted Drilling on Curved Surfaces with Haptic Guidance under Adaptive Admittance Control,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Kyoto, Japan, 2022, pp. 3723-3730, doi: 10.1109/IROS47612.2022.9982000. 

[5] D. Sirintuna, Y. Aydin, O. Caldiran, O. Tokatli, V. Patoglu, and C. Basdogan, “A Variable-Fractional Order Admittance Controller for pHRI,” IEEE International Conference on Robotics and Automation (ICRA), Paris, France, 2020, pp. 10162-10168, doi: 10.1109/ICRA40945.2020.9197288.

[6] Y. Sun, M. Van, S. McIlvanna, N. N. Minh, S. McLoone, and D. Ceglarek, “Adaptive admittance control for safety-critical physical human-robot collaboration,” *IFAC-PapersOnLine*, vol. 56, no. 2, pp. 1313-1318, 2023, doi: https://doi.org/10.1016/j.ifacol.2023.10.1772. 

[7] C. T. Landi, F. Ferraguti, L. Sabattini, C. Secchi, and C. Fantuzzi, “Admittance control parameter adaptation for physical human-robot interaction,”IEEE International Conference on Robotics and Automation (ICRA), Singapore, 2017, pp. 2911-2916, doi: 10.1109/ICRA.2017.7989338. 

[8] H. Zhan,  D. Ye, C. Zeng, and C. Yang, “Hybrid variable admittance force tracking and fixed-time position control for robot–environment interaction,” Robotic Intelligence and Automation, vol. 45, no. 1, pp. 1-12, 2025. doi: 

[9] ARISE Project, “Advanced AI and robotics for autonomous task performance,” Horizon Europe Project 101135959, [Online]. Available: https://cordis.europa.eu/project/id/101135959. 

[10] Y. Aydin, O. Tokatli, V. Patoglu and C. Basdogan, “A Computational Multicriteria Optimization Approach to Controller Design for Physical Human-Robot Interaction,” in IEEE Transactions on Robotics, vol. 36, no. 6, pp. 1791-1804, Dec. 2020, doi: 10.1109/TRO.2020.2998606.

[11] A. Madani, P. P. Niaz, B. Guler, Y. Aydin and C. Basdogan, “Robot-Assisted Drilling on Curved Surfaces with Haptic Guidance under Adaptive Admittance Control,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Kyoto, Japan, 2022, pp. 3723-3730, doi: 10.1109/IROS47612.2022.9982000. 

[12] Y. M. Hamad, Y. Aydin and C. Basdogan, “Adaptive Human Force Scaling via Admittance Control for Physical Human-Robot Interaction,” in IEEE Transactions on Haptics, vol. 14, no. 4, pp. 750-761, 1 Oct.-Dec. 2021, doi: 10.1109/TOH.2021.3071626.

[13] B. Guler, P. P. Niaz, A. Madani, Y. Aydin, C. Basdogan,

“An adaptive admittance controller for collaborative drilling with a robot based on subtask classification via deep learning,” in Mechatronics, vol. 86, 102851, 2022, doi: https://doi.org/10.1016/j.mechatronics.2022.102851.

[14] F. Dimeas and N. Aspragathos, “Online stability in human-robot cooperation with admittance control,” IEEE Transactions on Haptics, vol. 9, no. 2, pp. 267–278, Apr./Jun. 2016.

[15] J. E. Colgate and N. Hogan, “Robust control of dynamically interacting systems,” International Journal of Control, vol. 48, no. 1, pp.  65–88, 1988.

[16] S. P. Buerger and N. Hogan, “Complementary stability and loop shaping for improved human–robot interaction,” IEEE Transactions on Robotics, vol. 23, no. 2, pp. 232–244, Apr. 2007.