A Passivity-Based Approach for Variable Stiffness Control With Dynamical Systems

Youssef Michel, Matteo Saveriano, Dongheui Lee

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this paper, we present a controller that combines motion generation and control in one loop, to endow robots with reactivity and safety. In particular, we propose a control approach that enables to follow the motion plan of a first order Dynamical System (DS) with a variable stiffness profile, in a closed loop configuration where the controller is always aware of the current robot state. This allows the robot to follow a desired path with an interactive behavior dictated by the desired stiffness. We also present two solutions to enable a robot to follow the desired velocity profile, in a manner similar to trajectory tracking controllers, while maintaining the closed-loop configuration. Additionally, we exploit the concept of energy tanks in order to guarantee the passivity during interactions with the environment, as well as the asymptotic stability in free motion, of our closed-loop system. The developed approach is evaluated extensively in simulation, as well as in real robot experiments, in terms of performance and safety both in free motion and during the execution of physical interaction tasks. <italic>Note to Practitioners</italic>&#x2014;The approach presented in this work allows for safe and reactive robot motions, as well as the capacity to shape the robot&#x2019;s physical behavior during interactions. This becomes crucial for performing contact tasks that might require adaptability or for interactions with humans as in shared control or collaborative tasks. Furthermore, the reactive properties of our controller make it adequate for robots that operate in proximity to humans or in dynamic environments where potential collisions are likely to happen.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalIEEE Transactions on Automation Science and Engineering
StateAccepted/In press - 2023
Externally publishedYes


  • Dynamical Systems (DSs)
  • Variable Impedance Control (VIC)
  • passivity theory


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