Neuro-Robotics pp 157-178 | Cite as

Multi-directional Dynamic Mechanical Impedance of the Human Ankle; A Key to Anthropomorphism in Lower Extremity Assistive Robots

  • Mohammad Rastgaar
  • Hyunglae Lee
  • Evandro Ficanha
  • Patrick Ho
  • Hermano Igo Krebs
  • Neville Hogan
Part of the Trends in Augmentation of Human Performance book series (TAHP, volume 2)


The mechanical impedance of the human ankle plays a central role in lower-extremity functions requiring physical interaction with the environment. Recent efforts in the design of lower-extremity assistive robots have focused on the sagittal plane; however, the human ankle functions in both sagittal and frontal planes. While prior work has addressed ankle mechanical impedance in single degrees of freedom, here we report on a method to estimate multi-variable human ankle mechanical impedance and especially the coupling between degrees of freedom. A wearable therapeutic robot was employed to apply torque perturbations simultaneously in the sagittal and frontal planes and record the resulting ankle motions. Standard stochastic system identification procedures were adapted to compensate for the robot dynamics and derive a linear time-invariant estimate of mechanical impedance.

Applied to seated, young unimpaired human subjects, the method yielded coherences close to unity up to and beyond 50 Hz, indicating the validity of linear models, at least under the conditions of these experiments. Remarkably, the coupling between dorsi-flexion/plantar-flexion and inversion/eversion was negligible. This was observed despite strong biomechanical coupling between degrees of freedom due to musculo-skeletal kinematics and suggests compensation by the neuro-muscular system. The results suggest that the state-of-the-art in lower extremity assistive robots may advance by incorporating design features that mimic the multi-directional mechanical impedance of the ankle in both sagittal and frontal planes.


Multi-variable mechanical impedance Ankle impedance Powered ankle-foot prosthesis Directional Impedance of ankle 



The authors would like to acknowledge the support of Toyota Motor Corporation’s Partner Robot Division. H. Lee was supported in part by a Samsung Scholarship.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Mohammad Rastgaar
    • 1
  • Hyunglae Lee
    • 2
    • 3
  • Evandro Ficanha
    • 1
  • Patrick Ho
    • 4
  • Hermano Igo Krebs
    • 5
    • 6
  • Neville Hogan
    • 5
    • 7
  1. 1.Department of Mechanical Engineering-Engineering MechanicsMichigan Technological UniversityHoughtonUSA
  2. 2.Department of Biomedical EngineeringNorthwestern UniversityEvanstonUSA
  3. 3.Sensory Motor Performance ProgramRehabilitation Institute of ChicagoChicagoUSA
  4. 4.Parian LogisticsCambridgeUSA
  5. 5.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridgeUSA
  6. 6.Department of NeurologyUniversity of Maryland School of MedicineBaltimoreUSA
  7. 7.Department of Brain and Cognitive SciencesMassachusetts Institute of TechnologyCambridgeUSA

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