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Hybrid Impedance-Sliding Mode Switching Control of the Indego Explorer Lower-Limb Exoskeleton in Able-Bodied Walking

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Abstract

This paper proposes a novel hybrid controller for promoting safe human-robot interaction. The hybrid controller modifies a model-based impedance controller such that it uses impedance control but switches to sliding mode control under non-nominal conditions. Each control law is formulated with an inner-loop controller for feedback linearization and an outer-loop feedback controller for trajectory tracking. The outer-loop feedback torque is theoretically proven to have a smaller magnitude in hybrid control than in impedance control under an assumed condition, suggesting it may be the safer approach. To validate the mathematical assumption and purpose of the controller, a walking experiment is conducted where a healthy able-bodied subject using a lower-limb exoskeleton is randomly subjected to either hybrid or impedance control. Perturbations are induced through sudden changes in treadmill speed, resulting in operation outside nominal conditions for 15.9% of the experiment. The assumption made in the theory holds true for the majority of the experiment, failing only 14.3% of the time. The main results show a statistically significant reduction in average feedback torque magnitudes by 7.9%. This is accomplished without drastically affecting gait, with joint angle root-mean-square differences being 0.36° for the hip and 0.64° for the knee. This demonstrates how the hybrid controller can achieve similar gait patterns with lower feedback torque magnitudes, suggesting it is a promising alternative to impedance control.

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References

  1. Lajeunesse, V., Vincent, C., Routhier, F., Careau, E., Michaud, F.: Exoskeletons’ design and usefulness evidence according to a systematic review of lower limb exoskeletons used for functional mobility by people with spinal cord injury. Disabil. Rehabil. Assist. Technol. 11, 535–547 (2016)

    Article  Google Scholar 

  2. Swinnen, E., Duerinck, S., Baeyens, J., Meeusen, R., Kerckhofs, E.: Effectiveness of robot-assisted gait training in persons with spinal cord injury: a systematic review. J. Rehabil. Med. 42, 520–526 (2010)

    Article  Google Scholar 

  3. Lee, B.B., Cripps, R.A., Fitzharris, M., Wing, P.C.: The global map for traumatic spinal cord injury epidemiology: update 2011, global incidence rate. Spinal Cord. 52, 110–116 (2014)

    Article  Google Scholar 

  4. Bruns, J., Hauser, W.A.: The epidemiology of traumatic brain injury: a review. Epilepsia. 44, 2–10 (2003)

    Article  Google Scholar 

  5. Maas, A.I.R., Menon, D.K., Adelson, P.D., Andelic, N., Bell, M.J., Belli, A., Bragge, P., Brazinova, A., Büki, A., Chesnut, R.M., Citerio, G., Coburn, M., Cooper, D.J., Crowder, A.T., Czeiter, E., Czosnyka, M., Diaz-Arrastia, R., Dreier, J.P., Duhaime, A.C., et al.: Traumatic brain injury: integrated approaches to improve prevention, clinical care, and research. Lancet Neurol. 16, 987–1048 (2017)

    Article  Google Scholar 

  6. Roozenbeek, B., Maas, A.I.R., Menon, D.K.: Changing patterns in the epidemiology of traumatic brain injury. Nat. Rev. Neurol. 9, 231–236 (2013)

    Article  Google Scholar 

  7. Mahon, C.E., Farris, D.J., Sawicki, G.S., Lewek, M.D.: Individual limb mechanical analysis of gait following stroke. J. Biomech. 48, 984–989 (2015)

    Article  Google Scholar 

  8. Pennycott, A., Wyss, D., Vallery, H., Klamroth-Marganska, V., Riener, R.: Towards more effective robotic gait training for stroke rehabilitation: a review. J. NeuroEng. Rehabil. 9, 65 (2012)

    Article  Google Scholar 

  9. Louie, D.R., Eng, J.J.: Powered robotic exoskeletons in post-stroke rehabilitation of gait: a scoping review. Journal of NeuroEngineering and Rehabilitation. 13, 53 (2016)

    Article  Google Scholar 

  10. Anttila, H., Autti-Rämö, I., Suoranta, J., Mäkelä, M., Malmivaara, A.: Effectiveness of physical therapy interventions for children with cerebral palsy: a systematic review. BMC Pediatr. 8, 14 (2008)

    Article  Google Scholar 

  11. Williams, G.R.: Incidence and characteristics of total stroke in the United States. BMC Neurol. 1, 1 (2001)

    Article  Google Scholar 

  12. Campbell, S.K., Palisano, R.J., Orlin, M.N.: Physical Therapy for Children. Elsevier Saunders, St. Louis, MO (2012)

    Google Scholar 

  13. Alexander, M.A., Matthews, D.J., Murphy, K.P.: Pediatric Rehabilitation: Principles and Practice, 5th edn. Demos Medical Publishing, New York, NY (2015)

    Book  Google Scholar 

  14. Wren, T.A., Rethlefsen, S., Kay, R.M.: Prevalence of specific gait abnormalities in children with cerebral palsy: influence of cerebral palsy subtype, age, and previous surgery. J. Pediatric Orthopaedics. 25, 79–83 (2005)

    Google Scholar 

  15. Christensen, D., Braun, K.V.N., Doernberg, N.S., Maenner, M.J., Arneson, C.L., et al.: Prevalence of cerebral palsy, co-occurring autism spectrum disorders, and motor functioning – autism and developmental disabilities monitoring network, USA, 2008. Develop. Med. Child Neurol. 56, 59–65 (2014)

    Article  Google Scholar 

  16. Odding, E., Roebroeck, M.E., Stam, H.J.: The epidemiology of cerebral palsy: incidence, impairments and risk factors. Disability Rehabil. 28, 183–191 (2006)

    Article  Google Scholar 

  17. Yilmaz, D., Dehghani-Sanij, A.: A Review of Assistive Robotic Exoskeletons and Mobility Disorders in Children to Establish Requirements of Such Devices for Paediatric Population. In: Reinventing Mechatronics: Proceedings of Mechatronics, Glasgow (2018)

    Google Scholar 

  18. Miller, L.E., Zimmermann, A.K., Herbert, W.G.: Clinical effectiveness and safety of powered exoskeleton-assisted walking in patients with spinal cord injury: Systematic review with meta-analysis. Medical Devices (Auckland, N.Z.). 9, 455–466 (2016)

    Google Scholar 

  19. Federici, S., Meloni, F., Bracalenti, M., De Filippis, M.L.: The effectiveness of powered, active lower limb exoskeletons in neurorehabilitation: a systematic review. NeuroRehabil. 37, 321–340 (2015)

    Article  Google Scholar 

  20. Trevino, L., Vatcheva, K., Auer, M., Morales, A., Abdurrahman, L., et al.: A Single-Center Comparison Using Exoskeleton Rehabilitation for Cerebrovascular Accidents and Traumatic Brain Injury in a Cohort of Hispanic Patients. Math. Stat. Sci. Faculty Pub. Pres (2020)

    Book  Google Scholar 

  21. Carpino, G., Pezzola, A., Urbano, M., Guglielmelli, E.: Assessing effectiveness and costs in robot-mediated lower limbs rehabilitation: a meta-analysis and state of the art. J. Healthcare Eng. 2018, 1–9 (2018)

    Article  Google Scholar 

  22. Nolan, K.J., Karunakaran, K.K., Ehrenberg, N., Kesten, A.G.: Robotic exoskeleton gait training for inpatient rehabilitation in a young adult with traumatic brain injury. In: Annu. Int. Conf. IEEE Eng. Med. Biol. Soc. (EMBC), IEEE, Honolulu, HI, pp. 2809–2812 (2018)

    Google Scholar 

  23. Díaz, I., Gil, J.J., Sánchez, E.: Lower-limb robotic rehabilitation: literature review and challenges. J. Robot. 2011, e759764 (2011)

    Google Scholar 

  24. Bogue, R.: Exoskeletons and robotic prosthetics: a review of recent developments. Ind. Robot. 36, 421–427 (2009)

    Article  Google Scholar 

  25. Viteckova, S., Kutilek, P., Jirina, M.: Wearable lower limb robotics: a review. Biocybern. Biomed. Eng. 33, 96–105 (2013)

    Article  Google Scholar 

  26. Bogue, R.: Robotic exoskeletons: a review of recent progress. Ind. Robot. 42, 5–10 (2015)

    Article  Google Scholar 

  27. Chen, G., Chan, C.K., Guo, Z., Yu, H.: A review on lower extremity assistive robotic exoskeleton in rehabilitation therapy. Crit. Rev. Biomed. Eng. 41, 343–363 (2013)

    Article  Google Scholar 

  28. Marchal-Crespo, L., Reinkensmeyer, D.J.: Review of control strategies for robotic movement training after neurologic injury. J. NeuroEng. Rehabil. 6, 20 (2009)

    Article  Google Scholar 

  29. Jiménez-Fabián, R., Verlinden, O.: Review of control algorithms for robotic ankle systems in lower-limb orthoses, prostheses, and exoskeletons. Med. Eng. Phys. 34, 397–408 (2012)

    Article  Google Scholar 

  30. Ibarra, J.C.P., Siqueira, A.A.G.: Impedance Rontrol of Rehabilitation Robots for Lower Limbs, Review, in: SBR-LARS Robot, pp. 235–240. Symp. Robocontrol, IEEE, Sao Carlos, Sao Paulo, Brazil (2014)

    Google Scholar 

  31. Hogan, N.: Impedance control: an approach to manipulation: part I—theory. J. Dyn. Sys. Meas. Control. 107, 1–7 (1985)

    Article  MATH  Google Scholar 

  32. Hogan, N.: Impedance control: an approach to manipulation: part II—implementation. J. Dyn. Sys. Meas. Control. 107, 8–16 (1985)

    Article  MATH  Google Scholar 

  33. Hogan, N.: Impedance control: an approach to manipulation: part III—applications. J. Dyn. Sys. Meas. Control. 107, 17–24 (1985)

    Article  MATH  Google Scholar 

  34. Asada, H., Slotine, J.-J.E.: Robot Analysis and Control. John Wiley & Sons (1986)

    Google Scholar 

  35. Mohammadi, A., Gregg, R.D.: Variable Impedance Control of Powered Knee Prostheses Using Human-Inspired Algebraic Curves. Journal of Computational and Nonlinear Dynamics. 14, (2019)

  36. Yu, X., He, W., Li, Y., Xue, C., Li, J., Zou, J., Yang, C.: Bayesian estimation of human impedance and motion intention for human–robot collaboration. IEEE Transactions on Cybernetics. 51, 1822–1834 (2021)

    Article  Google Scholar 

  37. Yu, X., He, W., Li, Q., Li, Y., Li, B.: Human-robot co-carrying using visual and force sensing. IEEE Trans. Ind. Electron. 68, 8657–8666 (2021)

    Article  Google Scholar 

  38. Tran, H.T., Cheng, H., Rui, H., Lin, X., Duong, M.K., Chen, Q.M.: Evaluation of a fuzzy-based impedance control strategy on a powered lower exoskeleton. Int J of Soc Robotics. 8, 103–123 (2016)

    Article  Google Scholar 

  39. Spyrakos-Papastavridis, E., Childs, P.R.N., Dai, J.S.: Passivity preservation for variable impedance control of compliant robots. IEEE/ASME Transactions on Mechatronics. 25, 2342–2353 (2020)

    Article  Google Scholar 

  40. Laubscher, C.A., Sawicki, J.T.: A robust impedance controller for improved safety in human-robot interaction. J. Dyn. Sys., Meas. Control. 1–24 (2021)

  41. Søraa, R.A., Fosch-Villaronga, E.: Exoskeletons for all: the interplay between exoskeletons, inclusion, gender, and intersectionality. Paladyn J Behav. Robot. 11, 217–227 (2020)

    Article  Google Scholar 

  42. Dalley, S.A., Hartigan, C., Kandilakis, C., Farris, R.J.: Increased walking speed and speed control in exoskeleton enabled gait. In: IEEE Int. Conf. Biomed. Robot. Biomech. (Biorob), pp. 689–694. IEEE, Enschede (2018)

    Google Scholar 

  43. Indego Explorer User Manual Supplement 043–008-000 Rev A, Parker Hannifin Corporation (2018)

  44. Parker Hannifin Corporation, Indego Personal Data Sheet (2020)

  45. du Bois, J.L., Lieven, N.A.J., Adhikari, S.: Error analysis in trifilar inertia measurements. Exp. Mech. 49, 533–540 (2009)

    Article  Google Scholar 

  46. Korr, A.L., Hyer, P.: A Trifilar Pendulum for the Determination of Moments of Inertia. Frankford Arsenal Research and Development Group Pitman-Dunn Laboratories, Philadelphia, PA (1962)

    Book  Google Scholar 

  47. Winter, D.A.: Biomechanics and Motor Control of Human Movement, 4th edn. John Wiley & Sons, Hoboken, NJ (2009)

    Book  Google Scholar 

  48. Rose, J., Gamble, J.G.: Human Walking, 3rd Edition. Lippincott Williams & Wilkins (2006)

    Google Scholar 

  49. Goo A, Laubscher C, Sawicki JT (2022) Hybrid Zero Dynamics Control of an Underactuated Lower-limb Exoskeleton for Gait Guidance. Journal of Dynamic Systems, Measurement, and Control. https://doi.org/10.1115/1.4053946

  50. Tan, A.H., Godfrey, K.R.: The generation of binary and near-binary pseudorandom signals: an overview. IEEE Trans. Instrum. Meas. 51, 583–588 (2002)

    Article  Google Scholar 

  51. Redd, J., Lyon, C.: Spectral content of NRZ test patterns. Maxim Appl. Note. 3455(49), 10–14 (2004)

    Google Scholar 

  52. The OEIS Foundation, A011673 - OEIS, (n.d.)

  53. Winter, D.A.: The Biomechanics and Motor Control of Human Gait: Normal, Elderly and Pathological, 2nd edn. University of Waterloo Press (1991)

    Google Scholar 

  54. Laubscher, C.A., Farris, R.J., van den Bogert, A.J., Sawicki, J.T.: An anthropometrically parameterized assistive lower-limb exoskeleton. ASME J. Biomech. Eng. 143, (2021)

  55. Goo, A., Laubscher, C.A., Farris, R.J., Sawicki, J.T.: Design and evaluation of a pediatric lower-limb exoskeleton joint actuator. Actuators. 9, 16 (2020)

    Article  Google Scholar 

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Acknowledgments

The authors would like to thank the individuals at the Human Motion and Control Division at Parker Hannifin Corporation for their technical expertise and support with the Indego Explorer exoskeleton.

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C.A.L. developed the controller and composed the manuscript. C.A.L. and A.G. conducted the experiments. R.J.F. provided technical expertise on the exoskeleton. J.T.S. supervised and oversaw the work. All authors reviewed the manuscript.

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Correspondence to Jerzy T. Sawicki.

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Laubscher, C.A., Goo, A., Farris, R.J. et al. Hybrid Impedance-Sliding Mode Switching Control of the Indego Explorer Lower-Limb Exoskeleton in Able-Bodied Walking. J Intell Robot Syst 104, 76 (2022). https://doi.org/10.1007/s10846-022-01583-7

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