Skip to main content

First steps toward translating robotic walking to prostheses: a nonlinear optimization based control approach


This paper presents the first steps toward successfully translating nonlinear real-time optimization based controllers from bipedal walking robots to a self-contained powered transfemoral prosthesis: AMPRO, with the goal of improving both the tracking performance and the energy efficiency of prostheses control. To achieve this goal, a novel optimization-based optimal control strategy combining control Lyapunov function based quadratic programs with impedance control is proposed. This optimization-based optimal controller is first verified on a human-like bipedal robot platform, AMBER. The results indicate improved (compared to variable impedance control) tracking performance, stability and robustness to unknown disturbances. To translate this complete methodology to a prosthetic device with an amputee, we begin by collecting reference locomotion data from a healthy subject via inertial measurement units (IMUs). This data forms the basis for an optimization problem that generates virtual constraints, i.e., parameterized trajectories, specifically for the amputee . A online optimization based controller is utilized to optimally track the resulting desired trajectories. An autonomous, state based parameterization of the trajectories is implemented through a combination of on-board sensing coupled with IMU data, thereby linking the gait progression with the actions of the user. Importantly, the proposed control law displays remarkable tracking and improved energy efficiency, outperforming PD and impedance control strategies. This is demonstrated experimentally on the prosthesis AMPRO through the implementation of a holistic sensing, algorithm and control framework, resulting in dynamic and stable prosthetic walking with a transfemoral amputee.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13


  • Aghasadeghi, N., Zhao, H., Hargrove, L. J., Ames, A. D., Perreault, E. J., & Bretl, T.(2013). Learning impedance controller parametersfor lower-limb prostheses. IEEE/RSJ international conference on intelligent robots and systems (pp. 4268–4274).

  • Ames, A., Galloway, K., & Grizzle, J. (2012). Control lyapunovfunctions and hybrid zero dynamics. In IEEE 51st annual conference on decision and control (CDC) (pp. 6837–6842).

  • Ames, A., Vasudevan, R., & Bajcsy, R. (2011). Human-data based costof bipedal robotic walking. In Hybrid systems: Computation and control (pp. 153–162). Chicago, IL.

  • Ames, A. (2012). Human-inspired control of bipedal walking robots. IEEE Transactions on Automatic Control, 59, 1115–1130.

    MathSciNet  Article  Google Scholar 

  • Ames, A. (2012). First steps toward automatically generating bipedal robotic walking from human data. Robotic Motion and Control, 422, 89–116.

    MathSciNet  Google Scholar 

  • Ames, A. D., Galloway, K., Grizzle, J., & Sreenath, K. (2014). Rapidly exponentially stabilizing control lyapunov functions and hybrid zero dynamics. IEEE Transactions on Automatic Control, 59, 876–891.

    MathSciNet  Article  Google Scholar 

  • Atherton, D., & Majhi, S. (1999). Limitations of pid controllers. In American control conference (pp 3843–3847).

  • Au, S., Berniker, M., & Herr, H. (2008). Powered ankle-foot prosthesis to assist level-ground and stair-descent gaits. Neural Networks, 21(4), 654–666.

    Article  Google Scholar 

  • Blaya, J. A., & Herr, H. (2004). Adaptive control of a variable-impedance ankle-foot orthosis to assist drop-foot gait. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 12(1), 24–31.

    Article  Google Scholar 

  • Boehler, A., Hollander, K., Sugar, T., & Shin, D. (2008). Design, implementation and test results of a robust control method for apowered ankle foot orthosis (afo). In IEEE International conference on robotics and automation (pp. 2025–2030).

  • Dillingham, T. (2002). Limb amputation and limb deficiency: Epidemiology and recent trends in the united states. Southern Medical Journal, 95, 875–884.

    Google Scholar 

  • Fey, N., Simon, A., Young, A., & Hargrove, L. (2014). Controlling knee swing initiation and ankle plantarflexion with an active prosthesis on level and inclined surfaces at variable walking speeds. IEEE Journal of Translational Engineering in Health and Medicine, 2, 1–12.

    Article  Google Scholar 

  • Flowers, W., & Mann, (1977). Electrohydraulic knee-torque controller for a prosthesis simulator. ASME Journal of Biomechanical Engineering, 99(4), 3–8.

    Article  Google Scholar 

  • Gregg, R., Lenzi, T., Hargrove, L., & Sensinger, J. (2014). Virtual constraint control of a powered prosthetic leg: From simulation to experiments with transfemoral amputees. IEEE Transactions on Robotics, 30(6), 1455–1471.

    Article  Google Scholar 

  • Grimes, D., Flowers, W., & Donath, M. (1977). Feasibility of an active control scheme for above knee prostheses. ASME Journal of Biomechanical Engineering, 99(4), 215–221.

    Article  Google Scholar 

  • Herr, J. W. H., & Au, S. (2007). In Powered ankle-foot prosthesis. Biomechanics of the Lower limb in health, disease and rehabilitation (pp. 72–74).

  • Hitt, J., Oymagil, A. M., Sugar, T., Hollander, K., Boehler, A., & Fleeger, J. (2007). Dynamically controlled ankle-foot orthosis (dco) with regenerative kinetics: Incrementally attaining userportability. In IEEE international conference on robotics and automation (pp. 1541–1546).

  • Hogan, N. (1984). Impedance control: An approach to manipulation (pp. 304–313).

  • Hollander, K., & Sugar, T. (2007). A robust control concept forrobotic ankle gait assistance. In 2007 IEEE 10th international conference on rehabilitation robotics (pp. 119–123).

  • Hürmüzlü, Y., & Marghitu, D. (1994). Rigid body collisions of planar kinematic chains with multiple contact points. International Journal of Robotics Research, 13(1), 82–92.

    Article  Google Scholar 

  • Jiang, S., Partrick, S., Zhao, H., & Ames, A. (2012). Outputs of human walking for bipedal robotic controller design. American Control Conference (ACC), 2012, 4843–4848.

    Google Scholar 

  • Luinge, H. J., & Veltink, P. H. (2005). Measuring orientation of human body segments using miniature gyroscopes and accelerometers. Medical and Biological Engineering and Computing, 43(2), 273–282.

    Article  Google Scholar 

  • Ma, W.-L., Zhao, H., Kolathaya, S., & Ames, A. D.(2014). Human-inspired walking via unified pd and impedance control. In IEEE international conference on robotic and automation (pp. 5088–5094).

  • Miller, N., Jenkins, O. C., Kallmann, M., & Mataric, M. J. (2004) .Motion capture from inertial sensing for untethered humanoidteleoperation. In IEEE/RAS 4th International conference on humanoid robots (vol. 2, pp. 547–565).

  • Morris, B., Powell, M., & Ames, A. (2013). Sufficient conditionsfor the lipschitz continuity of qp-based multi-objective control ofhumanoid robots. In IEEE 52nd Annual conference on decision and control (CDC) (pp 2920–2926).

  • Oymagil, A. M., Hitt, J. K., Sugar, T., & Fleeger, J. (2007). Controlof a regenerative braking powered ankle foot orthosis. In IEEE 10th international conference on rehabilitation robotics (pp. 28–34).

  • Rarick, R., Richter, H., van den Bogert, A., Simon, D., Warner, H., & Barto, T.(2014). Optimal design of a transfemoral prosthesiswith energy storage and regeneration. In American control conference (pp 4108–4113).

  • Roetenberg, D., Luinge, H., & Slycke, P. (2009). Xsens mvn: full 6dof human motion tracking using miniature inertial sensors. Xsens Motion Technologies BV, Technical Report.

  • Sastry, S. (1999). Nonlinear systems: Analysis stability and control. New York: Springer.

    Book  MATH  Google Scholar 

  • Šlajpah, S., Kamnik, R., & Munih, M. (2013). Kinematics based sensory fusion for wearable motion assessment in human walking. Computer Methods and Pograms in Biomedicine, 116, 131–144.

    Article  Google Scholar 

  • Sup, F., Bohara, A., & Goldfarb, M. (2008). Design and control of a powered transfemoral prosthesis. The International Journal of Robotics Research, 27(2), 263–273.

    Article  Google Scholar 

  • Westervelt, E., Grizzle, J., Chevallereau, C., Choi, J., & Morris, B. (2007). Feedback control of dynamic bipedal robot locomotion. Boca Raton: CRC Press.

    Book  Google Scholar 

  • Winter, D. (1990). Biomechanics and motor control of human movement (2nd ed.). New York: Wiley-Interscience.

    Google Scholar 

  • Winter, D. (1991). The biomechanics and motor control of humangait: Normal, elderly, and pathological. Waterloo: University of Waterloo Press.

    Google Scholar 

  • Yadukumar, S. N., Pasupuleti, M., & Ames, A. (2012). Human-inspiredunderactuated bipedal robotic walking with AMBER on flat-ground,up-slope and uneven terrain. In IEEE international conference on intelligent robots and systems (pp. 2478–83). Portugal.

  • Zhao, H., & Ames, A. D. (2014). Quadratic program based control offully-actuated transfemoral prosthesis for flat-ground and up-slopelocomotion. IEEE, American control conference (pp. 4101–4107).

  • Zhao, H., Kolathaya, S., & Ames, A. D.(2014). Quadraticprogramming and impedance control for transfemoral prosthesis. IEEE international conference on robotic and automation (pp. 1341–1347).

  • Zhao, H., Ma, W.-L., Zeagler, M. B., & Ames, A. D.(2014). Human-inspired multi-contact locomotion with AMBER2. In IEEE International conference on cyberphysics system (pp 199–210).

  • Zhao, H., Powell, M., & Ames, A. D. (2013). Human-inspired motion primitives and transitions for bipedal robotic locomotion in diverse terrain. Optimal Control Applications and Methods, 35, 730–755.

    Article  MATH  Google Scholar 

Download references


This research is supported under: NSF CAREER Award CN-S-0953823 and Texas Emerging Technology Fund 11062013. This research has approval from the Institutional Review Board from Texas A&M University with IRB2014-0382F for testing with human subjects.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Huihua Zhao.

Additional information

This is one of several papers published in Autonomous Robots comprising the “Special Issue on Assistive and Rehabilitation Robotics”.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (mp4 9363 KB)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhao, H., Horn, J., Reher, J. et al. First steps toward translating robotic walking to prostheses: a nonlinear optimization based control approach. Auton Robot 41, 725–742 (2017).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Transfemoral prosthesis control
  • Real-time optimal control
  • Hybrid systems
  • Quadratic program
  • Optimization problem