Motivation and Previous Approaches

  • State of art powered prostheses are controlled using a collection of impedance controllers


  • 4-5 hours needed for tuning 30 parameters
  • Tuning must be repeated for each amputee


Previous single joint tuning methods

  • Rule-based fuzzy logic inference (Huang et al.) and adaptive dynamic programming (Wen et al.)


  • Cannot tune multiple joint parameters simultaneously
  • Not able to learn across different subjects

Proposed Approach

  • Virtual constraints with 4 parameters automatically tuned [1] using extremum seeking controller (ESC) [2]


  • No a priori knowledge of prosthesis/ human
  • Closed form of objective function is not required
  • Simultaneous K_p adaptation for different joints
  • Embedding a user comfort factor in the cost function

Structure of Extremum Seeking Adaptation for Powered Prosthetic Legs

  • The objective function, J(⋅), is computed using the prosthetic leg tracking error, Kp, and the user’s comfort preference

The Objective Function

  • A convex combination of tracking error and user comfort
  • The tracking error objective function is filtered through a low-pass filter

Working of ESC

  • K_p is perturbed with a periodic signal, d(t)
  • The gradient of J(⋅) with respect to K_p is estimated by multiplying J(⋅) with d(t)
  • The integrator updates K_p in the direction of the gradient





Bench-top Experimental Results


Future Work

  • Implement a time-invariant ESC, which uses the periodic walking trajectories as the dither signal
  • To solve a real-time multi-objective optimization, using ESC, as in [3]


[1] S. Kumar, A. Mohammadi, N. Gans, and R. D. Gregg, “Automatic tuning of virtual constraint-based control algorithms for powered knee ankle prostheses,” in 2017 IEEE CCTA, Aug 2017, pp. 812–818

[2] M. Krstic ́  and H.-H. Wang, “Stability of extremum seeking feedback for general nonlinear dynamic systems,” Automatica, vol. 36, no. 4, pp. 595–601, 2000

[3] S. Kumar and N. Gans, “Extremum seeking control for multi-objective optimization problems,” in IEEE CDC, 2016


This material is based upon work supported by the National Science Foundation under Grant Number 1728057. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.