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Title:Inverse optimal control for differentially flat systems with application to lower-limb prosthetic devices
Author(s):Aghasadeghi, Navid
Director of Research:Bretl, Tim
Doctoral Committee Chair(s):Bretl, Tim
Doctoral Committee Member(s):Perreault, Eric; Srikant, Rayadurgam; Jones, Douglas
Department / Program:Electrical & Computer Eng
Discipline:Electrical & Computer Engr
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Prosthetic control
Learning from demonstration
Abstract:Powered prosthetic devices have shown to be capable of restoring natural gait to amputees. However, the commercialization of these devices is faced by some challenges, in particular in prosthetic controller design. A common control framework for these devices is called impedance control. The challenge in the application of this framework is that it requires the choice of many controller parameters, which are chosen by clinicians through trial and error for each patient. In this thesis we automate the process of choosing these parameters by learning from demonstration. To learn impedance controller parameters for flat-ground, we adopt the method of learning from exemplar trajectories. Since we do not at first have exemplar joint trajectories that are specific to each patient, we use invariances in locomotion to produce them from pre-recorded observations of unimpaired human walking and from measurements of the patient’s height, weight, thigh length, and shank length. Experiments with two able-bodied human subjects wearing the Vanderbilt prosthetic leg with an able-bodied adaptor show that our method recovers the same level of performance that can be achieved by a clinician but reduces the amount of time required to choose controller parameters from four hours to four minutes. To extend this framework to learning controllers for stair ascent, we need a model of locomotion that is capable of generating exemplar trajectories for any desired stair height. Motivated by this challenge, we focus on a class of learning from demonstration methods called inverse optimal control. Inverse optimal control is the problem of computing a cost function with respect to which observed trajectories of a given dynamic system are optimal. We first present a new formulation of this problem, based on minimizing the extent to which first-order necessary conditions of optimality are violated. This formulation leads to a computationally efficient solution as opposed to traditional approaches. Furthermore, we develop the theory of inverse optimal control for the case where the dynamic system is differentially flat. We demonstrate that the solution further simplifies in this case, in fact reducing to finite-dimensional linear least-squares minimization. We show how to make this solution robust to model perturbation, sampled data, and measurement noise, as well as provide a recursive implementation for online learning. Finally, we apply our new formulation of inverse optimal control to model human locomotion during stair ascent. Given sparse observations of human walkers, our model predicts joint angle trajectories for novel stair heights that compare well to motion capture data. These exemplar trajectories are then used to learn prosthetic controllers for one subject. We show the performance of the learned controllers in a stair ascent experiment with the subject walking with the Vanderbilt prosthetic device.
Issue Date:2015-04-24
Rights Information:Copyright 2015 Navid Aghasadeghi
Date Available in IDEALS:2015-07-22
Date Deposited:May 2015

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