29-12-2012, 06:17 PM
Design of an Active 1-DOF Lower-Limb Exoskeleton with Inertia Compensation
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Abstract
Limited research has been done on exoskeletons to enable faster movements of the lower extremities.
An exoskeleton’s mechanism can actually hinder agility by adding weight, inertia and friction to the legs;
compensating inertia through control is particularly difficult due to instability issues. The added inertia
will reduce the natural frequency of the legs, probably leading to lower step frequency during walking.
We present a control method that produces an approximate compensation of an exoskeleton’s inertia.
The aim is making the natural frequency of the exoskeleton-assisted leg larger than that of the unaided
leg. The method uses admittance control to compensate the weight and friction of the exoskeleton.
Inertia compensation is emulated by adding a feedback loop consisting of low-pass filtered acceleration
multiplied by a negative gain. This gain simulates negative inertia in the low-frequency range. We tested
the controller on a statically supported, single-DOF exoskeleton that assists swing movements of the leg.
Subjects performed movement sequences, first unassisted and then using the exoskeleton, in the context
of a computer-based task resembling a race. With zero inertia compensation, the steady-state frequency
of leg swing was consistently reduced. Adding inertia compensation enabled subjects to recover their
normal frequency of swing.
Introduction
In recent years, different types of exoskeletons and orthotic devices have been developed to assist lower-limb
motion. Applications for these devices usually fall into either of two broad categories: (1) augmenting the
muscular force of healthy subjects, and (2) rehabilitation of people with motion impairments. Most of the existing
implementations in the former group are designed to either enhance the user’s capability to carry heavy
loads [Lee and Sankai, 2003, Kawamoto and Sankai, 2005, Kazerooni et al., 2005, Walsh et al., 2006] or reduce
muscle activation during walking [Banala et al., 2006, Sawicki and Ferris, 2009, Lee and Sankai, 2002].
Rehabilitation-oriented applications include training devices for gait correction [Jezernik et al., 2004, Banala et al., 2009]
and devices that apply controlled forces to the extremities in substitution of a therapist [Veneman et al., 2007].
Exoskeleton design and construction
We designed and built a stationary 1-DOF exoskeleton for assisting knee flexion and extension exercises
(Figure 1). Our aim was to use the pendular motion of the leg’s shank as a scaled-down model of the swing
motion of the entire leg when walking, and to investigate the effects of an active exoskeleton dynamics on
the kinematics and energetics of leg-swing motion.
In order to specify the torque requirements for our 1-DOF exoskeleton, we surveyed reported values of
knee torque during normal walking. Kerrigan [Kerrigan et al., 2000] reported an extensive study on the knee
joint torques of barefoot walking. The peak knee torques reported there were 0.34±0.15 N-m/kg-m for women
and 0.32±0.15 N-m/kg-m for men. Thus for a male subject with body mass of 80 kg and height of 1.80 m, the
peak knee torque during normal walking should be about 45 N-m. DeVita [DeVita and Hortobagyi, 2003]
reported peak knee torques ranging from 0.39 N-m/kg for obese subjects to 0.97 N-m/kg for lean subjects.
From these data, we concluded that an actuator-transmission combination capable of delivering about 20
N-m of continuous torque would be sufficient to produce significantly large assistive torques.
Assist through admittance control
In this section we discuss our general concept of exoskeleton-based assistance using admittance control. Then
we examine the question of whether an admittance controller can be used to compensate the inertia of the
user’s limb. A very simplified model of an admittance controller shows that, even assuming the very favorable
case of rigid coupling between the user’s limb and the exoskeleton, the coupled system will become unstable
before any inertia compensation is accomplished. However, an approximate form of inertia compensation
can be achieved by adding low-pass filtered acceleration feedback to the admittance controller.
Inertia compensation and sensor non-collocation
The effects of the torque sensor’s non-collocation can be demonstrated with a simplified model of the exoskeleton’s
mechanism and the human limb, shown in Figure 6. The drive portion of the exoskeleton’s
model consists of the servo motor’s inertia Im (reflected on the output shaft) and an output inertia Is, which
comprises the mechanical components located between the cable and the torque sensor, i.e. the major pulley and the torque sensor’s housing. The inertias are coupled by a spring of stiffness kc representing the cable,
and a damper bc representing dissipative effects. The exoskeleton’s arm inertia Iarm is rigidly coupled to Is
by the torque sensor at port S; we also assume a rigid coupling between the arm’s inertia and the inertia of
the human limb, Ih. The external torques acting on the system are the net human muscle torque h and the
exoskeleton’s actuator torque m.