Research Papers

Limit Cycles to Enhance Human Performance Based on Phase Oscillators

[+] Author and Article Information
Thomas G. Sugar

Polytechnic School,
Ira A. Fulton Schools of Engineering,
Arizona State University,
Mesa, AZ 85212
SpringActive, Inc.,
Tempe, AZ 85281
e-mail: thomas.sugar@asu.edu

Andrew Bates, Marc Mignolet, Philip New, Ragesh K. Ramachandran, Chase Wheeler

School for Engineering of Matter,
Transport & Energy,
Ira A. Fulton Schools of Engineering,
Arizona State University,
Tempe, AZ 85287

Matthew Holgate

SpringActive, Inc.,
Tempe, AZ 85281

Jason Kerestes

Polytechnic School,
Ira. A. Fulton Schools of Engineering,
Arizona State University,
Mesa, AZ 85212

Sangram Redkar

Polytechnic School,
Ira A. Fulton Schools of Engineering,
Arizona State University,
Tempe, AZ 85212

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received September 10, 2014; final manuscript received December 7, 2014; published online December 31, 2014. Assoc. Editor: Carl Nelson.

J. Mechanisms Robotics 7(1), 011001 (Feb 01, 2015) (8 pages) Paper No: JMR-14-1243; doi: 10.1115/1.4029336 History: Received September 10, 2014; Revised December 07, 2014; Online December 31, 2014

Wearable robots including exoskeletons, powered prosthetics, and powered orthotics must add energy to the person at an appropriate time to enhance, augment, or supplement human performance. This “energy pumping” at resonance can reduce the metabolic cost of performing cyclic tasks. Many human tasks such as walking, running, and hopping are repeating or cyclic tasks where assistance is needed at a repeating rate at the correct time. By utilizing resonant energy pumping, a tiny amount of energy is added at an appropriate time that results in an amplified response. However, when the system dynamics is varying or uncertain, resonant boundaries are not clearly defined. We have developed a method to add energy at resonance so the system attains the limit cycle based on a phase oscillator. The oscillator is robust to disturbances and initial conditions and allows our robots to enhance running, reduce metabolic cost, and increase hop height. These methods are general and can be used in other areas such as energy harvesting.

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Grahic Jump Location
Fig. 1

(a) ϕ, shown on a phase plot, is defined here as atan2(x·/ω,x). (b) Spring response with phase oscillator. m = 1 kg, b = 1 Ns/m, k = 50 N/m, c = 20 N, initial position = 1 m, and initial velocity = 0 m/s. (c) initial position = 6 m and initial velocity = 0 m/s.

Grahic Jump Location
Fig. 2

A phase portrait of the system shown in Fig. 1 with the two initial conditions from Fig. 1. The limit cycle is globally stable. The horizontal axis is in units of position and the vertical axis is in units of velocity.

Grahic Jump Location
Fig. 3

(a) Robotic hopper assembly. (b) Phase portrait of hopper dropped from three different initial positions each achieving the same steady state limit cycle. The cycle is noncircular because there is a flight phase [5]. The hopper can interact with the ground or can enter a flight phase governed by drag and gravity.

Grahic Jump Location
Fig. 4

(a) Actual position versus time of hopper experiencing two disturbances which limit height [5]. (b) Phase portrait of hopper experiencing two disturbances.

Grahic Jump Location
Fig. 5

The system oscillates back and forth at its natural frequency in a limit cycle. I = 0.25 kgm2, b = 0.007 Nm/(rad/s), k = 230 Nm/rad, c = 0.05 Nm, initial velocity = (2/3)*pi rad/s, and initial position = (1/9)*pi rad.

Grahic Jump Location
Fig. 6

The damping torque oscillates in a sine wave while the control torque generated by the sine of the phase angle behaves similar to a square wave. I = 0.25 kgm2, b = 0.007 Nm/(rad/s), k = 230 Nm/rad, c = 0.05, initial velocity = (2/3)*pi rad/s, and initial position = (1/9)*pi rad.

Grahic Jump Location
Fig. 7

The damping is shown positive instead of negative so it can be compared easily with the control power. The powers are similar but not equal. The energy for each curve over a cycle matches.

Grahic Jump Location
Fig. 8

The system is oscillating back and forth quickly and the spring torque is high resulting in large power oscillations in the spring

Grahic Jump Location
Fig. 9

(a) A powered exoskeleton is used to assist the torque needed at the hips [2]. (b) A powered PogoSuit is used to assist the hopping motion. A pneumatic cylinder oscillates the small mass up and down in phase with the user [4].

Grahic Jump Location
Fig. 10

(a) A rate gyro is mounted on each thigh. The signals and time durations for each leg differ [2]. (b) The phase angle for the left and right leg. The left and right control signals are shown in dashed lines [2]. The phase angle for the left and right leg is measured at 500 Hz in the microprocessor. As the leg swings forward, the control signal turns high and as the leg swings backward, the control signal turns low.

Grahic Jump Location
Fig. 11

At the natural frequency of the system, 10 rad/s, both the linear oscillator generator and the phase oscillator harvester can produce 12.5 W. The simulated measurement was taken at steady state with a constraint of 0.5 m oscillations. At 9 rad/s, the linear generator can produce 0.17 W while the nonlinear generator can produce 0.73 W. (0.04 W versus 0.36 W at 8 rad/s).




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