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Research Papers

An Energetic Control Methodology for Exploiting the Passive Dynamics of Pneumatically Actuated Hopping

[+] Author and Article Information
Yong Zhu

Department of Mechanical Engineering, Vanderbilt University, Nashville, TN 37235

Eric J. Barth

Department of Mechanical Engineering, Vanderbilt University, Nashville, TN 37235eric.j.barth@vanderbilt.edu

J. Dyn. Sys., Meas., Control 130(4), 041004 (Jun 04, 2008) (11 pages) doi:10.1115/1.2907355 History: Received October 24, 2006; Revised December 19, 2007; Published June 04, 2008

This paper presents an energetically derived control methodology to specify and regulate the oscillatory motion of a pneumatic hopping robot. An ideal lossless pneumatic actuation system with an inertia is shown to represent an oscillator with a stiffness, and hence frequency, related to the equilibrium pressures in the actuator. Following from an analysis of the conservative energy storage elements in the system, a control methodology is derived to sustain a specified frequency of oscillation in the presence of energy dissipation. The basic control strategy is to control the pressure in the upper chamber of the pneumatic cylinder to specify the contact time of the piston, while controlling the total conservative energy stored in the system to specify the flight time and corresponding flight height of the cylinder. The control strategy takes advantage of the natural passive dynamics of the upper chamber to provide much of the required actuation forces and natural stiffness, while the remaining forces needed to overcome the energy dissipation present in a nonideal system with losses are provided by a nonlinear control law for the charging and discharging of the lower chamber of the cylinder. Efficient hopping motion, relative to a traditional nonconservative actuator, is achieved by allowing the energy storing capability of a pneumatic actuator to store and return energy to the system at a controlled specifiable frequency. The control methodology is demonstrated through simulation and experimental results to provide accurate and repeatable hopping motion for pneumatically actuated robots in the presence of dissipative forces.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagrams of (a) a linear mass-spring system and (b) a vertical pneumatic system. An analysis of energetically lossless versions of both systems reveals equations of motion with an algebraic relationship between acceleration and position.

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Figure 2

Representative hopping trajectory

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Figure 3

Schematic of a pneumatic hopping robot showing inertial coordinates for the cylinder housing (x) and piston (y) positions. (x=0 at equilibrium pressures with y=0 when the piston is in contact with the ground.)

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Figure 4

Representative position-dependent velocity profile

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Figure 5

Representative position-dependent acceleration profile

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Figure 6

Hopping results for designed periods of Thop=0.4s and Tair=0.2s. Actual periods in simulation are Thop=0.39s and Tair=0.18s.

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Figure 7

Control mass flow rates ṁa and ṁa

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Figure 8

Photograph of the experimental setup

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Figure 9

Case I: hopping results for designed periods of Thop=0.35s and Tair=0.1s. Actual experimental periods are Thop=0.36s and Tair=0.14s.

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Figure 10

Case II: hopping results for designed periods of Thop=0.4s and Tair=0.2s. Actual experimental periods are Thop=0.46s and Tair=0.18s.

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Figure 11

Case III: hopping results for designed periods of Thop=0.45s and Tair=0.15s. Actual experimental periods (consistent after the fourth hop) are Thop=0.44s and Tair=0.17s.

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Figure 12

Case II: desired velocity (ẋd) and actual velocity (ẋ). Velocity tracking is achieved during contact only.

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Figure 13

Case II: desired pressure (Pad) and actual pressure (Pa) in chamber a. Pressure tracking is achieved during contact only.

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Figure 14

Case II: discrete valve control signals

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