Controlling the Apparent Inertia of Passive Human-Interactive Robots

[+] Author and Article Information
Tom Worsnopp

Mechanical Engineering Department, Northwestern University, Evanston, IL 60208greycloak@northwestern.edu

Michael Peshkin

Mechanical Engineering Department, Northwestern University, Evanston, IL 60208peshkin@northwestern.edu

Kevin Lynch

Mechanical Engineering Department, Northwestern University, Evanston, IL 60208kmlynch@northwestern.edu

J. Edward Colgate

Mechanical Engineering Department, Northwestern University, Evanston, IL 60208colgate@northwestern.edu

J. Dyn. Sys., Meas., Control 128(1), 44-52 (Nov 14, 2005) (9 pages) doi:10.1115/1.2168165 History: Received February 07, 2005; Revised November 14, 2005

Passive robotic devices may exhibit a spatially varying apparent inertia perceptible to a human user. The apparent inertia is the projection of the inertia matrix onto the instantaneous direction of motion. The spatial variation is due to the configuration dependence of the inertia matrix and relevant to many passive mechanisms, including programmable constraint machines or “cobots,” which use low-power steering actuators to choose the direction of motion. We develop two techniques for controlling the apparent inertia in cobots to emulate the desired inertial properties of a virtual object or mechanism. The first is a path-limiting method, which constraints the cobot to steer along certain paths where the apparent inertia and desired inertia are equivalent. The second uses a low-power actuator to control the apparent inertia by driving the device along its direction of motion. We illustrate these ideas for a two-link cobot we have built for experiments in human motor control and rehabilitation. For the actuated control method, we show that the power actuator can be relatively low power compared to the actuators of a traditional robot performing similar tasks.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

The unicycle two-link arm (UTLA) cobot is a two-degree-of-freedom haptic device used to display high-quality, software-defined constraints over a workspace large enough for the full motion of a user’s arm

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Figure 2

The motion of the cobot is unintuitive to a user when following certain virtual paths. When the endpoint moves around a circular path, for example, it feels as if it is rising and falling. These effects are the result of the apparent inertia varying.

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Figure 3

The apparent inertia of the cobot varies between 3kg and 15kg as a circle is traversed. The radius of the circle shown is 20cm.

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Figure 4

A three-dimensional plot of the apparent inertia (in kilograms) of the simplified UTLA model is shown as a function of the second joint angle (θ2) and the angle of motion (ϕ) of the endpoint. The shoulder joint angle (θ1) has no affect on the apparent inertia (it only shifts the values) and, thus, is excluded from consideration.

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Figure 5

The long axis of the inertia ellipse corresponds to a direction of low apparent inertia, and the short axis corresponds to a direction of high apparent inertia

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Figure 6

The intersection of the inertia ellipse of the cobot with the inertia ellipse of a point mass (i.e., a circle) can be used to determine the directions of motion in which the cobot will feel like the point mass. These directions are indicated by the arrows. Note that the cobot cannot emulate masses that are too large (small inertia circles) or too small (large inertia circles).

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Figure 7

The UTLA cobot is shown with two different inertia ellipses for two different configurations. The diameter of both ellipses tangent to the isomass contour are the same length, as indicated by the two double-headed arrows. A set of isomass contours is illustrated with the UTLA positioned in a starting configuration for an apparent inertia of mapp=3.30kg. Note that three ends of the two contours terminate at the boundaries of the workspace, while the fourth one spirals toward a limit cycle circle centered at the shoulder.

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Figure 8

Numerically computed maximum power for a wide range of point mass values for every configuration

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Figure 9

Numerically computed maximum power for a smaller range of point mass values for every configuration

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Figure 10

Using an 80W motor, the UTLA can emulate an 8kg mass over a very large workspace (0.7m2). The boundaries of the workspace are physically limited by the table edges on the top, bottom, and right side.




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