Stabilization of a Dynamic Walking Gait Simulation

[+] Author and Article Information
Mike Peasgood

Systems Design Engineering,  University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1 Canadamike@lair.uwaterloo.ca

Eric Kubica

Systems Design Engineering,  University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1 Canadaekubica@kingcong.uwaterloo.ca

John McPhee

Systems Design Engineering,  University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1 Canadamcphee@real.uwaterloo.ca

MSC.ADAMS is a mechanical system modeling and simulation package available from MSC Software. It provides a graphical interface for developing mechanical models (ADAMS∕View), and a simulation engine for both kinematic and dynamic analysis (ADAMS∕Solver).

J. Comput. Nonlinear Dynam. 2(1), 65-72 (Jul 06, 2006) (8 pages) doi:10.1115/1.2389230 History: Received March 18, 2006; Revised July 06, 2006

Forward dynamic simulations of human walking gait have typically simulated and analyzed a single step of the walking cycle, assuming symmetric and periodic gait. To enable simulations over many steps, a stabilizer is required to maintain the balance of the walking model, ideally mimicking the human balance control mechanism. This paper presents a feedback control system that stabilizes the torso orientation during a human walking gait dynamic simulation, enabling arbitrarily long simulations. The model is a two-dimensional mechanical simulation, in which the desired joint trajectories are defined as functions of time; the only external forces on the model are gravitational and ground reaction forces. Orientation or postural control is achieved by modulation of the rate at which lower limb joints move through angular trajectories. The controller design is based on a sequence of simple linear feedback controllers, each based on an intuitive control law. Controller parameters were determined iteratively using an optimization algorithm and repeated executions of the forward dynamics simulation to minimize control term errors. Results show the use of feedback control and joint speed modulation to be effective in maintaining balance for walking simulations of arbitrary length, allowing for analysis of steady-state walking.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

The mechanical simulation walking model was created using ADAMS. The HAT segment is a single rigid body, shown as multiple ellipsoids for visual clarity. The only external forces on the model are the ground reaction forces indicated at the feet.

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Figure 2

Ground reaction force contact model

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Figure 3

The feedback controller computes the joint torques required to drive the model simulation and consists of two components. The Balance Controller component (Sec. 3) determines the stabilized joint trajectories. The Joint Position Controller component (Sec. 3) drives the joints to the desired angles by specifying input joint torques to the dynamic model simulation.

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Figure 4

Graphical interpretation of the calculation of θp for a single limb. The error in the absolute position of the thigh is due to the rotation of the torso, plus the error in the hip angle: θp=θtorso+(θhip−θhip̱des).

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Figure 5

Balance controller subcomponents: The Velocity Controller (Sec. 31) attempts to maintain a constant speed by determining an appropriate forward pitch thetap̱des. The Pitch Controller (Sec. 32) attempts to achieve the specified pitch by varying the rate of joint trajectories with a time offset. The Joint Trajectory Calculation (Sec. 33) computes the desired joint angles using the input trajectory functions and the current time offset.

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Figure 6

Velocity control behavior over the simulation duration. The measured velocity was filtered using a moving window filter with a width of one stride period.

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Figure 7

Velocity control behavior of a single step. The torso velocity peaks and falls just after right heel contact (0%) and left heel contact (42%).

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Figure 8

Pitch control response over simulation duration. The measured and desired pitch were filtered using a moving window filter with a width of one stride period. The dotted line indicates the desired pitch θp̱des, which is the control variable used to modulate the average forward velocity.

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Figure 9

Pitch control response over a single step. For the steady-state walking steps, θp (Actual) is approximately equal to the torso orientation, and peaks at right (0%) and left (42%) heel contact events. This behavior is consistent with that observed in experimental measurements of human walking (10). The dotted line indicates θp̱des, the controller’s desired pitch angle, which decreases at heel contact in an attempt to compensate for the peaks in velocity seen in Fig. 7.




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