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Unformatted text preview: Tutorial: Limit cycle analysis Dani¨ el Karssen ([email protected]) & Martijn Wisse In this tutorial we are going investigate the behavior of a dynamic walker. The goal of this tutorial is to learn about limit cycles and the stability of these limit cycles. In this tutorial we will use a simulation of a simple walking robot. For this simulation you need to have a version of Matlab (version 6.5 or higher will certainly work and lower versions will probably work). Figure 1 shows the model that we are going to simulate. The model consists of two identical rigid legs which are connected at the hip with a rotational joint. The model is passive and gains energy by walking down a slope. We describe the state of the model with the absolute angles and angular velocities of the two legs with respect to the normal of the ground. g γ φ st φ sw C B L R y x Figure 1: Simple dynamic walking model A part of the simulation is provided 1 . The file Step.m is a Matlab function that simulates one step of the model. The simulation integrates the equations of motion until the swing foot hits the ground. After this event is detected, the integration is stopped and an impact calculation is done to determine the state of the model after the impact. Also the legs are swapped so that the swing leg becomes the new stance leg and visa versa. The equations of motion and impact equations are determined with the TMTmethod 2 . How this is done for this model can be found in the file DeriveEOM.m ....
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 Fall '08
 Teel,A
 Derivative, Gate, limit cycle, Jacobian

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