CS685 - Homework 2, due Oct 14th,Jana Koˇseck´a1. Consider a differential drive model of the mobile robot with a configuration space [x, y, θ]T,where we can control linear and angular velocity of the robotvandω. The kinematic modeldescribing the motion of the mobile robot is as follows:˙x=vcos(θ)˙y=vsin(θ)˙θ=ωImplement the closed loop feed-back control lawv=kρρ(1)ω=kαα+kββ(2)described in class, whereρ, α, βis the configuration of the robot expressed in polar coordinates(with respect to the goal). As a part of this exercise you will need to use the function writtenfor homework 2, which simulates the odometry of the mobile robot. You will need to write afunction[x,y,theta] = goTo(xg), which keeps on applying the control law and simulatingthe robot forward checking the flag which indicates that the goal position is reached.Ex-periment with different values ofkρ, kα, kβand describe any observations and strategies youchose to decide whether the goal was reached. Test the control law for variety of initial/goalpositions. Hand in the plots of
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