Path Following for a Differential Drive Robot - MATLAB & Simulink
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I have the Kinematical model of Skid-Steering Robot with Differential Drive is illustrated in the below figure. Lambda_L is the Left wheel slipping so Lambda_R the are assumed constants 0.01, c is half of the distance between the tow wheels, r is the radios of the wheel. I'm trying to set the speed of the right wheel tow times of the Left wheel, so the Robot have to follow circular trajectory theoretically, what I'm dong is just to plot this trajectory on simulation.
I have:
Vox=Vmx.Cos(Theta)
Voy=Vmx.Sin(Theta)
so:
X=Vox.t=Vmx.Cos(Theta).t
Y=Voy.t=Vmx.Sin(Theta).t
I know that theta must rotate 2 Pi radiant, theta is the integration of Wz the angular speed, **my question (problem) How to draw the trajectory of the robot in (x,y) plane the Robot follow according the Kinematic model.**
my code:
r=0.25;
c=0.5;
lamda_L=0.01;
lamda_R=0.01;
w_L=0.1;
w_R=4*w_L;
t=0:0.1:6.28;
eita=(r/2)*[1-Lamda_L,1-Lamda_R ;(Lamda_L-1)/c,(1-Lamda_R)/c]*[w_L ; w_R];
Vm_x = eita(1,:)
wz=eita(2,:);
for i=1:63%%calculation of theta
theta(i)=i*wz;
end
Vox=Vm_x*cos(theta);
Voy=Vm_x*sin(theta);
y=zeros(1,63);
x=zeros(1,63);
x=Vox.*t;
y=Vox.*t;
plot(x,y)
the simulation is provided with the Image below: https://www.dropbox.com/s/m1up2sb5gym2k75/ssmr.jpg?dl=0
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