new_position=deadReckonTimeVelocityTaylor(position,vr,vl,t,bw)

%% Author: epokh
%% Website: www.epokh.org/drupy
%% This software is under GPL


function new_position=deadReckonTimeVelocityTaylor(position,vr,vl,t,bw)
%% This function calculate the new position of the robot
%% with a linearized version (Taylor 1th order) of the direct kinematics
%% it's good to use in a line follower approach!

x0=position(1);
y0=position(2);
theta0=position(3);
sr=vr*t;
sl=vl*t;
theta=theta0+(vr-vl)*t/bw;
x=x0+(sr+sl)/2;
y=y0+(sr+sl)*(sr-sl+2*bw*theta0)/(4*bw);
new_position=[x,y,theta];

end