Each wheel W i {\displaystyle W_{i}} is described by its coordinates ( x i , y i ) {\displaystyle (x_{i},y_{i})} , so that a configuration of the robot can be given by the six scalars ( x 1 , y 1 , x 2 , y 2 , x 3 , y 3 ) {\displaystyle (x_{1},y_{1},x_{2},y_{2},x_{3},y_{3})} . Also, each wheel W i {\displaystyle W_{i}} can impulse a velocity v i = ( v x , i , v y , i ) {\displaystyle \mathbf {v} _{i}=(v_{x,i},v_{y,i})} to the robot. However, because all three wheels are connected by the rigid robot frame, their relative velocities are zero (unless the frame breaks):