Planar rigid body transformations A transformation g = (p,R) SE(2) consists of a translation p R 2 and a 22 rotation matrix R. We represent this in homogeneous coordinates as a 3 3 matrix: g = R p 0 1 . A twist b se(2) can be represented by a 3 3 matrix of the form: b= v b 0 0 b = 0 0 R,v R 2 . The twist coordinates for b se(2) have the form = (v,) R 3 . Note that v is a vector in the plane and is a scalar. (a) Show that the exponential of a twist in se(2) gives a rigid body transformation in SE(2). Consider both the pure translation case, = (v, 0), and the general case, = (v,), 6= 0