You are given the following description of the frames on a mobile robot: The robot's coordinate frame, {R}, has its origin located at the robot's center of mass, its x axis pointing forward, and its z axis pointing up. The robot is equipped with two cameras, both of which have the same orientation: the cameras' z axes are pointing forward, while their y axes are pointing down. The cameras' coordinate frames are denoted by {C_1} and {C_2}. The position of the origin of the frame of camera 1 with respect to the robot is^R PC_1_org = [0.5 0.1 0.2]^T (units are meters). The origin of the coordinate frame of camera 2 lies on the positive x axis of the coordinate frame of camera 1. The distance between the origins of two frames is 0.2 m. Draw a figure showing these frames and compute the following: (i) Compute the transformations^R _C_1 T, ^C_1 _C_2 T, and^R _C_2 T. (ii) Compute the transformation^C_1 _R T (iii) The robot's position with respect with the "global" frame, {G} is^G P R_org = [1 1 0]^T. The robot's z axis is parallel to the z axis of the global frame, while the robot's x axis forms an 180 degree angle with the x axis of the global frame. Compute and^G _R T and^G _C_1 T. (iv) The two cameras observe the point^G P = [-1 1 0.3]^T. Compute the 3D coordinates of this point with respect to the frames {C_1} and {C_2}. All derivations should be carried out without the use of a computer. You should use all relevant properties of transformation matrices when computing the various transformations. Also note that the verbal descriptions "forward", "up", "down", imply that the axes of the associated frames are aligned (i.e., the angles between different frames' axes can only be 0 degree, 90 degree, 180 degree, etc.)