Question

Problem 2 (50 points). Consider the diagram shown below. A robot base is set up 1m from a table. A frame {Fo} is attached to the base of the robot such that the yo passes through the two legs of the table. The tabletop is 1m high and 1m square. A frame {Fi} is fixed to the edge of the table. A cube measuring 20 cm on each side is placed at the center of the table and a frame {F2} is defined at the center of the cube. A camera is situated directly above the center of the cube (2m above the tabletop) and a frame {F}} is attached to the camera. Find the homogenous transformation relating each of these frames to the base frame {Fo}. Also find the homogenous transformation matrix that relates the frame {Fo} to {F}}. Camera {fz Z3 → X3 2m - --- ---- Robot -- - - Object x) / 1m. Table 1 m

Answer 1

ANSWER Given that Camera #{F} 93 5323 am ? Robot a lobject ZIVA Acm {F} yi In

Let 'H; denotes pose of Fiframe wide Fi frame. Now is sol y z °H;lo 10 14 Y smo 0 0 1 1 IzJ Loo 0 il sa y z li o o 0.5 lo 10 0. 54 y Tool 0.1 [2] looo I Jo - Toooly Y F2 1-1 0 0 1. 9 21 O Now [Hz = it with is which can be found by successing matrise multiplication,