4. You are designing a simulation system for a robot with the following kinematic model: * = -(li sin 01 + 12 sin(@1 +82))wi - 12 sin(@: +82)w2 (l; cos 6, + la cos(@, + 02))wi + la cos(@: +02)w2 j 21 02 2 where x, y, 0,02 : states of the robot wy, W2 : inputs of the robot and 11=1.3, 12-1.5 are constants. Please answer the following questions based on the above model. (Marks: 45%) (a) Please write down the discrete-time version of the robot kinematics. (10%) (b) Please use Matlab script to write a program of the robot kinematics for input signals wl=sin(3.1*t), w2=sin(5.4*1+1.8). (15%) (c) You realize that the generated behaviour of the robot in simulation is different from your experimental results with the real robot. What are possible reasons? (5%) (d) Please calculate the inputs wl and w2 so that i=1.1, =-1.2 when 0, 0, 02=1.57.(15%)