For a differential drive mobile robot as shown in the picture, program in Matlab to simulate the paths shown in Figure 3.20 of the Textbook, where the robot is initially on a circle in the ry plane. All movements should have smooth trajectories toward the goal in the center. Verify the control parameters given in equation (3.59) of the Textbook, or give the parameters that you use to generate similar trajectories. \B goal Ay Ar Robot trajectory Robot trajectory 50 50 4 40 30 30 - 2 20 1 10 -1 -10- -2 -20- -30 -30 -40 -40- -50 -50- -60 -40 -20 20 40 60 -60 -40 -20 20 xImm] 40 60 x (mm] Figure 3.20 -k,pcos a k, sina ka - kp (3.58) %3D -k, sina In figure 3.20 you find the resulting paths when the robot is initially on a circle in the xy plane. All movements have smooth trajectories toward the goal in the center. The con- trol parameters for this simulation were set to k = (k,, k, kp) = (3, 8,-1.5). (3.59) %3! [ww) A