1. (15 points)Consider the case study: \"Moving to a Pomnt\\f\f104 Chapter 4 - Mobile Robot Vehicles 0 1 2 3 4 5 6 7 8 9 10 which is shown in Fig. 4.5 for a number of starting poses. In each case the vehicle has moved forward and turned onto a path toward the goal point. The final part of each path is a straight line and the final orientation therefore depends on the starting point. 4.1.1.2 Following a Line Another useful task for a mobile robot is to follow a line on the plane* defined by ax + by + = 0. This requires two controllers to adjust steering. One controller ey = _Kdd, ch =0 turns the robot toward the line to minimize the robot's normal distance from the line d (; brC) '(x:}': l) va +b' The second controller adjusts the heading angle, or arientation, of the vehicle to be parallel to the line Fig.4.5. Simulation results for sl drivepeoint for different initial poses. The goal is (5, 5) 2-dimensional lines in hemogeneous form are discussed in Sect.C.2.1. 4.1.1.2 Following a Line Another useful task for a mobile robot is to follow a line on the plane* defined by 2-dimensional lines in homogeneous ax + by + = 0. This requires two controllers to adjust steering, One controller form are discussed in Sect.C.2.1. Gy = _Kdd, Kd =10 turns the robot toward the line to minimize the robot's normal distance from the line d (,b?)*{-"'?y: 1} vat +b The second controller adjusts the heading angle, or orientation, of the vehicle to be parallel to the line 0" = tan' 2 b using the proportional controller y = K.l': (* = '], K =0 The combined control law v =Ksd+K,(0" 2 0) turns the steering wheel so as to drive the robot toward the line and move along it. The Simulink model >> 5l driveline is shown in Fig. 4.6. We specify the target line as a 3-vector (a, b, c) >> L [1 -2 4]