Image-based homing for robots can be implemented by generating heading command inputs to a steering system based on the following guidance algorithm. Suppose the robot shown in Figure P3.13(a) is to go from point R to a target, point T, as shown in Figure P3.13(b). If R_x, R_y, and R_z are vectors from the robot to each landmark, X, Y, Z, respectively, and T_x, T_y, and T_z are vectors from the target to each landmark, respectively, then heading commands would drive the robot to minimize R_x - T_x; R_{y -} T_y; and R_z - T_z simultaneously, since the differences will be zero when the robot arrives at the target (Hong, 1992). If Figure P3.13(c) represents the control system that steers the robot, represent each block—the controller, wheels, and vehicle—in state space. An animation PowerPoint presentation (PPT) demonstrating this system is available for instructors atwww.wiley.com/college/nise.

FIGURE P3.13

a. Robot with television imaging system;10

b. vector diagram showing concept behind image-based homing;10

c. heading control system

Spherical mirror Camera T Robot R, R: (a) (b) Heading Heading Controller Steering, Wheels Wheel Vehicle Actual command ommand angle heading error K1(s + a) (s + b) 1. (c) HI