DP7.3 A rover vehicle has been designed for maneuver

ing at 0.25 mph over Martian terrain. Because Mars is 189 million miles from Earth, and it would take up to 40 minutes each way to communicate with Earth

[22, 27], the rover must act independently and reli

ably. Resembling a cross between a small flatbed truck and an elevated jeep, the rover is constructed of three articulated sections, each with its own two indepen

dent, axle-bearing, one-meter conical wheels. A pair of sampling arms—one for chipping and drilling, the other for manipulating fine objects—extend from its front end like pincers. The control of the arms can be represented by the system shown in Figure DP7.3.

(a) Sketch the root locus for K, and identify the roots for K = 2 and 25.

(b) Determine the gain K that re

sults in a percent overshoot to a step of P.O. = 1%. (c)

Determine the gain that minimizes the settling time

(with a 2% criterion) while maintaining a percent overshoot of P.O. ≤ 1%. 

FIGURE DP7.3 Mars vehicle robot control system. Controller K(s+4s+32) R(s) S Manipulator U(s) 1 Y(s) (s+3)(s+10)