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Section 4.8 Design Examples 257
For low frequencies (|,v| < 1), the sensitivity can be approximated by

Si s (4.61)

where K 2: 20. Thus, the sensitivity of the system is reduced by increasing the gain,
K. In this case, we choose K = 20 for a reasonable design compromise. •

EXAMPLE 4.3 Mars rover vehicle
The solar-powered Mars rover named Sojourner landed on Mars on July 4,1997, and
was deployed on its journey on July 5,1997. The rover was controlled by operators on
Earth using controls on the rover [21,22]. The Mars rovers, aptly dubbed Spirit and
Opportunity, are known as the twin Mars Exploration Rovers and landed on the
planet in 2004. These new rovers differ in size and capability from the Sojourner
rover. Sojourner was about 65 cm (2 ft) long and weighed 10 kg (22 lb), while Spirit
and Opportunity are each 1.6 m (5.2 ft) long and weigh 174 kg (384 lbs). Sojourner
traveled a total distance of about 100 m during its 12 weeks of activity on Mars. Spir-
it has traveled over 7 km and Opportunity has traveled over 19 km. Opportunity has
traveled over 32 times further than expected for a successful mission. The Mars
Exploration Rovers are more autonomous; each carries its own telecommunications
equipment, camera, and computers, whereas the Sojourner housed most of its equip-
ment on the lander left at the base site. The solar-powered Mars rover Spirit is shown
in Figure 4.20. The vehicle is controlled from Earth by sending it path commands, r(t).
A very simplified model of a rover is depicted in Figure 4.21. The system may be
operated without feedback, as shown in Figure 4.21(a), or with feedback, as shown
in Figure 4.21(b). The goal is to operate the rover with modest effects from distur-
bances such as rocks and with low sensitivity to changes in the gain K.
The transfer function for the open-loop system is
Y(s) K
Us) = 2 (4.62)
R(s) s + 4s + 5'

FIGURE 4.20
Mars Exploration
Rovers are
significantly more
capable than their
predecessor, the
Mars Pathfinder
Sojourner.
(Courtesy of NASA.)