The attitude controller in the above paper measured the pitch and roll of the rover. It then used a fuzzy logic system to determine the speed at which the rover should travel. It uses the membership functions shown in Figure 11.3 in the paper, together with 15 rules which are also summarised in Figure 11.3. However, there are no numbers on the axes and the membership functions for the output velocity are not shown. From other papers by the same authors it is possible to get a bit more information. Based on this, the three membership functions are shown below, this time with some numbers on the axes. membership -50 -25 25 50 Roll (*) NEGATIVE membership ZERO membership POSITIVE membership Figure 3 Roll For roll the sets are: a. NEGATIVE b. ZERO C. POSITIVE membership w 50 Pitch () -50-25 0 25 NEGATIVE HIGH membership NEGATIVE LOW membership ZERO membership POSITIVE LOW membership POSITIVE HIGH membership Figure 4 Pitch For pitch the sets are: a. NEGATIVE HIGH b. NEGATIVE LOW C. ZERO d. POSITIVE LOW e. POSITIVE HIGH membership 1 Speed (m/s) 0.25 0.50 0.75 SLOW membership MODERATE membership FAST membership Figure 5 Speed For speed the sets are: SLOW MODERATE . FAST a. Re-write the 15 rules in the form of roll is NEGATIVE and pitch is NEGATIVE LOW then speed is MODERATE. (3 marks) b. With a pitch of -30 degrees and a roll of +10 degrees: i. Using Figure 6, what are the membership values of pitch and roll? (4 marks) ii. Using Table 2, write down the inferred membership values of speed. (4 marks) ii. Using Table 3 write down the defuzzified value of speed when centre of area defuzzification is used. (5 marks) c. The attitude control is only one part of the speed control system. The other part is traction management, which takes an estimated value for the traction and also recommends a speed for the rover. How does the rover decide what speed to travel when faced with one speed from the attitude controller and one from the traction management system? (2 marks) 1.0 0.8 0.6 0.4 0.2 0.0 10 15 20 25 05 Figure 6 A right-angled triangle. It shows that as you move along the horizontal to the right by 5, the vertical drops by 0.2 Table 2 Minimum values of the two input conditions Roll Pitch NEGATIVE LOW ZERO NEGATIVE HIGH POSITIVE POSITIVE LOW HIGH NEGATIVE ZERO POSITIVE Table 3 Maximum values for the membership functions of speed Speed Rule Rule Rule 1 2 3 Rule 4 Rule 5 Rule 6 Rule 7 Rule 8 Rule 9 Rule 10 SLOW MODERATE FAST