x is the distance along the global x-axis (xg) [m] y is the distance along the...
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x is the distance along the global x-axis (xg) [m] y is the distance along the global y-axis (y) [m] y is the heading angle of the rover, i.e. the angle between global x-axis (xg) and rover x-axis (x) and clockwise rotation is positive [radians]. v. is the longitudinal velocity along the rover x-axis (x) [m/s] is the lateral velocity along the rover y-axis (y) [m/s] vend is the commanded longitudinal velocity along the rover x-axis (x) [m/s] Semd is the commanded steering wheel angle [radians] C1-91 are the coefficients computed during system identification We approximate the rover to a linear, time-invariant (LTI) system when driving in a straight line and get the following continuous-time state space representation: 0 0 0.0055 1 X 0 0 0,3390 -0,1020 y 00 0 V -0.0506 -1,6400 00 0 where we observe v (i.e. C = [ 0 0 0 1] X 1.1 [6 point(s)] Show that Gr(s) = s+1.64' respect to the commanded velocity input. 0 0 0 1.6400 0.0013 0.1072 1.4950 0 3 Uphill terrain vcmd 8cmd ] Flat terrain Figure 3: Side view of rover on varying terrain. The open-loop system, shown in Fig. 4, represents the effect of driving the rover forward on roads of different inclines, with c(t) =V, e(t) = vcmd and 8 cmd = 0. For simplicity, we assume the robot either drives on flat terrain (r(t) = 0) or on a hill of con- stant, predefined incline (r(t) = S(t-to), where to is the time at which the rover starts driving up the incline). This is shown in Fig. 3. Let D(z) = 1 and sampling period T = 0.05s. Solve the following questions 1.1 1.5 by hand and 1.6 with Simulink. (3) 164, where GR (s) is the transfer function of the rover with x is the distance along the global x-axis (xg) [m] y is the distance along the global y-axis (y) [m] y is the heading angle of the rover, i.e. the angle between global x-axis (xg) and rover x-axis (x) and clockwise rotation is positive [radians]. v. is the longitudinal velocity along the rover x-axis (x) [m/s] is the lateral velocity along the rover y-axis (y) [m/s] vend is the commanded longitudinal velocity along the rover x-axis (x) [m/s] Semd is the commanded steering wheel angle [radians] C1-91 are the coefficients computed during system identification We approximate the rover to a linear, time-invariant (LTI) system when driving in a straight line and get the following continuous-time state space representation: 0 0 0.0055 1 X 0 0 0,3390 -0,1020 y 00 0 V -0.0506 -1,6400 00 0 where we observe v (i.e. C = [ 0 0 0 1] X 1.1 [6 point(s)] Show that Gr(s) = s+1.64' respect to the commanded velocity input. 0 0 0 1.6400 0.0013 0.1072 1.4950 0 3 Uphill terrain vcmd 8cmd ] Flat terrain Figure 3: Side view of rover on varying terrain. The open-loop system, shown in Fig. 4, represents the effect of driving the rover forward on roads of different inclines, with c(t) =V, e(t) = vcmd and 8 cmd = 0. For simplicity, we assume the robot either drives on flat terrain (r(t) = 0) or on a hill of con- stant, predefined incline (r(t) = S(t-to), where to is the time at which the rover starts driving up the incline). This is shown in Fig. 3. Let D(z) = 1 and sampling period T = 0.05s. Solve the following questions 1.1 1.5 by hand and 1.6 with Simulink. (3) 164, where GR (s) is the transfer function of the rover with
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Fundamentals Of Momentum Heat And Mass Transfer
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6th Edition
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