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MIT2_017JF09_p35 - 35 LANDING VEHICLE CONTROL 35 129...

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35 LANDING VEHICLE CONTROL 129 35 Landing Vehicle Control A controlled vehicle that is landing onto a target in the horizontal plane is equipped with a vision-based navigation system. The system gives very good resolution at low altitudes, but, unfortunately, poor resolution at high altitudes. This effect is modeled as σ ν 2 = 0 . 05 z 2 , where z is the altitude and σ ν 2 is the variance of the noise ν in the measurement y = x + ν ; x is the true horizontal position of the craft. The sensor noise ν is considered to be of zero mean, and to have Gaussian distribution, at any particular altitude. There are no other effects, say due to roll, pitch, or yaw, in this sensor. We consider the horizontal positioning problem in one direction only, e.g., North-South. The vehicle gets a measurement y once per second, and descends at a steady rate of 2 m/s . A controller applies a corrective thrust force according to T = k × sign ( y ), and the vehicle physically responds to thrust with a velocity change: x ¨ = T . The vehicle physical behavior is also affected by a horizontal drift disturbance (due to current or winds). This is steady in time and constant over all altitudes, but its magnitude on any
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