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See Sec C9 for more information To examine how this problem affects the algorithm in Sec 152, a variable at the top of Fig 151 called SlipValue has been set We also have the statement rSlip SlipValue in the PlaceRobot subroutine in Fig 155 Notice that SlipValue is set to 0 Try changing this value to 5, 10, 20, 50, and 70 to see how it affects the robot The algorithm in Sec 152 assumed an ideal robot that moves as commanded When we simulate a real robot though, the algorithm fails Can the algorithm be modi ed to resolve this issue In order to resolve the problem we need to understand why the algorithm fails Of course it failed because the robot did not move as expected, but this is not the direct reason for failure.

the burst time plan tells station A that a burst intended for it follows at time TA after the SORF marker received by it. Likewise, for station B, the propagation delay is tB, and the received bursts start at TB after the SORF markers received at station B. The propagation delays for each station will differ, but typically they are in the region of 120 ms each. The burst time plan also shows a station when it must transmit its bursts in order to reach the satellite in the correct time slots. A major advantage of the TDMA mode of operation is that the burst time plan is essentially under software control so that changes in traffic patterns can be accommodated much more readily than is the case with FDMA, where modifications to hardware are required. Against this, implementation of the synchronization is a complicated process. Corrections must be included for changes in propagation delay which result from the slowly varying position of the satellite (see Sec. 7.4). In general, the procedure for transmit timing control has two stages. First, there is the need for a station just entering, or reentering after a long delay, to acquire its correct slot position, this being referred to as burst position acquisition. Once the time slot has been acquired, the traffic station must maintain the correct position, this being known as burst position synchronization.

Let us extend the result of the above example from y = x 3 to an arbitrary differentiable function y = f (x). Consider a small change x in the value of the argument x. The new value of the argument is then x + x, and the new value of y will be f (x + x). Hence, the change y in the value of the function is y = f (x + x) f (x)

If you do a search on the code of the entire program you will nd that the commands rTurn and rForward are used in only two subroutines: GotoPoint and DockWithCharger The direct reason the algorithm fails is due to the fact that the robot does not arrive at the expected intermediate node The GotoPoint subroutine calculates the heading to turn then turns the robot to that heading It does not check that the robot actually turned to exactly that heading Also the algorithm calculates the distance to the point and forwards the robot that amount It again does not check that the robot actually moved that distance without turning or slipping The indirect reason for the failure is motor/wheel slip, but the direct reason is that the algorithm does not verify that the robot actually arrived at the desired coordinates.

For near-earth satellites, below about 1000 km, the effects of atmospheric drag are significant. Because the drag is greatest at the perigee, the drag acts to reduce the velocity at this point, with the result that the satellite does not reach the same apogee height on successive revolutions. The result is that the semimajor axis and the eccentricity are both reduced. Drag does not noticeably change the other orbital parameters, including perigee height. In the program used for generating the orbital elements given in the NASA bulletins, a pseudo-drag term is generated, which is equal to one-half the rate of change of mean motion (ADC USAF, 1980). An approximate expression for the change of major axis is a > a0 c n0 n0 nr0(t t0) d

(2.16)

So all we need to do is modify the algorithm of GotoPoint to ensure that the robot actually arrives at the desired point..

The ratio of the change in the function value to the change in the argument is y f (x + = x x) f (x) x

where the 0 subscripts denote values at the reference time t0, and n 0 is the first derivative of the mean motion. The mean anomaly is also changed, an approximate value for the change being: M nr0 2 (t t0)2 (2.17)