PDF《Parameterized Maneuver Learning for》

two stall turns of the same altitude may still reach their peaks at different times. To account for this, we use a dynamic programming algorithm known as dynamic time warping (DTW) in the speech-recognition literature [15] and the Needleman-Wunsch algorithm in the biological sequence alignment literature [10]. Dynamic time warping is often used to align multiple sequences to a single reference sequence. The standard DTW algorithm performs poorly when the two sequences vary greatly in magnitude, shape, or duration [8]. For sequences with differences in magnitude, e.g. the top of a stall turn, DTW will change the time scale to match the exact magnitudes of the trajectories for as long as possible, rather than matching the overall shape of the trajectories. Our largest stall turns are up to two or three times larger and longer than our smallest stall turns. Dynamic time warping leads to unnatural alignments with abrupt changes in the time alignment rate (the difference in time from one time step to the next). Because our trajectories correspond to physically feasible ?ights, we expect alignment rate to remain fairly constant Fig. 2. Helicopter position during a stall turn: before (left) and after (right) alignment. between time steps. Hence we modify DTW by adding a penalty2 for changes in the time alignment rate. This algo- rithm prod........