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# ps5_hints - Let's consider the Fixed Arrival Time problem...

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Let's consider the Fixed Arrival Time problem. We want to find a minimum fuel solution that takes our craft from to starting (x, y) position to the target (x, y) position so that it arrives at (exactly) time T and we want to get there in N time steps each of time t. T/N= t. There is no notion of negative fuel so we can instead think in terms of thrust in four dimensions ForwardThurstX (ft x ), BackwardThrustX(bt x ), ForwardThrustY(ft y ) and BackwardThrustY(bt y ). This is by no means the only way of representing this information—it is just an example designed to be easy to understand. Therefore our objective function is to minimize J T as follows: = 1 0 min min N i i T U U U Cost i i We will assume that thrust in each direction burns the same amount of fuel so: Cost T = ( ) 1 1 1 1 Where U i = i i i i bty fty btx ftx We are solving to get a sequence of N states S 0 … S N-1 resulting from a sequence of N control inputs U 0 … U N-1 .

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