A trajectory that is not optimal (the blue line does not match the green line)
An optimal trajectory (the blue line matches the green line).
What do optimal trajectories look like in the State-Space view?
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A trajectory that is not optimal (the blue line does not match the green line) |
An optimal trajectory (the blue line matches the green line). |
Derivation of Optimal Trajectories
The theoretically calculated optimal trajectories (the green lines) show the spacecraft free-falling for as long as possible before switching the thrusters on as late as possible. This optimality with respect to the given reward function is proven in the paper. Note that it may be surprising that this strategy is best, but think of the converse: in the extreme case of braking early and descending slowly throughout the whole flight, much fuel would be wasted in nearly hovering. Also, note that with the given reward function, the objective is not to land at zero velocity, since that would be excessively wasteful of fuel. The objective is simply to maximise the given reward function, which is what the green curves do.