I hope I am understanding correctly in that you already have a recording of the robot with the jetpack landing, but that it does not sound realistic perceptually. If this is the case, the quickest and easiest solution would be to use a convolution reverb with the appropriate HRTF impulse. There are several factors that affect sound perception, such as time, intensity, pitch, etc that you can use to your advantage to tweak the results until you are happy although, considering your budgetary constraints, you need to decide how much time you are willing to spend. You could also try some of the following techniques, but bear in mind that the time vs results ratio is not proportional:
1) The robot is obviously moving down and most likely, I am guessing, toward you? This will affect the characteristics of the sound in relation to time. A gradual increase in pitch will provide the effect of motion toward you (Doppler). Also, higher frequencies will gradually become more evident as it gets closer to you.
2) Amplitude will also gradually increase as the robot is approaching you.
3) The recording should correctly represent the space in terms of reflections from surrounding buildings and objects. Your words "in the distance" give the impression that it is a large open space. Careful application of reverb can assist you to recreate a fair representation of this space. This can be very time consuming and it is doubtful you will improve on the convolution reverb.
4) Ideally you do not want the same sound coming from the left and right channels, as this is the information that your brain uses to create a stereo spectrum and automatically place the origin of that sound in front of you. Obviously, it will not work to use only one channel, as your brain will place the origin of the sound to that side and it will still not be behind you. It will not help to use a stereo file, as there will almost always be elements that are present in both channels. This then gives your brain sufficient information to create a stereo spectrum, which it will automatically place in front of you.
One way to fool your brain is to increase the pitch of one channel by 1-2 semitones and decrease the other by exactly the same, although I find this technique is more effective with a musical source.
Another simple trick is to use a twin mono recording, but invert the phase of one channel. The phase cancellation should prevent your brain from creating a stereo spectrum and fool it into perceiving that the sound is coming from behind you.
Personally, all things considered, I would probably take the approach of using the convolution reverb and then tweaking it to taste with 1 and 2 above using straightforward pitch, amplitude and EQ envelopes. Hope my "convoluted" reply helps.