Adam Hibberd
In my last post I explained how my software development, Optimum Interplanetary Trajectory Software (OITS), seems to achieve miracles of intelligent design in a fashion analogous to evolution, though in fact with both cases evidently no intelligence is involved - instead simple mechanisms combined with iteration are at work.
This concept stimulated me to examine an alternative approach to trajectory optimization, namely Evolutionary Neurocontrol, a paradigm used extensively by an acquaintance of mine, Bernd Dachwald, and with a good deal of success. He exploited the technique at the turn of this century to solve optimal solar sail trajectories, for example to escape the Solar System in minimum time.
But you may ask what is Evolutionary Neurocontrol?
Let us say that you wish to find your way to the nearest pub in minimum time. Humans, or more accurately human minds have different capabilities in this regard. Some minds will reach the destination rather quickly and some will take their time. In fact some will be utterly hopeless and have no chance whatsoever. Let us discard the LESS successful ones, and keep the MORE successful ones (so competition), add a bit of genetic mutation (and so variation) into the mix and iterate onwards from generation to generation (inheritance) until we arrive at the optimal solution: the perfect pub-finding mind.
This is all very fine in concept but how do we apply this to a software tool?
One solution is to model our mind by using a straight forward ANN (Artificial Neural Network) and the evolutionary process can be simulated by what is known as a Genetic Algorithm (GA), there being many alternative software libraries for both of these available in open source.
I wanted to apply the technique to laser sail trajectories, where both the laser and the sail are orbiting the Earth. Furthermore the target (or objective) is to achieve a certain hyperbolic excess velocity V∞ as quickly as possible. I assume that the acceleration generated by the laser beam on the sail is low and is constant, for example 0.1 gee (where 1 gee = 9.8 m/s/s).
The parameters for the GA to optimize are the set of weights and biases for the ANN. In addition, to make the ANN work we need some kind of inputs to help the ANN achieve its ulimate goal. These are simply the current state parameters of position and velocity of the sail - or rather their difference w.r.t the target state. Output generated by the ANN after each simulation time step is the attitude of the laser sail, which governs the direction of thrust induced by the laser beam as it reflects off the sail's surface.
Initial results are promising and refer to the Figure below which shows the optimal laser sail trajectory, the blue line, and the laser orbiting the Earth along the red line. It supposes that both laser AND sail start off in the SAME Geosynchronous Orbit (GSO), with their initial locations in this orbit optimized by the GA and that the inclination of this orbit is ALSO optimized.
I end this little report with the motto of the Initiative for Interstellar Studies (i4is): "Scientia ad Sidera" ,and wish you all achieve your optimal trajectory in life, or as close to it as is feasibly possible.