The QuestionMy research concerns the question of how to get from A to B, when B is moving, you don't know how far away it is, nor do you know how fast it's going. I hope to find this out by studying the hunting habits of predatory insects that must intercept targets with limited information about them. Insects work on a timescale and energy budget that simply cannot be matched by modern engineering and so I hope to help inform the design of engineered systems of the future, that might require less energy to effectively do their job.

Pursuit
Pursuit is the most basic way in which to reach a target. You simply head to where you perceive your target to be. It's really that simple, provided you've made it over the evolutionary hurdles of developing a sensory system capable to telling you where you're going and a motile system to get you there. Going in a straight line is (all other things being equal) the fastest way of getting to a position in space. Complications can certainly arise in the form of obstacles, regions that are more difficult to cross etc. but if you can visually see your goal on the other side of a field, you'll most likely take a straight line to it.
This becomes an inefficient method of guidance when your target is moving relative to you. By the time you've taken a step forward, so has your target and the position you're aiming for will have changed. Continue in this vein and you'll always be chasing where your target used to be. If you're travelling faster than your target, you will eventually hit it, but you'll have used a lot more energy than you really needed to. To take a more optimum course, you need is to correct your steering towards a future meeting point; you need to intercept your target.
Interception
Interception (heading to where your target is going to be in the future) is not an easy task. Calculating the future meeting position requires extensive computation and exact knowledge of the distance, speed, and heading of your target. The simplest possible means to intercept a target would be to head a fixed angle ahead of where you currently perceive the target to be. This will not take you on an optimal (shortest) path to your target, but it will likely take you on a shorter path than pure pursuit. Aiming a fixed angle ahead of your target is called deviated pursuit, and it requires little modification from a pure pursuit system and very limited computation.
If you had perfect information about your target, its movement, and your own, you could potentially calculate the straightline route toward a future meeting point. This would need to be updated should your target change its course, or either of you change your speed. The planar (2D) representation of how to do this is represented below:
The problem with this methodology and the reason it's rarely implemented is the extent of knowledge and computational requirements used to calculate the interception course. This calculation will take time, inducing a greater lag between stimulus and response. The stimulus here is a change in the speed or heading of your target, or an updating of your knowledge about that target. If your target is attempting to dodge and evade you, you want the shortest possible time delay for reaction.
Fundamentally the greatest barrier to absolute calculation implementation in predatory animals is the difficulty in obtaining absolute information about the target. While conspecifics (animals of the same species) may be able to make assumptions about the size and therefore distance of each other whilst intercepting, generalist predators such as our predatory insects are not able to assume such information accurately. Instead what is needed is a way to approximate and interception course; simply and quickly determining how much lead to give a target without knowing much about it.
Fundamentally the greatest barrier to absolute calculation implementation in predatory animals is the difficulty in obtaining absolute information about the target. While conspecifics (animals of the same species) may be able to make assumptions about the size and therefore distance of each other whilst intercepting, generalist predators such as our predatory insects are not able to assume such information accurately. Instead what is needed is a way to approximate and interception course; simply and quickly determining how much lead to give a target without knowing much about it.
Proportional Navigation
The task of a homing missile is analogous to that of an animal predator, and so it follows that the designers of missiles may have hit upon ideas that would assist us in understanding aerial predation. Proportional navigation (pronav) is a guidance law developed postWWII in order to aid the guidance of military missiles toward moving targets. Pronav remains the defining basis for the majority of modern missiles, and now my and separately the Taylor lab's research has begun to show may be a useful means of understanding how animals navigate to moving targets.
Proportional navigation is a very simple concept at route. Fundamentally it revolves around measuring a single rotation; the rotation of the lineofsight (sometimes called the range vector) that connects the target to the predator. This rotation is measured relative to the external world, and then magnified and applied to the velocity vector.
Proportional navigation is a very simple concept at route. Fundamentally it revolves around measuring a single rotation; the rotation of the lineofsight (sometimes called the range vector) that connects the target to the predator. This rotation is measured relative to the external world, and then magnified and applied to the velocity vector.