Home » How does one prevent homing missiles from orbiting their targets?

How does one prevent homing missiles from orbiting their targets?


First of all, you should make all calculations about what acceleration to apply in the missile’s frame of reference (that’s where the missile is stationary and everything else moves around it, also often called “object coordinates” or “local coordinates” in game engines, though in our case we want the velocity to be exactly zero as well).

The idea then is not to aim for the target, but to aim for the place where the target will be at the estimated time of impact. So the general algorithm looks like this:

  1. Estimate how much time it will take for the missile to reach the target. If the target is flying directly at it (remember, the missile is stationary), it can be as simple as calculating distance / speed, in other cases it can be more complicated. If the target can try and evade you won’t be able to make a perfect estimate anyway, so it’s ok to not be very precise.

  2. Assuming constant speed (1st degree estimate) or constant acceleration (2nd degree estimate) of the target, calculate where it will be at the estimated time above.

  3. Calculate acceleration which will lead to the missile to be at roughly the same spot at the same time.

  4. Re-project the acceleration back from the missile’s frame of reference to the global one, use that.

The important part here is to get the time estimate in the rough ballpark, and to not forget the missile’s acceleration capabilities while doing so. For example, a better estimate for “the target is straight ahead of us and flying in our direction” would be to solve the equation ..

distance = speed x time + 1/2 x acceleration x time2

… for time (use negative speed for objects flying straight away from the missile), with the solution you’re looking for using the standard quadratic formula being …

time = (√(speed2 + 2 x acceleration x distance) – speed) / acceleration

Adding additional parameters – drag, for example – quickly turns this into differential equations with no algebraic solutions. This is why rocket science is so hard.

@Martin Sojka already told you what to do. Instead of improving his response I want to propose you another simpler aproach: DELOCK

As I said in Projected trajectory of a vehicle?, objects with limited steering capabilities do “project” a couple of shadow cirles: two regions that can not be reached via direct steering (a torus and an hypertorus in higher dimensions).

When you see that you target is entering in one of such steering shadows, you can stop homing your target and keep another direction for a limited amount of time.

The delocking trigger can be computed easily by aproximating your tori with a (double) cone*:

Delock trigger

You have to simply compute the scalar product between your (normalized) direction vector and your target displacement vector ( TargetObject /|TargetObject| ).

As the scalar product goes to zero, your target direction becomes perpendicular to your direction leading to a circular trajectory**. When the target falls into the cyan region you can invert your steering direction so you can put it outside the unreachable area and re-homing.

* To be honest this is not a cone… is another kind of ruled surface generated by (semi) revolution of two non parallel lines around an axis passing through the intersection and perpendicular to the bisector line; The projection on a 2D plane is the same as the double cone, but the rotation axis is perpendicular to the one that generates the cone.

** That trajectory is unlikely to be circular nor elliptic or even closed. The chances are that the trajectory will follow a spirograph like path (an hypotrochoid) in 2D or even other monsters in 3 and up dimensions. You can not reach the center of such curves anyway and they look like circles so “circular” trajectory.

Your guidance system is built on the assumption that accelerating directly towards the target will eventually cause the objects to collide. Since that assumption is false, the guidance AI based on that assumption is likewise unsuccessful.

So stop accelerating directly towards the target. Add some logic to detect if the target’s position is somewhat perpendicular to the direction of the missile’s motion. If so, then the missile needs to accelerate towards the target, but also slow down its forward motion. So rather than going directly towards the target, it biases the direction of its acceleration so that the current speed in its direction of motion is slowed down.

Also, you’ll need a trigger to make sure that you’re not going too slow. So add some threshold speed such that, if you’re below that threshold, you stop doing the biasing.

One last thing: no guidance system will be perfect. The reason missiles can intercept targets in real life is that targets move much slower than the missiles themselves, and the targets are not particularly nimble (relatively speaking). If your missiles are not going to be many times faster than the targets they chase, then they will miss a lot.

Related Solutions

How to download package not install it with apt-get command?

Use --download-only: sudo apt-get install --download-only pppoe This will download pppoe and any dependencies you need, and place them in /var/cache/apt/archives. That way a subsequent apt-get install pppoe will be able to complete without any extra downloads....

What defines the maximum size for a command single argument?

Answers Definitely not a bug. The parameter which defines the maximum size for one argument is MAX_ARG_STRLEN. There is no documentation for this parameter other than the comments in binfmts.h: /* * These are the maximum length and maximum number of strings...

Bulk rename, change prefix

I'd say the simplest it to just use the rename command which is common on many Linux distributions. There are two common versions of this command so check its man page to find which one you have: ## rename from Perl (common in Debian systems -- Ubuntu, Mint,...

Output from ls has newlines but displays on a single line. Why?

When you pipe the output, ls acts differently. This fact is hidden away in the info documentation: If standard output is a terminal, the output is in columns (sorted vertically) and control characters are output as question marks; otherwise, the output is...

mv: Move file only if destination does not exist

mv -vn file1 file2. This command will do what you want. You can skip -v if you want. -v makes it verbose - mv will tell you that it moved file if it moves it(useful, since there is possibility that file will not be moved) -n moves only if file2 does not exist....

Is it possible to store and query JSON in SQLite?

SQLite 3.9 introduced a new extension (JSON1) that allows you to easily work with JSON data . Also, it introduced support for indexes on expressions, which (in my understanding) should allow you to define indexes on your JSON data as well. PostgreSQL has some...

Combining tail && journalctl

You could use: journalctl -u service-name -f -f, --follow Show only the most recent journal entries, and continuously print new entries as they are appended to the journal. Here I've added "service-name" to distinguish this answer from others; you substitute...

how can shellshock be exploited over SSH?

One example where this can be exploited is on servers with an authorized_keys forced command. When adding an entry to ~/.ssh/authorized_keys, you can prefix the line with command="foo" to force foo to be run any time that ssh public key is used. With this...

Why doesn’t the tilde (~) expand inside double quotes?

The reason, because inside double quotes, tilde ~ has no special meaning, it's treated as literal. POSIX defines Double-Quotes as: Enclosing characters in double-quotes ( "" ) shall preserve the literal value of all characters within the double-quotes, with the...

What is GNU Info for?

GNU Info was designed to offer documentation that was comprehensive, hyperlinked, and possible to output to multiple formats. Man pages were available, and they were great at providing printed output. However, they were designed such that each man page had a...

Set systemd service to execute after fstab mount

a CIFS network location is mounted via /etc/fstab to /mnt/ on boot-up. No, it is not. Get this right, and the rest falls into place naturally. The mount is handled by a (generated) systemd mount unit that will be named something like mnt-wibble.mount. You can...

Merge two video clips into one, placing them next to each other

To be honest, using the accepted answer resulted in a lot of dropped frames for me. However, using the hstack filter_complex produced perfectly fluid output: ffmpeg -i left.mp4 -i right.mp4 -filter_complex hstack output.mp4 ffmpeg -i input1.mp4 -i input2.mp4...

How portable are /dev/stdin, /dev/stdout and /dev/stderr?

It's been available on Linux back into its prehistory. It is not POSIX, although many actual shells (including AT&T ksh and bash) will simulate it if it's not present in the OS; note that this simulation only works at the shell level (i.e. redirection or...

How can I increase the number of inodes in an ext4 filesystem?

It seems that you have a lot more files than normal expectation. I don't know whether there is a solution to change the inode table size dynamically. I'm afraid that you need to back-up your data, and create new filesystem, and restore your data. To create new...

Why doesn’t cp have a progress bar like wget?

The tradition in unix tools is to display messages only if something goes wrong. I think this is both for design and practical reasons. The design is intended to make it obvious when something goes wrong: you get an error message, and it's not drowned in...

OpenSSH: How to end a match block

To end up a match block with openssh 6.5p1 or above, use the line: Match all Here is a piece of code, taken from my /etc/ssh/sshd_config file: # Change to no to disable tunnelled clear text passwords PasswordAuthentication no Match host

Redirecting the content of a file to the command “echo”

You can redirect all you want to echo but it won't do anything with it. echo doesn't read its standard input. All it does is write to standard output its arguments separated by a space character and terminated by a newline character (and with some echo...