From The TimeSplitters Wiki

Homing Launcher
Ammo	1/
Fire Rate bullets per sec/cartridge time	single/triple
Reload Time	2-3 seconds
Damage (per Single Shot) Head/Body/Leg	100% (if it hits target)
Type	Rocket
Zoom	None
Primary Fire	A homing rocket
Secondary Fire	3 homing rockets (if sufficient ammo)
Games	TS2

The Homing Launcher is a weapon featured in TS2. It is like a homing version of the Rocket Launcher. For that reason it is often considered more valuable than the normal rocket launcher.

Appearence

The Homing Launcher, like the rocket launcher, has a very bulky appearence. It looks more dangerous, however, due to the cautioning yellow-black strips on it. The whole thing is mostly a grayish metal, but the handle and parts of the launching tubes themselves are red. Unlike the rocket launcher, the homing launcher actually features 3 seperate tubes for the secondary fire of 3 rockets.
Additionally, there is a difference between the rockets themselves. While a normal launcher shoots largish rockets with smoke coming out, the homing rockets are light blue with a slick, almost plasma-like trail behind them. Some speculate that homing rockets are indeed plasma, and that's why they are in the plasma weapon set.

Dodging Homing Rockets

It is very hard to dodge homing rockets, as obviously, they are homing. The best suggestion is if you are by a turn in a corridor, turn sharply and the rocket will most likely hit the wall. If you are in an open space, try running to the sides, although you are most likely dead.