Central locking on my 2002 camry won't lock and make three beep sound?

SOURCE: Camry central door locking not working after alarm going off.

there is a sensor on the door lock in the door if it goes bad or falls off it will do that take the door panel off window up and look at the back side of the lock a small snap ring holds it on some even come unplugged

SOURCE: Alarm and central door locking.

Replace the alarm control box, it is usually under the driver seat, or in the extreme left corner of the dash. If the box under the driver seat got wet for any reason, expect bizaare things to happen; in any case, replace the box.

SOURCE: how to fix the remote

Your question is pretty vague, but maybe the following will help you...

if you have a new remote or wish to add a remote, you can open the glovebox and you will find a slot at the top right hand side, slide your working remote in, you will see the security light on the dash glow red continuously. Take out the working and put in the non working within 5 seconds. The red light will go out and your new or replacement remote should now be programmed to your car.

SOURCE: my car has started locking itself

look in manual or notify dealer about lock setting should be able to undo auto lock setting with key fob

SOURCE: How can I program the door locks on my 2002 Camry

Put the key in the ignition, turn to the on position. Open the driver's door and remove the key (keep door open). Put the key in and out 4 times (in/ out only without any turning of the key) with the key out at the end. Hit drivers side unlock button 5 times. Wait at least ten seconds and shut the driver's door. Away you go. It will stay like this unless you remove the cars battery - if so you will have to do that sequence again. Works for most if not all toyotas