Install arp-scan (sudo apt-get install arp-scan) and add the following line to the script:

IPs=$(sudo arp-scan --localnet --numeric --quiet --ignoredups | grep -E '([a-f0-9]{2}:){5}[a-f0-9]{2}' | awk '{print $1}')

Now you have all the active IP addresses in the IPs variable.

Note: this will only work on a directly connected network, i.e. not accessed through a router.

PS: If you install gawk the command can be shortened to (thanks belacqua):

IPs=$(sudo arp-scan --localnet --quiet --ignoredups | gawk '/([a-f0-9]{2}:){5}[a-f0-9]{2}/ {print $1}')