I'm sure there are other ways to do this but since it is on your network, you could ping a range of ip addresses and arp the same range. Then match up the mac to ip.
You may also have success using nmap on the range of ip addresses....
nmap -sP 192.168.1/24
For example: I setup a loop to ping 10 addresses on a range of 192.168.1/24
Code:
#!/bin/bash
for ((i=1; i<=10; i++));do
ping -c 1 192.168.1.$i 2>&1 >/dev/null
arp -a 192.168.1.$i
done