Welcome.
sudo needs to be configured for each specific combination of command + account. So to run
udhcpc from the account 'foobar' append the following to /etc/sudoers using the program
visudo
Code:
%foobar ALL=(root:root) /sbin/udhcpc -i eth0
Or
Code:
%foobar ALL=(root:root) NOPASSWD:/sbin/udhcpc -i eth0
Mind the spacing in either case and be sure to use the correct path for udhcpc.
For background see Michael W Lucas' talk "sudo: You're Doing It Wrong", which has a video and slides available. It is long but thorough.