Using current kerberos credentials, how to allow user to run a script / command on multiple servers without being prompted for password?

Issue

• Using current kerberos credentials, how to allow user to run a script / command on multiple servers without being prompted for password?

• For example,
  Trusted user is logged into Server A using valid kerberos credentials. That user also has access to perform a task on Servers B, C, D and E.
  From server A, he wants to be able to run a script that restarts the service on all 4 servers.
  This should be accomplished by running "ssh@serverb service restart" from Server A without password prompt.