arduino robot

Is it feasible to control an arduino robot over a WiFi network by sending signals from a computer to a phone on the robot that is connected the arduino through usb cable?

I suppose that it is possible, but it would be easier, I think, to use an ESP8266 WiFi module on the robot to receive the commands over WiFi.

an arduino robot

Just as a matter of interest, do you mean one of these, or just any old robot based on an Arduino?