Maximizing Contact Area for Force Sensor

I am a student participating in a collegiate design class. We have been tasked with building a robot that will combat an opposing robot. Each robot is approximately 15 pounds and the playing area is limited to roughly 100 ft2. The concept for the robot calls for a method to sense physical engagement with the opponent. We want to use multiple sensors so that the robot will know what location on the robot the contact occurred (front, side, back).

We want to maximize the area for which the sensor can read contact as the location of contact is unknown. The sensor will need to send an analog signal to an Arduino Uno microcontroller. The power supply can be adapted to the needs of the sensor. The total amount budgeted is ~$45.

We do not care about the intensity of the contact, only the general location. A possible solution is to use a keyboard membrane. The problem with this is the output is a USB or PS/2. Is it possible to cut into the USB cord and attach the output signal to the analog connection on the Arduino?