Webcam and Arduino don't sit well in the same sentence.
I was thinking along the lines of the possibility of Raspberry Pi running the object avoidance and communicating commands with the arduino.
If you're looking for a simple technique I'd suggest a line-generating laser mounted above your camera and pointed at the floor about a meter ahead of the robot. Any obstacles will show up with a red line on them, and it's relatively straightforward picking out that red line from the image.
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via Egeo 16