Crap.
I took apart the robot to put some Velcro on the big battery today, and I had to disassemble the electronics to get inside. When I reassembled it, I accidentally reassembled the wiring incorrectly, without noticing it, and I short-circuited the 5 V line to GND when I connected the ultrasonic range sensor. A minute or so after I turned on the power, I smelled something like melting plastic.
I have some spare parts to test, but I'll likely have to order at least a new Arduino Uno.
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Update: Based on my test with a spare Arduino Uno R2 board, it's just the Arduino Uno R3 board that burned out. The Arduino Motor Shield R3 board seems fine, the Wireless SD shield wasn't really being used, the ultrasonic range sensor seems more-or-less fine, and the Raspberry Pi seems fine. A test of the robot with the Arduino Uno R2 in place seems to indicate the function is normal, though I don't recall if the Arduino application had never said usbmodem as the serial port on the Raspberry Pi. Regardless, it seems to upload properly to the Arduino.
The burned-out Arduino Uno R3 smells kind of funny, like melted epoxy. I ordered a couple more from Amazon; they're about $8 cheaper than at Radio Shack.
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On a different note, I went to a local hobby store after work today and picked up a set of soft racing tires to replace the hard tires on the robot. These fit the wheels, and they should provide better traction.
When I mentioned that I was using them for a robot, the guy who helped me find the tires asked me to bring the robot in to show him. Unfortunately, he'll have to wait for me to rebuild it, now that the Arduino Uno has burned out.