1. Simple Arduino board with LED lights that turn on/off through a timed sequence
That's pretty simple. Plug into pin 13 and ground
http://arduino.cc/en/Tutorial/Blink2. Use lights or possibly a stepper motor position (as a form of analog dial) to reflect the output of
sensors: thermistors, proximity, circuit voltage, etc.
http://arduino.cc/en/Tutorial/AnalogReadSerial(redirect to your out pin rather than serial, same concept)
3. Synchronize the rotational speed of two or more rotors
Same rotors? Same output = same speed. Or is there another concern?
4. Perform range estimation and triangulation with one transmitter (remote) and three receivers (on the Arduino)
Hrm. Fixed sensor bracket, I assume? As you need to know the distance between the receivers to triangulate. Then it's just signal strength and direction, then do the math. Simple RDF? Or are you doing sound, light, motion, etc?
5. Robot 1 - Wheeled or possibly tracked. Senses and climbs curbs or other obstacles. Follows me on a walk around the neighborhood (by me carrying the transmitter and it tracking via receiver)
Build normal robot. Put an IR blinker on your belt spelling out a specific pattern. Have robot track to pattern. Curb = impact sensors.
6. Robot 2 - Helicopter. Hover 3 feet off the ground (via downwards facing proximity sensor), balance (via gyro and accelerometer sensors), and perform a controlled landing autonomously
Buy autopilot hardware. Srly. Same yourself some sanity. They make them already for hobbyists.
7. Robot 2 - Hover 3 feet off the ground, follow a radio beacon(held by me as I walk around), monitor battery life and land autonomously when low on power
Buy autopilot hardware and figure out the control code.
8. Robot 2 - small solar panel recharger installed. Digital altimeter circuit and GPS circuits installed. Attain 100ft AGL, follow a programmed set of GPS coordinates, return home and recharge autonomously, then follow that route again and return home
Voltaic Systems for your solar panels. Digital altimeter and GPS = Sparkfun.
9. Robot 2 - Altitude test. See how high it can go before it reaches a "point of no return" and have it return home safely with a log for maximum altitude on a full battery charge. Wind may make this one tricky, and it may be a series of attempts, pushing my luck and tolerance for lost helicopter(s)
... Good luck. Incorporate automated recovery system (ie, parachute)
10. Robot 2 - Pre-program a series of safe landing spots (roofs of grocery stores and such, probably) as GPS coordinates. Send the helicopter on a multi-day expedition where it repeatedly lands and recharges itself. Have it land, on float pontoons, in my parents' swimming pool in their backyard, 8 miles away
... Good luck, if you accomplish this, give me a call. I'll have you an engineering slot at Sikorsky Innovations in under a week.