Gyro
Is pretty stable. (see the android sensor app)
I'm confident it can maintain angle error of < 5 deg over 30 second integration.
It can reach < 1deg, even.
This is enough for RH/RR navigation.
This form one of #proprioception
About 500 JPY. FWIW, (IR emitter + sensor) * 2 is 200 JPY.
3-axis gyro is obviously better choice than bunch of LEDs and incomplete measurement (esp. messy layouting of PCBs).