Output Voltage difference

You could test with a resistor I suppose, ideally you would need a low value resistor such as a 2Ω.
If you do this be warned, it would have to be a resistor with a large power tolerance:
P = V² ÷ I = (8.3 × 8.3) ÷ 2 = 34.4W
Most people do not have those type of resistors lying around (you tend to find them in audio devices).
They look very bulky, like these ones.

You could use a higher resistance, but the effect will be less motor like.
The normal through-hole style resistors like these can be as low as 0.25W, so something like 330Ω or more should be okay:
P = V² ÷ I = (8.3 × 8.3) ÷ 330 = 0.21W

Be warned, the resistors are likely to get hot when you are running it, be careful not to touch them or place them on anything easily combustible.

Here are the results I get using two of the small motors we sell with a power supply.
Supply = 7.0v

• PBR.SetMotors(0.5):
  V+ = 6.9v
  M1 = 2.8v
  M2 = 2.6v
• PBR.SetMotors(-0.5):
  V+ = 6.9v
  M1 = -2.8v
  M2 = -2.7v
• PBR.SetMotors(1):
  V+ = 6.5v
  M1 = 5.7v
  M2 = 6.0v
• PBR.SetMotors(-1):
  V+ = 6.8v
  M1 = -6.2v
  M2 = -6.2v
• PBR.SetMotors(0):
  V+ = 7.0v
  M1 = 0v
  M2 = 0v
  

The trouble is that these motors are only rated for 3v, so I am over-running them beyond 50%.

At 50% output forward and reverse are basically the same.
At 100% the motors actually run properly in reverse, but they get hot.
At 100% the motors run slightly lower, but now they start screeching after running for a while.

The screeching sound is the PicoBorg Reverse protecting itself from an over-current situation by turning off for short bursts.
As chance would have it at a 7v supply with these particular motors it gets upset in one direction, but not the other.

If I turn the power up any further it is too much for both motors in either direction.
It just so happens in this case that one direction has a slightly lower tolerance to over-current then the other.

What I am wondering is do you hear any unusual buzzing, tapping, or screeching from either the motors or the board?
You may only hear it after running them constantly for a minute or two (it tends to get louder as things warm up).
If you do it is probably suggesting they cannot cope with the full 8.3v supply power.

The non-linearity is not surprising, motors are not perfectly linear with regards to voltage.
In particular there is a threshold level below which the motor will not rotate, this was about 0.1 with the setup I used last time.
The amount of load on the motor will also affect the speed, this can be increased by:

• Moving up slopes
• Carrying more weight
• Motors or gears getting worn out
• Changes in temperature

The PicoBorg Reverse also has what is known as dead-time in the PWM.
This dead-time is a very brief period of time where the output is not connected to V+ or GND, what is typically known as tri-stated.
This also causes some non-linearity as the motor can behave like a generator during this time and affect the voltage it is seeing.

Also any wheel spin or track slip can cause a higher RPM reading even though the robot will likely be moving slower.

Since you can read the RPM you could try and write some code to maintain a steady RPM by increasing or decreasing the power level on the fly if you wanted.
Are the encoders connected to the Raspberry Pi already?

Glad to hear this is helping you out ^_^

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