Electronic – Negative voltage on AA battery

you want a voltage divider. if you care about power dissipation, there are a couple of things you can do:

• use a fairly high impedance voltage divider, with a capacitor on the output terminal, and buffer it with a low-power op-amp. Make sure you use an RC filter between op-amp and ADC, values of this RC filter are typically around 50-200 ohms, 1000pf. This serves to keep voltage stable when the ADC is switching between channels and charge is transferred between the ADC's internal capacitor and the outside pin. An op-amp alone cannot do this. If you don't buffer the high-impedance voltage divider, you will get errors due to ADC leakage current and charge transfer.

• switch the voltage divider, e.g. connect/disconnect it to the supply voltage, so you can do this only occasionally when you want. A PFET would work, just be careful with how you drive it.

In place of the LM7805, using a Low Drop Out (LDO) regulator such as MIC29300-5.0WT would allow operation at as little as 5.37 volts, providing 3 amperes at that voltage, enough for your Beagleboards but not the motors.

The more expensive MIC29500-5.0WT at $5.46 apiece on Digikey would provide the 5 amps you might want instead.

• Tapping between batteries is best avoided with unbalanced loads.
• And yes, the batteries loaded higher would deplete earlier, with unpredictable outcomes.
• In stepping down 6 to 7.5 volts to 5 volts at 5 amps using an LDO, up to 12.5 watts of heat would necessarily be dissipated at the regulator: Power dissipated as heat = voltage difference * average current = 2.5 * 5

However, realistically the batteries won't be at 7.5 volts under load, and not for long anyway. Also, the continuous current drawn would not be 5 amperes through the regulator. Your design would ideally provide the motors with unregulated power, so your "step down about 4-5 amps" deserves a revisit. Besides, voltage is stepped down, not current, at least in this context.

Switching (buck) regulators would waste less heat, roughly around 15% that of the LDO, but they usually need more voltage headroom to operate. YMMV, searching DigiKey might yield what you need.

Why is your hub needing to be powered from the same power as your car motors? Your hub should be at your base station, the car would just carry a WiFi dongle of some sort, ideally?

Suggestions:

1. Edit: [15-Oct-2012] Provide regulated power only to the logic parts, drive the motors directly off the battery, and add a hefty decoupling capacitor before the regulator to work around motor inductive spikes. If your batteries can handle 4 motors of 2 amp each, they can handle the initial surge the capacitor will need.
2. Provide a diagram of some sort, of what is being attempted, and some clarity on how the powered hubs got aboard the moving car. This will enable more helpful answers.