Is there a change in the voltage/current when motor is locked up? How can one sense this?
You should be able to measure the current during normal load operation (from experimentation) and then measure the current during an overload (stall) condition, and then use a shunt resistor (like, a 1% 0.1 ohm resistor) and an op-amp based comparator circuit to indicate when it has reached it's end-point/cannot move any further. 

Measure the resistance across the motor terminals (this is assuming a simple 2 terminal DC brushed motor) with an ohm-meter. Then you can estimate the stall current by Ohms law, V = IR, meaning I_stall = V_applied / R_motor. 

As the motor begins to move and starts generating back EMF, it will reduce the input current to something more reasonable. 

When the motor meets something which stops the output shaft from moving, the resistance reduces again back to the motor's armature resistance (R_motor i mentioned earlier).