This project would be massively easier if you were able to use servo motors instead of controlling the DC motor positions yourself. You will need to use H-bridge driver circuits, and I suggest you look for external boards, rather than shields, to avoid pin conflicts. Some motor drivers also include current sensing capability which would remove the need for you to measure that directly, but of course you still need connections to the driver to receive that data so that doesn't change your solution substantially, but just reduces the external component count. Note that on slow moving or stationary motors current is not easily related to torque so you might want to consider using some form of force/pressure sensor instead.
On the software side you will presumably also need to provide some sort of closed loop control algorithm for each degree of freedom. PID may be overkill for that but would certainly do the job, and there's a PID library for the Arduino.