How to generate constant movement given variable opposing resistance?
There are two main approaches to control torque. 

The first is open-loop using a device such as a brushed DC or BLDC motor that has torque (more or less) proportional to current. So you control the current. 

The second is to use a torque sensor (inline with the shaft or indirectly through the motor mount, for example) and adjust the motor drive to attempt to maintain the constant torque. An encoder is of no use for torque- it can only measure angular motion (often only relative motion at that). 

The above answers the question in your title. In the text you ask about torque/movement. As Dave Tweed points out you can only control one of the two at once. It's like a CC/CV power supply. The power supply can only be in one mode at a time- constant current or constant voltage. If you fix the torque then the  force on the motor shaft will determine the motion. If you fix the motion, then to torque must adjust to the force on the motor shaft.