roboteq ax3500 dc motor controller
That's a fine controller to put power into a DC motor. It can also read quadrature encoders to figure out how fast the motor is turning. However, without other "homing" sensors, it's not possible to get the absolute position control out of that controller that you will typically need for a robotic arm.
Separately, 20 kilo lifting force times your arm length (looks like two half-meter segments?) plus lifting the arm itself (say, 5 kg) means 25 kg times 100 cm == 2500 kgcm torque, or 250 Nm. That's... a lot. You will want a motor with a gearbox, rather than a direct-drive motor, for this amount of torque.
Typically, at these power ranges, you will select the gearbox separate from the motor, and then integrate them yourself. Additionally, you will want to select a quadrature encoder, and some way of "homing" the main axles, to get the appropriate closed-loop absolute control.
Suppliers of industrial motors include Maxon and Kollmorgen and Dynetic and NMB. I'm sure you'll find something there if you go looking for an appropriate gearbox plus motor plus encoder combination.
Also note that the AX3500 is "not recommended for new designs."
