You could use prismatic joints for moving platforms along their paths. You just have to create a joint between the ground body and the platform and set the motorEnabled=true, maxMotorSpeed=(speed), motorTorque=(variable based on platform's weight), limitEnabled=true, lowerLimit=0, *breath* and upperLimit=(distance between current point and next point), and give it an axis pointing from its current location toward its next location with a magnitude of 1. And then every frame, you just check the joint's limitState to see if it's AtUpper (or something like that), at which point you destroy that joint and create another for the next point. At least, if you're using the Box2D physics engine. I don't know how any others work.
It's as simple as that!