"Voltage-current dynamics" means the response of the motor current to applied voltage (ignoring, it appears, the back-emf generated by the motor -- presumably the controller is fast enough that it can ignore that).
It looks like the author meant "current position dynamics" to mean the response of the vehicle position to motor current. Even if that's not the author's intent, it's as good a way to view it as anything.
Basically, there's a fast inner loop controlling the motor current (and, hence, torque), and a slower outer loop controlling the body dynamics. As long as that inner loop is fast enough, the outer loop will be mostly sensitive to the vehicle's characteristics, rather than the characteristics of the inner loop, making the whole control system more robust.