A first step towards truly versatile robot assistants consists of building up experience with simple tasks such as the cooperative manipulation of objects. This paper extends the state-of-the-art by developing an assistant which actively cooperates during the point-to-point transportation of an object. Besides using admittance control to react to interaction forces generated by its operator, the robot estimates the intended human motion and uses this identified motion to move along with the operator. The offered level of assistance can be scaled, which is vital to give the operator the opportunity to gradually learn how to interact with the system. Experiments revealed that, while the robot is programmed to adapt to the human motion, the operator also adapts to the offered assistance. When using the robot assistant the required forces to move the load are greatly reduced and the operators report that the assistance feels comfortable and natural.