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The number of robots working in industry significantly increases due to their capacity to realize operations that requires flexibility, rapidity and accuracy. However, as quick flexible manipulators are essential to achieve this performance leading to a minor production time and small energy consumption, more resourceful control algorithms must be implemented, which can cope with important parameters variations, such as inertia. On the other side, even if predictive control has proved to be an efficient control strategy in industry, the maintenance of a high level of performances may be impossible to reach with a fixed predictive controller in case of important parameters variations. A solution is then to develop an adaptive version of the predictive controller for systems with parametric disturbances. This paper presents a direct version of adaptive generalized predictive control. The algorithm is rewritten in an original form minimizing a performance index, using a least-squares type strategy for the controller parameters on line identification and including a conditional updating test in the adaptation loop. An application of this structure to a robotic joint is finally developed, and a comparison between fixed predictive control and adaptive predictive control strategies stresses the advantages of adaptation in case of important inertia variations.