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The problem of planning a trajectory for robots starting in an initial state and reaching a final state in a desired interval of time is tackled. We propose an approach based on model predictive control to solve the problem of point-to-point trajectory generation for a given final time. We discuss various choices of models, objective functions, and constraints for generating trajectories to transfer the state of the robot, while respecting physical limitations on the motion as well as fulfilling computational real-time requirements. Extensive simulation results illustrate the use of the approach, and experiments on an industrial robot in a challenging ball-catching task show the effectiveness of the approach also in demanding scenarios with real-time constraints on the computation. This paper was motivated by the problem of generating movements to transfer a robot from its current state to a new position and velocity at a certain time …