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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. Note to Practitioners—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, when the target state and the final time may require correction at a high rate. For example, for picking small objects from a conveyor belt with a variable feed rate, an off-line planning would fail, since the motion has to be adjusted as soon as the speed is changed. Under the assumption that the desired pickup position and velocity and arrival time can be predicted, the approach in this paper is applicable. The movements can be optimized, for example, for energy efficiency or for reduction of vibrations in the robot. We discuss how to mathematically express the desired performance criteria and other requirements on the motion, such as not violating a maximum joint speed. Quick reactions to sensor inputs are computationally demanding. Thus, we limit ourselves to a class of motion-generation problems that lends itself to numerical optimization. Additionally, we save computation power by gradually refining the motion. [ABSTRACT FROM AUTHOR]