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This paper presents newly developed algorithms for automatic adaptation of motion for a robotic rehabilitation device. The algorithms adapt the gait pattern of patients that walk on a treadmill. Three different algorithms were developed. The first one is based on inverse dynamics and online minimization of the human-machine interaction torque. The second one is based on direct dynamics and estimation of the desired variation in the gait-pattern acceleration. The third algorithm is based on impedance control and direct adaptation of the gait pattern angular trajectories. The algorithms were tested and compared in computer simulations and actual experiments on healthy subjects and patients. In simulations, all algorithms have adapted the gait pattern toward the desired one, which led to a greater than 40% reduction of interaction torques. The impedance-control-based algorithm performed best in the experiments.