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We present nonlinear control algorithms to compensate for kinematic error in harmonic drives, thus forming a solid basis to improve their performance in precision positioning applications. Kinematic error, defined as deviation between expected and actual output positions, influences performance by producing static positioning error and inducing dynamic vibration effects. Its compensation is difficult because of its nonlinear behavior and dependence on drive type, assembly, environmental conditions, and drive load. The Lyapunov-based closed-loop control algorithms presented in this paper compensate for the kinematic error irrespective of its form in setpoint and trajectory tracking applications. Simulation and experimental results obtained with a dedicated harmonic drive test setup verify the effectiveness of the proposed controllers.