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A novel open-loop minimal energy on-off servo system and control strategy are described for ensuring specified displacements from new microscale piezoelectric rotational joints under extremely strict power budgets. The rotational joints are driven by thin-film lead-zirconate-titanate actuators and are targeted for use in autonomous terrestrial microrobots. A lumped-parameter, second-order model of anticipated joint behavior is utilized to estimate the natural frequency and damping ratio of the robot joints, which, in turn, are used to identify necessary sampling rates and switching drive circuit parameters for implementation of on-off control. An identified model of leg joint behavior is then used to both verify lumped-parameter modeling and to optimize on-off input sequences to the rotary joint. The optimization procedure incorporates energy costs from both switching and holding an input voltage on microactuators that behave as a capacitive load, while ensuring that specified final states of a dynamic system are achieved at a specified point in time. Optimization is done via a new application of binary programming. In addition, modest robustness of the system response to parameter variation can be produced during control sequence generation. Optimized input sequences are applied to both macroscale piezoelectric actuators and to prototype thin-film piezoelectric leg joints, and show that specified actuator motions can be achieved with energy consumption of less than 5 μJ per movement.