Three low-power control strategies for piezoelectric actuators based on on-off or related switching control approaches are described. These strategies are targeted for leg actuation in autonomous micro-robots, where available power is severely constrained, below the power level that more conventional analog or pulse-width-modulation drive circuitry, switching rates, and/or sampling frequency would require. The first strategy optimizes the sequence of ‘on’ and ‘off’ transitions over a finite number of steps to minimize actuator energy while ensuring that a system moves to a desired set of final states. Transitions are selected via convex optimization by binary programming. The second strategy optimizes a set of commands to a drive circuit including charge recovery components to improve both power consumption and positioning accuracy, with optimal transitions chosen using mixed integer quadratic programming. The third strategy is proposed to account for modeling error using step to step adaptation of input sequences with limited sensor measurements.

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