Convergence Time Estimation for Iterative Adaptive On-Off Control of a Micro-Robotic Leg Joint

Iterative adaptive on-off control is a potential control strategy for ultra-low-power control of micro-actuators that behave as capacitive loads. Such an approach allows for relatively low sensor sampling frequencies and the use of simple switched inputs, which can be implemented at lower power levels than control with analog inputs and real-time feedback. A technique is presented for estimating the convergence time of an on-off controller proposed for controlling stepping motion in autonomous micro-robots. Error in measured outputs at each iteration are estimated using upper bounds on output error as a function of error in on-off switching times and lower bounds on the change in on-off switching times from iteration to iteration. While a strict upper bound on error is not provided by the final error estimator, simulation and experimental results from the test case of a piezoelectric micro-robotic leg joint indicate reasonable agreement between estimated error and full controller behavior. Convergence estimates may then be used to improve controller design with respect to total energy consumed.