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A technique is presented for estimating the number of iterations needed for convergence of iterative adaptive ON-OFF controllers to optimal switching times, for certain controllers proposed for managing stepping motion in autonomous microrobots. An upper bound on output error as a function of error in ON-OFF switching times is obtained, and lower bounds on the change in switching times from iteration-to-iteration are used to estimate output error evolution. The simulation and experimental results from the test case of a piezoelectric microrobotic leg joint indicate reasonable agreement between estimated and actual error. The use of convergence estimates to improve controller design with respect to total energy consumption is then described.

A model-free on-off iterative adaptive controller is described for application to microscale servo systems performing repeated motions under extremely strict power constraints. The approach is motivated by the needs of piezoelectric actuators in autonomous microrobots, where power consumption in analog circuitry and/or for position sensing may be much larger than that of the actuators themselves. The control algorithm adjusts switching instances between “on” and “off” inputs to the actuator to minimize an objective function using simultaneously perturbed stochastic approximation of the gradient with just a single sensor measurement in each iteration. Convergence conditions for the gradient approximation are shown to apply when the possibility for a range of possible switching times minimizing the objective function is accounted for, while a method is proposed for avoiding local minima for plants with bounded nonlinearities. The algorithm is tested on a prototype piezoelectric microactuator.

A novel model-free iterative adaptive controller is presented for lowpower control of piezoelectric actuators. The controller uses simple adaptation rules based on known general behavior of piezoelectric actuators to adjust onoff switching times to drive piezoelectric actuators through a desired transient step motion. Adaptation rules are based on small numbers of measurements taken during each iteration of the actuator movement. Combined with the use of only on-off control inputs, controller implementation can be possible at much lower overall power levels than would be needed to implement a conventional control strategy such as through pulse-width-modulation (PWM) with real-time feedback. Such power savings are particularly important for the intended controller application to piezoelectric microactuators driving autonomous terrestrial micro-robots. A method for predicting convergence of systems with nominally linear dynamics and unknown, bounded nonlinearities is described, and applied to a sample target piezoelectric actuator. The controller is tested in simulation and experimentally on a piezoelectric cantilever actuator, and shows predicted convergence to the desired response.

An on-off iterative adaptive controller has been developed that is applicable to servo systems performing repeated motions under extremely strict power constraints. The motivation for this approach is the control of piezoelectric actuators in autonomous micro-robots, where power consumption in analog circuitry and/or for position sensing may be much larger than that of the actuators themselves. The control algorithm optimizes the switching instances between ‘on’ and ‘off’ inputs to the actuator using a stochastic approximation of the gradient of an objective function, namely that the system reach a specified output value at a specified time. This allows rapid convergence of system output to the desired value using just a single sensor measurement per iteration and discrete voltage inputs.