Decentralized phase regulation of cyclic robotic systems

Abstract

Control algorithms are difficult to scale up to large decentralized systems because of potentially complex couplings between components. As a result, many such systems function conservatively---damping out most of their energy and moving slowly or in a start-stop fashion. Synthesis tools for dynamical behaviors that admit a modular, bottom-up approach attempt to address this problem. Without such tools, the full potential of modern actuators, sensors and computing power likely cannot be realized, dooming robots (and more generally, physically situated computing systems) to a clumsy and inefficient future. This dissertation describes efforts to provide a formal basis for designing and verifying decentralized control algorithms for robotic systems such as factories, dynamic manipulators, hoppers and walkers. The methods are based on <italic>synthesis</italic> and, particularly, composition. The idea behind the compositional approach is simple. A designer should not have to start from scratch when building complicated systems. Instead knowledge of how to make a machine do two tasks separately should be leveraged to make the machine do the two tasks in some combination. To avoid the complexity of arbitrary couplings, we consider systems that may be decomposed in very regular ways. In particular, we focus on methods for coordinating multiple cyclic behaviors, based on defining ideal, model dynamical systems called <italic>reference fields</italic>. In using reference fields to control coupled cyclic systems, it is assumed that each cyclic system can be continuously actuated. However, many tasks in robotics, such as juggling and hopping, allow only intermittent control. Thus, we also show that reference fields can be used as the basis for controlling these more complicated tasks. Finally, reference fields are applied to the control of a six-legged, scampering robot and the performance of the approach is examined with respect to the speed and power consumption of the robot.