Systematic Design of the Time-Independent and Computable Controller Based on Zero-Division-Avoidable Smoother for a Desired Orbit in Phase Space

Abstract

This letter proposes a method to systematically design a time-independent controller for a desired orbit in phase space. A time-independent controller is essential in robots that physically interact with humans or the environment. An approach to designing such a controller is based on the virtual dynamics of the desired orbit (VDDO), in which the desired orbit is assumed as a constraint. However, depending on the desired orbit, zero-division happens, and then the computation of control input breaks down. To address this issue, a zero-division-avoidable smoother, which functions as a low-pass filter and maintains computability even when the computation includes zero-division, is applied to compute the controller input based on the VDDO. This application establishes a systematic design of a VDDO-based controller that avoids zero-division. We investigated the performance of the proposed controller via experiments and simulations for three given orbits: a unit circle, super-ellipse, and spiric section. Results showed that the proposed time-independent controller can avoid zero-division while approaching the desired orbits. Furthermore, an experiment in which a human forces a robot to stop showed that the robot could restart from an unfavorable state and approach the desired orbits once more.