Systematic Design of the Time-Independent and Computable Controller Based on Zero-Division-Avoidable Smoother for a Desired Orbit in Phase Space
Ken Masuya
AI summary
Problem
Time-independent orbit controllers often fail computationally when constraint derivatives vanish, and standard regularization methods trap robots in place after external disturbances. This gap prevents reliable deployment in unpredictable human-robot interaction scenarios.
Approach
The method integrates a zero-division-avoidable smoother into the Virtual Dynamics of the Desired Orbit framework, reformulating control input calculation as an optimization problem that preserves previous inputs to maintain computability and enable restart.
Key results
- Eliminates computation breakdown from zero-division across complex phase-space orbits
- Achieves accurate tracking for unit circles, super-ellipses, and spiric sections in simulation
- Demonstrates autonomous restart capability after forced human stops in physical experiments
- Outperforms standard VDDO and L2-regularized controllers in robustness and tracking error
Why it matters
Provides a reliable control foundation for robots operating in unpredictable, physically interactive environments where singularities and external forces are common.
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.