Attitude Estimated Constraint Circular Motion Control for Underactuated Unicycle Robots

Abstract

This paper investigates the problem of motion confinement for an underactuated unicycle robot while stabilizing it along a desired circular trajectory. It is considered that only the robot's position is available for feedback, and its heading angle measurements are not available. To address this, we design an observer for the robot's position and heading angle estimates using only available <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">position</i> measurements. Leveraging these state estimates and the barrier Lyapunov function (BLF), we propose a variable gain-based control design relying on a composite Lyapunov function that simultaneously captures the desired control objectives and convergence of observer errors. It was shown that the proposed controller not only asymptotically stabilizes the motion of the unicycle robot on the desired circular path but also restricts its trajectories within the predefined circular boundary almost everywhere. Furthermore, we elaborate on how the state constraints imposed in the original problem formulation are effectively enforced through the estimated variables. Both numerical simulations and real-time experiments on the Khepera IV robot are provided.