A Relaxed Quadratic-Program-based Framework for Trajectory Tracking of Unicycle Robots with Singularity Avoidance

2026-06-22

AI Summary

This work addresses the singularity issue in dynamic feedback linearization (DFL) for single-wheel robot trajectory tracking, which arises at zero velocity and prevents maneuvers such as stopping and reversing. To overcome this limitation, the authors propose an optimal control framework based on quadratic programming (QP). By introducing slack variables, the DFL constraints are reformulated into a QP problem with equality constraints, and tunable parameters are incorporated to ensure feasibility for any system state and reference trajectory while preserving local Lipschitz continuity of the feedback law. The approach effectively eliminates the zero-velocity singularity, thereby expanding the range of admissible trajectories without compromising theoretical rigor or practical applicability. High-fidelity simulations on the TurtleBot3 Waffle platform within a ROS 2–Gazebo environment demonstrate precise trajectory tracking performance, including during stop-and-reverse maneuvers.

Abstract

Dynamic feedback linearization (DFL) is a classical technique for trajectory tracking of unicycle-type mobile robots, but the resulting DFL-based controller becomes singular when the linear velocity vanishes, rendering standard DFL-based controllers unsuitable for stop-and-reverse maneuvers. This paper proposes a quadratic-program (QP)-based optimal control framework that avoids this singularity, while establishing local Lipschitz continuity of the resulting feedback law. Our approach reformulates the DFL constraints as an equality-constrained QP with a slack variable, ensuring feasibility for all states and reference signals, including at points where the robot's velocity vanishes. By introducing slack variables and tunable parameters, we demonstrate that the singular configuration can be avoided for a large class of reference trajectories. The effectiveness of the proposed approach for trajectory tracking is demonstrated through ROS 2-Gazebo simulations on a TurtleBot3 Waffle robot. The code is available at https://gradslab.github.io/DFL_QP_Unicycle/

Problem

• trajectory tracking
• unicycle robots
• singularity avoidance
• dynamic feedback linearization
• quadratic programming

Innovation

• quadratic programming
• dynamic feedback linearization
• singularity avoidance
• unicycle robots
• trajectory tracking