Singularity-Free Tracking of Unicycle Robots

A relaxed quadratic-program reformulation of dynamic feedback linearization that stays well-defined even at zero velocity — enabling stop-and-reverse maneuvers.

arXiv:2606.23355 Code & project page Publication (CCTA 2026)

Dynamic feedback linearization (DFL) is a classical way to make a unicycle-type robot track a trajectory — but the standard DFL controller becomes singular when the linear velocity vanishes. That makes it unusable for exactly the maneuvers robots need most: stopping, reversing, and tight turns.

We reformulate the DFL constraints as an equality-constrained quadratic program (QP) with a slack variable. The QP is feasible for all states and references — including where the robot’s velocity is zero — and we prove the resulting feedback law is locally Lipschitz continuous. Tunable parameters let the controller steer around the singular configuration for a large class of reference trajectories.

Standard DFL controller stalling near zero velocity
Standard DFL — the control law degrades near the zero-velocity singularity.
Proposed QP-based controller tracking smoothly through stop-and-reverse
Proposed QP framework — smooth, singularity-free tracking on a TurtleBot3 Waffle.

Highlights

  • Guarantees feasibility and local Lipschitz continuity of the feedback everywhere, including at zero velocity.
  • Enables stop-and-reverse maneuvers that classical DFL cannot handle.
  • Validated in ROS 2 / Gazebo on a TurtleBot3 Waffle robot.

A Relaxed Quadratic-Program-based Framework for Trajectory Tracking of Unicycle Robots with Singularity Avoidance — Hamza Tariq, Usman Ali, Adeel Akhtar (IEEE CCTA 2026).