A Relaxed Quadratic-Program-based Framework for Trajectory Tracking of Unicycle Robots with Singularity Avoidance
2026-06-22 • Robotics
Robotics
AI summaryⓘ
The authors address a problem in controlling unicycle-type robots where the usual method stops working when the robot's speed hits zero, making it hard to perform stop-and-reverse moves. They create a new control method using a type of optimization called quadratic programming that avoids this issue by allowing more flexibility in the calculations. Their method guarantees smooth control behavior and works for a wide range of robot movements, including when the robot is stopped. They tested their approach using robot simulations to show it can successfully follow paths without running into the previous problem.
dynamic feedback linearizationunicycle robottrajectory trackingquadratic programmingoptimal controlLipschitz continuitysingularityslack variablesRos 2Gazebo simulation
Authors
Hamza Tariq, Usman Ali, Adeel Akhtar
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/