解决轮式机器人轨迹跟踪中的奇异点问题，让停走反转更稳定。
A Relaxed Quadratic-Program-based Framework for Trajectory Tracking of Unicycle Robots with Singularity Avoidance
- 用带松弛变量的二次规划重构控制约束，避免奇异点。
- 在速度为零时仍能保持控制可行性，支持停走反转动作。
- 适合需要高鲁棒性的移动机器人控制场景。
动态反馈线性化（DFL）是轮式移动机器人轨迹跟踪的经典方法，但当线速度为零时会导致控制器奇异，无法用于停走反转操作。本文提出一种基于二次规划（QP）的最优控制框架，通过引入松弛变量将DFL约束重构成等式约束的QP问题，确保所有状态和参考轨迹下（包括速度为零点）的可行性，并证明了反馈律的局部利普希茨连续性。通过调节松弛变量与可调参数，可在一大类参考轨迹上有效避免奇异配置。在TurtleBot3 Waffle机器人上基于ROS 2-Gazebo的仿真验证了该方法的有效性。代码已公开于 https://gradslab.github.io/DFL_QP_Unicycle/
原文摘要 · Abstract (English)
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/
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。