This paper presents a framework for safe navigation of a unicycle point robot to a goal position in an environment populated with obstacles from almost any admissible state, considering input limits. We introduce a novel QP formulation to create a Cinfinity-smooth vector field with reduced total bending and total turning. Then we design an analytic, non-linear feedback controller that inherently satisfies the conditions of Nagumo's theorem, ensuring forward invariance of the safe set without requiring any online optimization. We have demonstrated that our controller, even under hard input limits, safely converges to the goal position. Simulations confirm the effectiveness of the proposed framework, resulting in a twice faster arrival time with over 50\% lower angular control effort compared to the baseline.

翻译：本文提出一种面向障碍物环境中几乎任意可达初始状态、考虑输入极限的独轮点机器人安全导航至目标位置的框架。我们引入一种新型二次规划（QP）公式，生成具有降阶总弯曲和总转向的C无穷光滑向量场。进而设计一种解析非线性反馈控制器，该控制器天然满足Nagumo定理条件，无需任何在线优化即可确保安全集的前向不变性。我们已证明，即使在严格输入极限下，该控制器仍能安全收敛至目标位置。仿真结果验证了所提框架的有效性，与基线方法相比，到达时间缩短一倍，角控制能耗降低超过50%。