AI 中文总结
本文针对受位置级避障相对阶2安全约束的力控非完整移动机器人，提出基于缩放的互CBF构造方法，推导充分条件并经数值仿真验证其有效性。
AI 中文摘要
本文研究了力控非完整移动机器人的控制障碍函数（CBF）构造，该机器人受位置级避障产生的相对阶为2的安全约束。提出一种基于缩放的互障碍构造方法，在与原始物理安全函数关联的互障碍的分子中引入与运动相关的正缩放因子。所得障碍函数精确定义在物理安全集的内部，在其边界处变为奇异，从而保留原始安全约束的经认证内部域，同时恢复一阶控制权限。针对力控非完整机器人模型，推导了所提构造定义互CBF的充分条件，且在满足诱导互CBF条件的控制器下，物理安全集的内部是前向不变的。进一步采用标量严格反馈系统，在显式结构假设下为潜在的高阶相对阶级联提供结构解释。数值仿真验证了诱导的安全集几何及其与基于优化的避障控制框架的集成效果。
英文摘要
This paper studies the construction of control barrier functions (CBFs) for force-controlled nonholonomic mobile robots subject to relative-degree-two safety constraints arising from position-level obstacle avoidance. A scaling-based reciprocal barrier construction is proposed, in which a positive motion-dependent scaling factor is placed in the numerator of a reciprocal barrier associated with the original physical safety function. The resulting barrier is defined exactly on the interior of the physical safe set and becomes singular on its boundary, thereby preserving the certified interior domain of the original safety constraint while recovering first-order control authority. For a force-controlled nonholonomic robot model, sufficient conditions are derived under which the proposed construction defines a reciprocal CBF, and the interior of the physical safe set is forward invariant under controllers satisfying the induced reciprocal-CBF condition. A scalar strict-feedback system is further used to provide a structural interpretation of the underlying higher-relative-degree cascade under explicit structural assumptions. Numerical simulations demonstrate the induced safe-set geometry and its integration with an optimization-based control framework for obstacle avoidance.
CommentsThe paper has been accepted for publication in the ASME Letters in Dynamic Systems and Control
