基于控制障碍函数的机器人有限时间预设性能安全跟踪控制
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郑州大学电气与信息工程学院

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TP273

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国家自然科学基金面上项目(62273311),河南省杰出青年科学基金项目(242300421051),河南省杰出外籍科学家工作室项目(GZ2025001).


Finite-time prescribed performance safe tracking control for robotic systems based on control barrier function
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Natural Science Foundation of China (62273311), Henan Provincial Science Foundation for Distinguished Young Scholars (242300421051), Outstanding Foreign Scientist Project in Henan Province (GZ2025001).

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    摘要:

    本文提出了一种基于控制障碍函数(Control Barrier Function, CBF)的机器人有限时间预设性能安全轨迹跟踪控制方法。针对机器人系统在笛卡尔空间下的位置安全约束问题,本文构造了笛卡尔空间有限时间控制障碍函数(Cartesian-space Finite-time CBF, CFCBF)。该函数基于笛卡尔空间动力学构建,将系统动能与安全约束结合,通过引入与系统动能相关的障碍函数构造方式,对相对阶为 2 的位置约束进行能量型重构,实现了向相对阶为 1的约束条件的等价映射。在此基础上,为解决障碍物环境下的机器人安全跟踪问题,设计了一种具有有限时间预设性能的安全轨迹跟踪控制器。通过将 CFCBF 与预设性能约束融合到二次规划优化框架,实现了对具有预设性能约束的机器人系统在障碍物环境中的安全跟踪与避障控制。基于Lyapunov稳定性理论,证明了所设计控制器能够保证系统跟踪误差在预定性能边界内的有限时间收敛。仿真验证表明,该方法在保证机器人系统避障安全的同时,能够实现轨迹跟踪误差有限时间收敛,提升了系统的控制精度和动态性能。

    Abstract:

    This paper proposes a finite-time prescribed performance safe tracking control (FPPSTC) method for robotic systems based on the control barrier function (CBF). To address the position safety constraint problem of robotic systems in Cartesian space, a Cartesian-space finite-time CBF (CFCBF) is constructed, which combines the system kinetic energy with the safety constraints by directly established based on the dynamic characteristics of the task space. By leveraging the kinetic energy of the system, the position safety constraint with a relative degree of 2 is reformulated into an equivalent barrier function condition with a relative degree of 1.} On this basis, to deal with the trajectory tracking and obstacle avoidance problem of robotic system in an obstacle environment, a FPPSTC scheme is designed by integrating the CFCBF and prescribed performance constraints into a quadratic program (QP) optimization framework. Based on Lyapunov stability theory, it is further proved that the designed controller can guarantee the finite-time convergence of the tracking error within the predefined performance boundaries. Simulation results show that the proposed method can ensure safe tracking for the robotic systems while achieving finite-time convergence of trajectory tracking error, thereby improving the control accuracy and dynamic performance of the system.

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  • 收稿日期:2025-11-16
  • 最后修改日期:2026-05-29
  • 录用日期:2026-05-29
  • 在线发布日期: 2026-06-16
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