用控制屏障函数避免机器人系统奇异点，提升轨迹跟踪稳定性。
Task-Space Singularity Avoidance for Control Affine Systems Using Control Barrier Functions
- 基于状态相关输入输出矩阵特征值识别奇异配置，构建安全屏障。
- 仿真显示控制输入尖峰降低100倍，轨迹跟踪更平滑。
- 适合需要高精度轨迹控制的机械臂与医疗机器人场景。
机器人和动力系统中的奇异点出现在控制输入到任务空间运动的映射失去秩时，导致无法确定控制输入。这限制了系统在期望方向产生力和力矩的能力，并阻碍精确轨迹跟踪。本文提出一种针对控制仿射系统的控制屏障函数（CBF）框架，用于避免此类奇异点。通过状态依赖的输入输出映射矩阵的特征值识别奇异构型，并构建屏障函数以保持远离秩亏区域。给出了基于执行器动态的安全性理论保证条件。在平面2自由度机械臂和磁驱动针上进行的仿真表明，系统能平稳跟踪轨迹，同时避开奇异构型，相比原始控制器，控制输入尖峰减少高达100倍。
原文摘要 · Abstract (English)
Singularities in robotic and dynamical systems arise when the mapping from control inputs to task-space motion loses rank, leading to an inability to determine inputs. This limits the system's ability to generate forces and torques in desired directions and prevents accurate trajectory tracking. This paper presents a control barrier function (CBF) framework for avoiding such singularities in control-affine systems. Singular configurations are identified through the eigenvalues of a state-dependent input-output mapping matrix, and barrier functions are constructed to maintain a safety margin from rank-deficient regions. Conditions for theoretical guarantees on safety are provided as a function of actuator dynamics. Simulations on a planar 2-link manipulator and a magnetically actuated needle demonstrate smooth trajectory tracking while avoiding singular configurations and reducing control input spikes by up to 100x compared to the nominal controller.
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