This work introduces an analytical approach for detecting and estimating external forces acting on deformable linear objects (DLOs) using only their observed shapes. In many robot-wire interaction tasks, contact occurs not at the end-effector but at other points along the robot's body. Such scenarios arise when robots manipulate wires indirectly (e.g., by nudging) or when wires act as passive obstacles in the environment. Accurately identifying these interactions is crucial for safe and efficient trajectory planning, helping to prevent wire damage, avoid restricted robot motions, and mitigate potential hazards. Existing approaches often rely on expensive external force-torque sensor or that contacts occur at the end-effector for accurate force estimation. Using wire shape information acquired from a depth camera and under the assumption that the wire is in or near its static equilibrium, our method estimates both the location and magnitude of external forces without additional prior knowledge. This is achieved by exploiting derived consistency conditions and solving a system of linear equations based on force-torque balance along the wire. The approach was validated through simulation, where it achieved high accuracy, and through real-world experiments, where accurate estimation was demonstrated in selected interaction scenarios.

翻译：本研究提出了一种仅通过观察形状来检测和估计作用于可变形线性物体外部力的分析方法。在许多机器人-线缆交互任务中，接触并非发生在末端执行器，而是发生在机器人本体的其他位置。当机器人间接操作线缆（例如通过轻推）或线缆作为环境中的被动障碍物时，此类场景就会出现。准确识别这些交互对于安全高效的轨迹规划至关重要，有助于防止线缆损坏、避免机器人运动受限并降低潜在风险。现有方法通常依赖昂贵的外部力-扭矩传感器，或要求接触发生在末端执行器才能实现精确的力估计。我们的方法利用深度相机获取的线缆形状信息，并在线缆处于或接近静态平衡的假设下，无需额外先验知识即可同时估计外部力的作用位置和大小。这是通过利用推导出的一致性条件，并求解基于线缆受力-扭矩平衡的线性方程组来实现的。该方法通过仿真验证达到了高精度，并在实际实验中，在选定的交互场景下展示了准确的估计能力。