修正机器人接触操作中的刚度不对称问题，提升控制稳定性。
A Physically Consistent Stiffness Formulation for Contact-Rich Manipulation
- 从任务空间刚度推导出显式包含克里斯托费尔符号的对称关节空间刚度
- 实验表明忽略修正项会导致显著刚度不对称误差
- 适用于需要稳定物理交互的复杂操作机器人
在接触丰富的操作中，确保阻抗控制机器人具有对称刚度对于实现物理上合理且稳定的交互至关重要。传统方法忽略了弯曲空间中基向量的变化，导致关节空间刚度矩阵不对称，违背了无源性和守恒性原理。本文通过显式引入克里斯托费尔符号，直接从任务空间刚度矩阵推导出物理一致的对称关节空间刚度公式。该修正解决了长期存在的刚度建模不一致问题，保证了能量守恒与系统稳定。我们在一个机器人系统上进行了实验验证，结果表明忽略这些修正项会引发显著的刚度不对称误差。研究将理论洞察与实际控制应用相衔接，为稳定且可解释的机器人交互提供了稳健框架。
原文摘要 · Abstract (English)
Ensuring symmetric stiffness in impedance-controlled robots is crucial for physically meaningful and stable interaction in contact-rich manipulation. Conventional approaches neglect the change of basis vectors in curved spaces, leading to an asymmetric joint-space stiffness matrix that violates passivity and conservation principles. In this work, we derive a physically consistent, symmetric joint-space stiffness formulation directly from the task-space stiffness matrix by explicitly incorporating Christoffel symbols. This correction resolves long-standing inconsistencies in stiffness modeling, ensuring energy conservation and stability. We validate our approach experimentally on a robotic system, demonstrating that omitting these correction terms results in significant asymmetric stiffness errors. Our findings bridge theoretical insights with practical control applications, offering a robust framework for stable and interpretable robotic interactions.
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