Abstract This work considers the problem of dynamic identification for robotic mechanisms given noisy measurements of configuration variables and applied torques. Conventionally, this problem is solved via least-squares, exploiting linearity properties of the inverse dynamics model for rigid-body systems. However, the nonlinear dependency of this model on configurations and velocities gives rise to bias in the resultant estimates when using noisy or even filtered data. Further, these biases can cause parameters of best fit to be non-physical, potentially leading to an ill-posed forward dynamic model. The main contribution of this paper is to propose a sequential semidefinite optimization procedure to both (1) ensure the physical consistency of the identified model and (2) maintain the statistical consistency of the estimator. The new method validates both a direct and inverse dynamic identification model (DIDIM), and also ensures that intermediate iterates of the algorithm remain physically valid. Due to these favorable properties, the method is named a Physically-Consistent DIDIM (PC-DIDIM) approach. Recent statistical hypothesis tests for instrumental variable approaches are generalized for application with a PC-DIDIM approach. Experimental results with a six-degree-of-freedom industrial robot supported by Monte Carlo simulations show the effectiveness of the new method and robustness benefits in comparison to conventional least-squares and the vanilla DIDIM method.

中文翻译：

---

用于物理和统计一致机器人识别的顺序半定优化

摘要 这项工作考虑了给定配置变量和施加扭矩的噪声测量的机器人机构的动态识别问题。通常，这个问题是通过最小二乘法解决的，利用刚体系统的逆动力学模型的线性特性。然而，当使用嘈杂甚至过滤数据时，该模型对配置和速度的非线性依赖性会导致结果估计出现偏差。此外，这些偏差可能导致最佳拟合参数非物理，可能导致不适定的前向动态模型。本文的主要贡献是提出了一个顺序半定优化程序，以（1）确保识别模型的物理一致性和（2）保持估计量的统计一致性。新方法验证了直接和逆向动态识别模型 (DIDIM)，并确保算法的中间迭代保持物理有效性。由于这些有利的特性，该方法被命名为物理一致 DIDIM (PC-DIDIM) 方法。最近用于工具变量方法的统计假设检验被推广用于 PC-DIDIM 方法的应用。蒙特卡罗模拟支持的六自由度工业机器人的实验结果表明，与传统的最小二乘法和普通 DIDIM 方法相比，新方法的有效性和鲁棒性优势。该方法被命名为物理一致 DIDIM (PC-DIDIM) 方法。最近用于工具变量方法的统计假设检验被推广用于 PC-DIDIM 方法的应用。蒙特卡罗模拟支持的六自由度工业机器人的实验结果表明，与传统的最小二乘法和普通 DIDIM 方法相比，新方法的有效性和鲁棒性优势。该方法被命名为物理一致 DIDIM (PC-DIDIM) 方法。最近用于工具变量方法的统计假设检验被推广用于 PC-DIDIM 方法的应用。蒙特卡罗模拟支持的六自由度工业机器人的实验结果表明，与传统的最小二乘法和普通 DIDIM 方法相比，新方法的有效性和鲁棒性优势。