Abstract Among the proposed formulations for rigid multibody dynamics, the minimal coordinates approach permits to parametrize the system motion with the minimal amount of degrees of freedom without the need of additional constraints equations. This leads to a system of ordinary differential equations to describe the motion which enables a straightforward combination of the model with control or estimation algorithms. However, an explicit relation between the model full coordinates and a minimal number of parameters is not always available or easily obtainable, especially for spatial closed-loop mechanisms. In this work, we therefore propose to deploy deep learning to find an approximation of such motion mappings. More specifically, an autoencoder neural network architecture is exploited for the nonlinear dimensionality reduction from full to minimal coordinates. A novel neural-network training scheme is introduced, which exploits the multibody model dynamics information to optimize the decoder-function derivatives so that they represent the tangent space and the curvature of the minimal coordinates manifold. This scheme leads to an effective description of the motion manifold which can be used to express the dynamics in minimal coordinates. The approach is validated on two reference rigid body mechanisms.

中文翻译：

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将多体系统模型降阶到最小坐标的深度学习

摘要 在提出的刚性多体动力学公式中，最小坐标方法允许以最小的自由度对系统运动进行参数化，而无需额外的约束方程。这导致了一个常微分方程系统来描述运动，这使得模型与控制或估计算法的直接组合成为可能。然而，模型全坐标和最少数量参数之间的明确关系并不总是可用或容易获得，尤其是对于空间闭环机制。因此，在这项工作中，我们建议部署深度学习来找到此类运动映射的近似值。进一步来说，自编码器神经网络架构被用于从完整坐标到最小坐标的非线性降维。引入了一种新的神经网络训练方案，它利用多体模型动力学信息来优化解码器函数导数，以便它们表示切线空间和最小坐标流形的曲率。该方案导致对运动流形的有效描述，可用于在最小坐标中表达动力学。该方法在两个参考刚体机构上得到验证。该方案导致对运动流形的有效描述，可用于在最小坐标中表达动力学。该方法在两个参考刚体机构上得到验证。该方案导致对运动流形的有效描述，可用于在最小坐标中表达动力学。该方法在两个参考刚体机构上得到验证。