In general, multibody models are described with a set of redundant coordinates and additional constraints. Their dynamics is thus expressed through differential algebraic equations. As an alternative, the minimal coordinate formulation permits to describe a rigid system with the minimal number of variables leading to ordinary differential equations which can be employed in a coupled state/input estimation scheme. However, in some cases the explicit relation between the full-system coordinates and the minimal coordinates may not be available or analytically obtainable, as for closed-loop mechanisms. In this work, a previously presented deep learning framework to find the non-linear mapping and reduce a generic multibody model from redundant to minimal coordinates is employed. The resulting equations are then exploited in an extended Kalman filter where the unknown inputs are considered as augmented states and jointly estimated. The necessary derivatives are given and it is shown that acceleration measurements are sufficient for the estimation. The method is experimentally validated on a slider–crank mechanism.

通常，多实体模型是用一组冗余坐标和附加约束来描述的。因此，它们的动力学通过微分代数方程表示。作为替代，最小坐标公式允许描述具有最小数量的变量的刚性系统，从而导致可以在耦合状态/输入估计方案中使用的常微分方程。但是，在某些情况下，如闭环机制那样，可能无法获得或无法解析地获得整个系统坐标与最小坐标之间的明确关系。在这项工作中，采用了先前介绍的深度学习框架来查找非线性映射并将通用多体模型从冗余坐标简化为最小坐标。然后，在扩展的卡尔曼滤波器中利用所得的方程式，其中未知输入被认为是扩充状态，并被联合估计。给出了必要的导数，并表明加速度测量值足以进行估计。该方法在曲柄滑块机构上经过实验验证。