Partial Torque Tensor and Its Building Block Representation for Dynamics of Branching Structures Using Computational Graph

The Euler–Lagrange and Newton–Euler methods are typically used to derive equations of motion for serial-link manipulators. We previously proposed a partial Lagrangian method, which is similar to the Lagrangian method, for handling the equations of motion analytically. Moreover, the proposed method can efficiently handle multi-link analyses, similar to the Newton–Euler method. The partial Lagrangian method organizes the Lagrangian, which is obtained from the link structure, and torque, which is obtained by differential operations, into a table that can be easily handled by both manual calculations and computer analysis. Furthermore, by representing it using a computational graph, it is possible to perform dynamic analysis while maintaining the structure of a system. By observing the intermediate nodes of this computational graph, it is possible to observe how the torque generated at a particular link affects the joint. Organizing the structure with graphs allows us to consider complex systems as a collection of subgraphs, making this method highly compatible with our proposed partial Lagrangian approach. This study shows that the partial torque tensor can be used as an analog of the