When modeling complex robot systems such as branched robots, whose kinematic structures are a tree, current techniques often require modeling the whole structure from scratch, even when partial models for the branches are available. This paper proposes a systematic modular procedure for the dynamic modeling of branched robots comprising several subsystems, each composed of an arbitrary number of rigid bodies, providing the final dynamic model by reusing previous models of each branch. Unlike previous approaches, the proposed strategy is applicable even if some subsystems are regarded as black boxes, requiring only twists and wrenches at the connection points between them. To help in the model composition, we also propose a weighted directed graph representation where the weights encode the propagation of twists and wrenches between the subsystems. A simple linear operation on the graph interconnection matrix provides the dynamics of the whole system. Numerical results using a 38-DoF fixed-base branched robot composed of nine subsystems show that the proposed formalism is as accurate as a state-of-the-art library for robotic dynamic modeling. Additional results using a 39-DoF holonomic branched mobile manipulator composed of ten subsystems demonstrate the fidelity of our model to a modern robotics simulator.

翻译：在复杂机器人系统（如运动学结构呈树状的分支机器人）建模过程中，即使已存在各分支的局部模型，现有技术通常仍需从头构建整体模型。本文提出一种系统化的模块化流程，用于由多个子系统构成的分支机器人动力学建模——每个子系统包含任意数量的刚体，通过复用各分支已有模型获得最终动力学模型。与现有方法不同，即使部分子系统被视为黑箱模型，本文策略依然适用，仅需子系统连接点处的旋量（twist）与力旋量（wrench）信息。为辅助模型组合，我们进一步提出带权有向图表示方法，其中权重编码了子系统间旋量与力旋量的传播关系。通过对图连接矩阵进行简单线性运算，即可获得整个系统的动力学方程。采用由九个子系统构成的38自由度固定基座分支机器人进行的数值实验表明，所提形式化方法与现有最先进机器人动力学建模库具有同等精度。基于十个子系统构成的39自由度完整约束分支移动机械手的附加实验结果，验证了模型与现代机器人仿真器的一致性。