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 24-DoF fixed-base branched robot composed of eight subsystems show that the proposed formalism is as accurate as a state-of-the-art library for robotic dynamic modeling. Additional results using a 30-DoF holonomic branched mobile manipulator composed of three subsystems demonstrate the fidelity of our model to a modern robotics simulator and its capability of dealing with black box subsystems. To further illustrate how the derived dynamic model can be used in closed-loop control, we also present a simple formulation of a model-based wrench-driven pose control for branched robots.

翻译：在模拟分支机器人等运动学结构为树形的复杂机器人系统时，现有技术通常需要从头开始对整个系统建模，即使已存在各分支的局部模型。本文提出一种系统化的模块化流程，用于由多个子系统（每个子系统由任意数量的刚体组成）构成的分支机器人的动力学建模，通过复用各分支的现有模型来获得最终动力学模型。与既有方法不同，所提策略即使将某些子系统视为黑箱模型仍可适用，仅需获取子系统间连接点的旋量和力旋量即可。为辅助模型组合，我们还提出一种加权有向图表示法，其中权重编码了子系统间旋量和力旋量的传播关系。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。基于包含八个子系统的24自由度固定基座分支机器人数值实验表明，所提形式化方法与当前最先进的机器人动力学建模库精度相当。进一步采用包含三个子系统的30自由度全向分支移动机械手进行验证，结果证明了模型相对于现代机器人仿真器的保真度及其处理黑箱子系统的能力。为说明导出动力学模型如何用于闭环控制，我们还给出了分支机器人基于模型的力驱动位姿控制的简洁公式。