  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 their time derivatives, and wrenches at the
connection points between those subsystems. To help in the model composition,
we also propose a weighted directed graph representation where the weights
encode the propagation of twists and their time derivatives, 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.
