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In this paper, we present a novel general framework grounded in the factorgraph theory to solve kinematic and dynamic problems for multi-body systems.Although the motion of multi-body systems is considered to be a well-studiedproblem and various methods have been proposed for its solution, a unifiedapproach providing an intuitive interpretation is still pursued. We describehow to build factor graphs to model and simulate multibody systems using both,independent and dependent coordinates. Then, batch optimization or afixed-lag-smoother can be applied to solve the underlying optimization problemthat results in a highly-sparse nonlinear minimization problem. The proposedframework has been tested in extensive simulations and validated against acommercial multibody software. We release a reference implementation as anopen-source C++ library, based on the GTSAM framework, a well-known estimationlibrary. Simulations of forward and inverse dynamics are presented, showingcomparable accuracy with classical approaches. The proposed factor graph-basedframework has the potential to be integrated into applications related withmotion estimation and parameter identification of complex mechanical systems,ranging from mechanisms to vehicles, or robot manipulators.

A general framework for modeling and dynamic simulation of multibody systems using factor graphs