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

TL;DR

This paper introduces a unified factor graph-based framework for modeling and simulating multibody systems, enabling efficient optimization and validation against existing methods, with open-source implementation.

Contribution

A novel general framework using factor graphs for multibody system simulation, providing an intuitive, unified approach with open-source tools.

Findings

Comparable accuracy with classical methods in simulations

Efficient sparse nonlinear optimization approach

Open-source C++ implementation available

Abstract

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