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Multibody dynamics simulators are an important tool in many fields, includinglearning and control for robotics. However, many existing dynamics simulatorssuffer from inaccuracies when dealing with constrained mechanical systems dueto unsuitable integrators with bad energy behavior and problematic constraintviolations, for example for contact interactions. Variational integrators arenumerical discretization methods that can reduce physical inaccuracies whensimulating mechanical systems, and formulating the dynamics in maximalcoordinates allows for easy and numerically robust incorporation of constraintssuch as kinematic loops or contacts. Therefore, this article derives avariational integrator for mechanical systems with equality and inequalityconstraints in maximal coordinates. Additionally, efficient graph-basedsparsity-exploiting algorithms for solving the integrator are provided andimplemented as an open-source simulator. The evaluation of the simulator showsimproved physical accuracy due to the variational integrator and the advantagesof the sparse solvers. Comparisons to minimal-coordinate algorithms showimproved numerical robustness and application examples of a walking robot andan exoskeleton with explicit constraints demonstrate the necessity andcapabilities of maximal coordinates.

Variational Integrators and Graph-Based Solvers for Multibody Dynamics in Maximal Coordinates