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Linear-Time Variational Integrators in Maximal Coordinates

Linear-Time Variational Integrators in Maximal Coordinates Jan Bruedigam and Zachary Manchester Most robotic systems are parameterized using minimal (generalized) coordinates. However, maximal coordinates have several advantages over minimal coordinates, including native handling of closed kinematic loops and nonholonomic constraints. This paper describes a linear-time variational integrator formulated in maximal coordinates. The variational formulation prevents constraint drift and has favorable conservation properties. A sparse matrix factorization allows the dynamics of a loop-free mechanism with n links to be computed in O(n) (linear) time. Additional constraints that introduce loops can also be handled without incurring much computational overhead. Experimental results show speed competitive with state-of-the-art minimal-coordinate algorithms and improved performance in several scenarios. Find the code at: https://github.com/janbruedigam/Const...