Coriolis Factorizations and their Connections to Riemannian Geometry
CoRR(2023)
摘要
Many energy-based control strategies for mechanical systems require the
choice of a Coriolis factorization satisfying a skew-symmetry property. This
paper explores (a) if and when a control designer has flexibility in this
choice, (b) what choice should be made, and (c) how to efficiently perform
control computations with it. We link the choice of a Coriolis factorization to
the notion of an affine connection on the configuration manifold and show how
properties of the connection relate with ones of the associated factorization.
Out of the choices available, the factorization based on the Christoffel
symbols is linked with a torsion-free property that limits the twisting of
system trajectories during passivity-based control. The machinery of Riemannian
geometry also offers a natural way to induce Coriolis factorizations for
constrained mechanisms from unconstrained ones, and this result provides a
pathway to use the theory for efficient control computations with
high-dimensional systems such as humanoids and quadruped robots.
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