Initial closed-loop mechanism implementation #149
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…bian, to be used for constraint Jacobian as well
Adds maximal_coordinates, which takes a mechanism and turns it into a height-one tree with floating joints at the tree edges, while the joints of the input mechanism become non-tree edges in the maximal-coordinates-mechanism. Also fixes a bug in the constraint bias computation. Test asserts that doing dynamics for a random Mechanism and for a maximal-coordinates version of that Mechanism results in the same spatial accelerations.
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Initial support for closed-loop mechanisms (see #85).
The
attach!function now figures out whether the predecessor and successor are already part of theMechanism, and if so, creates aNonTreeEdgeinstead of adding a new vertex and edge to the tree.Also adds a
maximal_coordinatesfunction that takes aMechanismand creates an equivalentMechanismwith allRigidBodys attached directly to the world using aQuaternionFloatingjoint, while adding all of the joints of the inputMechanismasNonTreeEdges (i.e. loop constraints). A test verifies that doing dynamics for a randomMechanismand its correspondingmaximal_coordinatesversion gives the same result.For now,
Mechanismmanipulation functions likesubmechanism,reattach!, etc. don't supportMechanisms withNonTreeEdges (they throw an error when such edges are present).Long-term, I'd like to switch to a proper graph structure for the
Joint/RigidBodygraph in aMechanism(perhapsGraphfromGraphs.jl).Still need to implement constraint projection in the integrator.
Also fix some minor type issues.