Question: Natural parametrization of curve

Let a piecewise-linear curve be defined by a listlist. For example,

LL := [[1.1, 2.04], [1.97, 4.04], [2.96, 2.97], [4.5, 6.4], [5.08, 7.21], [1.1, 4.04], [1.1, 2.04]]:
plot(LL);

How to find its natural parametrization in Maple? A procedure is desired. See Wiki for info.

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