  With the goal of using chiral interactions at various orders to explore
properties of the few-body nuclear systems, we write the recently developed
local chiral interactions as spherical irreducible tensors and implement them
in the hyperspherical harmonics expansion method. We devote particular
attention to three-body forces at next-to-next-to leading order, which play an
important role in reproducing experimental data. We check our implementation by
benchmarking the ground-state properties of $^3$H, $^3$He and $^4$He against
the available Monte Carlo calculations. We then confirm their order-by-order
truncation error estimates and further investigate uncertainties in the charge
radii obtained by using the precise muonic atom data for single-nucleon radii.
Having local chiral Hamiltonians at various orders implemented in our
hyperspherical harmonics suites of codes opens up the possibility to test such
interactions on other light-nuclei properties, such as electromagnetic
reactions.
