Question: Why spline_mapping is used to update paramerter?

[ppap36]

Hello! I am a master student studying mjpc.
When I was studying https://github.com/google-deepmind/mujoco_mpc/tree/main/mjpc/planners/gradient algorithnm,
I was looking at these codes:
https://github.com/google-deepmind/mujoco_mpc/blob/9bd2037498056a0ab9cf9463ab841e40fef54142/mjpc/planners/gradient/planner.cc

    // compute spline mapping linear operator
    mappings[policy.representation]->Compute(
        candidate_policy[0].times, candidate_policy[0].num_spline_points,
        trajectory[0].times.data(), trajectory[0].horizon - 1);

    // compute total derivatives
    mju_mulMatTVec(candidate_policy[0].parameter_update.data(),
                   mappings[policy.representation]->Get(),
                   candidate_policy[0].k.data(),
                   model->nu * (trajectory[0].horizon - 1),
                   model->nu * candidate_policy[0].num_spline_points);

From my point of view, I assume k and parameter_update are the same thing, and i don't know why mappings are used.

Can someone have an idea? Thanks a lot!