[plancherb1]

RBDReference(robot, use_joint_dynamics=True, friction_model="tanh", friction_width=w) replaces the Coulomb term friction*sign(qd) by the smooth friction*tanh(qd/w). The default friction_model="sign" is unchanged.

The inverse-dynamics gradient carries the slope (friction/w) sech^2(qd/w) on the velocity diagonal, so forward_dynamics_gradient follows by composition. Both second-order inverse-dynamics references add -(2 friction/w^2) tanh(qd/w) sech^2(qd/w) to the qd-qd triple diagonal of the reduced output after the mimic fold, so fdsva_so follows as well. The width is one scalar or one value per velocity slot, 0.03 rad/s by default.

inverse_dynamics_gradient_bpass_dqd takes qd as a keyword argument because the tanh slope depends on it; the only caller passes it.

Tests (tests/test_joint_dynamics_friction_model.py) check the closed forms of the bias and both derivatives against the per-body fold, the gradient against central differences of inverse and forward dynamics, and the second order against central differences of the gradients, at rest, inside the width, at the width and outside it, on fr3 (friction and a mimic joint) and floating iiwa14 (root skipped). The sign model's bias, slope and zero curvature are pinned.

This is item 1 of the GRiD 0.5.4 batch (GATO issue A2R-Lab/GATO#20).

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