Module aba 

Articulated Body Algorithm (ABA) — O(n) forward dynamics.

Given (q, v, tau), compute qdd (joint accelerations). Three passes over the kinematic tree:

1. Forward pass: compute velocities, bias forces
2. Backward pass: compute articulated inertias, bias forces
3. Forward pass: compute accelerations

Supports single-DOF (revolute, prismatic) and multi-DOF (spherical, free) joints.

Functions

aba

Run the Articulated Body Algorithm.

aba_with_external_forces

Run ABA with optional external spatial forces applied to each body.