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Kinematics & IK

Forward kinematics

caliper-kinematics computes forward kinematics from a frozen Model: given a joint configuration q, it places every frame in the world. It also produces the geometric Jacobian in two flavors:

  • world (LWA-style), and
  • body (LOCAL).

These two flavors match the two reference frames Pinocchio exposes, which is why the oracle can check them directly. FK and the world Jacobian are Pinocchio-validated to residuals on the order of 1e-9…1e-15.

Singularity analysis

The kinematics crate also computes singularity metrics from the Jacobian: the singular-value spectrum, Yoshikawa manipulability, and the condition number, plus the manipulability ellipsoid (eigendecomposition) and a redundant-arm nullspace. The scalar metrics (σ, manipulability, condition number) are cross-checked against a NumPy SVD in the oracle. The ellipsoid eigendecomposition and the nullspace are re-derived-correct but validated only against Caliper itself (no external reference); a "singular joint" classification is treated as advisory, not a hard guarantee.

Inverse kinematics

caliper-ik provides two IK paths:

  1. Iterative CLIK — damped-least-squares / Levenberg–Marquardt closed-loop inverse kinematics with:

    • manipulability-gated damping (more damping near singularities),
    • per-step clamping,
    • joint-limit handling,
    • multi-restart to escape poor local basins.

  2. Analytic 6R IK (caliper_ik::analytic) — a closed-form solver for the standard 6R wrist-partitioned geometry, returning the discrete set of branch solutions.

How IK is verified

The IK solver is validated by the FK∘IK round-trip: solve for q, run FK, and confirm the resulting pose matches the target to tolerance. That closure is strong evidence the solver converges to correct configurations, but note the honest caveat — it is self-consistent against Caliper's own FK, not checked against an independent task-space DLS reference. Because FK itself is externally validated against Pinocchio, a correct FK∘IK closure is meaningful, but a defect shared between FK and IK would not be caught by this test alone.