Dynamics & simulation

caliper-dynamics implements the standard rigid-body dynamics algorithms on the frozen Model:

• RNEA — the Recursive Newton–Euler Algorithm for inverse dynamics: given (q, q̇, q̈), compute the joint torques τ.
• CRBA — the Composite Rigid Body Algorithm for the joint-space mass (inertia) matrix M(q).
• Forward dynamics — given (q, q̇, τ), compute q̈ (using M and the RNEA bias term).
• Simulator — a semi-implicit (symplectic-style) Euler integrator with gravity, advanced by explicit step(dt) calls.

Conventions

Spatial quantities follow the [v; ω] twist ordering and are Pinocchio-compatible, matching caliper-spatial. This alignment is what lets the oracle compare against Pinocchio directly.

How dynamics is verified

RNEA, CRBA, and forward dynamics are externally cross-validated against Pinocchio to residuals on the order of ~1e-9. (An earlier RNEA sign bug was in fact caught by exactly this external cross-validation, which is part of why the oracle exists.) The Simulator's integrators are checked for energy-bounded behavior rather than against an external reference.

Honest note. The Simulator is validated as energy-bounded, and its energy reporting assumes Earth gravity — a documented assumption, not a bug. The native simulation path has no collision built in; collision is a separate crate that plugs into the control/safety layer.