Collision

caliper-collision is a self-contained, pure-nalgebra collision checker — no parry/rapier (they were deliberately rejected to keep the dependency surface lean). CollisionModel builds primitive colliders from a Model's parsed <collision> geometry, places them by forward kinematics at a configuration q, and reports:

• self-collisions — between link pairs, excluding an auto-seeded adjacency allowlist (adjacent links are expected to touch), and
• world collisions — against a ground half-space and world boxes.

It implements caliper_hal::SafetyCheck, so the control loop / safety layer can reject a colliding command.

Geometry

• Box ↔ box — the separating-axis theorem (15 axes, Ericson), including the edge-edge degeneracy.
• Sphere/box and half-space — closed form.
• Cylinders — conservatively approximated by their tight oriented bounding box (this errs toward detecting a collision, which is the safe direction).
• Capsules — swept spheres (a core segment ⊕ a sphere of radius): capsule ↔ sphere/half-space/capsule use closed-form point-segment / segment-segment distances; capsule ↔ box/convex reuse GJK via the capsule's exact support function.
• Mesh — arrives as the convex hull of its vertices and is checked with GJK (boolean origin-in-Minkowski-difference).

Penetration depth (EPA)

On overlap, CollisionModel::contacts runs EPA (the Expanding Polytope Algorithm) on top of GJK to recover a Contact for each colliding pair: a unit separation normal (the outward normal of the Minkowski difference), a penetration depth, and a witness point.

Honesty about coverage

The checker is re-derived-correct and, by construction, cannot under-report for the geometry it handles. But two things are called out explicitly:

• Colliders that cannot be reduced to the supported primitives (some mesh / capsule cases) are surfaced loudly via an uncovered_frames report rather than silently dropped — you always know what was not checked.
• The native Simulator has no collision; collision is only enforced where the SafetyCheck is wired in (the control/safety layer).