crx-kinematics

Forward and inverse kinematics for the FANUC CRX family of collaborative robots. These are Python bindings for the Rust crate crx-kinematics, and require only numpy.

The inverse kinematics is complete and direct. For a reachable flange pose it returns every joint configuration that reaches it, up to the sixteen this architecture allows, and it does so without seeding, sampling, or iterating toward a single answer. The method is derived in full in LINEAR_METHOD.md.

pip install crx-kinematics

import numpy as np
from crx_kinematics import Crx

robot = Crx.crx10ia()

# Forward: joint angles in controller degrees to a 4x4 flange pose.
target = robot.fk([10, -80, 10, 20, -20, 45])

# Inverse: every configuration that reaches the pose, as an (n, 6) array.
solutions = robot.ik(target)

# Or just the one nearest to where the arm already is.
best = robot.ik_closest(target, [0, 0, 0, 0, 0, 0])
print(np.round(best.joints, 6), best.residual, best.kind)

Joint angles are in degrees as the robot controller reports them, including the FANUC convention where the J3 value is measured against J2 rather than against the world. All six kinematically distinct models are available as Crx.crx3ia() through Crx.crx30ia(), and Crx.from_params builds a robot from the four link dimensions directly.

Poses cross the boundary as 4x4 NumPy arrays. A target may also be any object with an as_numpy() method returning one, which is how an engeom Iso3 can be passed straight through without either package depending on the other:

from engeom.geom3 import Iso3

solutions = robot.ik(Iso3.from_xyzwpr(600, 0, 700, 180, 0, 0))

ik returns joint angles only. ik_detailed returns the same solutions with the residual and the kind of configuration attached, and fk_all returns the pose of every frame in the chain.

Several configurations are mathematically degenerate, including the wrist center landing on the J1 axis, which an operator can enter directly and which defeats other implementations of this architecture. They are enumerated with their treatment in the derivation.

Link Meshes

The package carries visual geometry for the CRX-5iA and the CRX-10iA: seven triangle meshes each, covering the stationary base and the six moving links. Vertices are returned as an (n, 3) array of float64, and faces are returned as an (m, 3) array of uint32. Vertex coordinates are in millimeters.

from crx_kinematics import Crx, CrxModel, LinkMeshes

robot = Crx.crx10ia()
meshes = LinkMeshes.load(CrxModel.Crx10iA)

for link in meshes.posed(robot, [10, -80, 10, 20, -20, 45]):
    print(link.vertices.shape, link.faces.shape)

Index 0 contains the stationary base. Index i contains the link that moves with frame i - 1 of fk_all. The final mesh is the flange, whose mating face lies on the z = 0 plane of the pose reported by fk.

An engeom Mesh3 accepts these array shapes and data types, so drawing the robot requires no conversion:

from engeom.geom3 import Mesh3

drawable = [Mesh3(link.vertices, link.faces) for link in meshes.posed(robot, joints)]

LinkMeshes.load raises ValueError for the other four models. LinkMeshes.is_available checks whether geometry is present without raising an exception.

The interactive_ik.py example in examples combines the meshes with the solver. It draws the robot in a PyVista window and uses the keyboard to move the flange target. After every key press, it solves the inverse kinematics and moves the arm. The example requires engeom and pyvista in addition to this package.

License

Licensed under either of Apache License, Version 2.0 or MIT license at your option.

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