Forward & Inverse Kinematics

This page shows how to compute the forward and inverse kinematics of FANUC industrial arms and CRX cobots with the Fanuc SDK, offline or with the controller. Inverse kinematics (IK) and forward kinematics (FK) let you move between joint space and Cartesian space. FK computes the tool pose from known joint angles, while IK finds joint angles for a desired pose. The kinematics utilities in the Fanuc SDK are offline helpers: you can evaluate poses and joint solutions without connecting to a controller, for simulation, path validation and checks before deployment.

Industrial arms and cobots

Two solvers

The SDK has two analytical solvers and chooses the right one:

• OPW industrial arms: Classical 6-axis Fanuc robots with an ortho-parallel base and spherical wrist, based on the paper An Analytical Solution of the Inverse Kinematics Problem of Industrial Serial Manipulators with an Ortho-parallel Basis and a Spherical Wrist by Mathias Brandstötter, Arthur Angerer, and Michael Hofbaur.
• CRX collaborative arms: Fanuc CRX cobots that have their own closed-form solver and optional dual solutions, based on paper Geometric Approach for Inverse Kinematics of the FANUC CRX Collaborative Robot by Manel Abbes and Gérard Poisson.

Choice of the solver

KinematicsUtils.InverseKinematics() reads DhParameters.KinematicsCategory:

• KinematicsCategory.Opw: it calls Opw.OpwKinematicsUtils.InverseKinematics (industrial robots).
• KinematicsCategory.Crx: it calls Crx.CrxKinematicsUtils.InverseKinematics (CRX cobots).

So one entry point covers every arm.

Offline kinematics

Run forward kinematics (FK)

static void Main()
{
// Load robot geometry
var dh = DhParameters.FromArmKinematicModel(ArmKinematicModels.CRX10iA);

// Joint angles in degrees (Fanuc convention)
var jointsDeg = new JointsPosition { J1 = 0, J2 = -30, J3 = 45, J4 = 0, J5 = 60, J6 = 90 };

// Compute pose: returns XYZ + WPR
CartesianPosition pose = KinematicsUtils.ForwardKinematics(jointsDeg, dh);
}
}

Solve inverse kinematics (IK) for an OPW robot

static void Main()
{
// OPW industrial robot
var dh = DhParameters.FromArmKinematicModel(ArmKinematicModels.ARCMate120iD);
var target = new CartesianPosition { X = 800, Y = 0, Z = 450, W = 180, P = 0, R = 90 };
JointsPosition[] solutions = KinematicsUtils.InverseKinematics(target, dh);

// CRX cobot with dual solutions
var dhCrx = DhParameters.FromArmKinematicModel(ArmKinematicModels.CRX10iAL);
var targetCrx = new CartesianPosition { X = 400, Y = 250, Z = 650, W = 0, P = 90, R = 0 };
JointsPosition[] crxSolutions = CrxKinematicsUtils.InverseKinematics(
    targetCrx, dhCrx,
    includeDuals: true
);
}
}

Solve inverse kinematics (IK) for a CRX cobot

The CRX solver uses a closed-form geometric approach and returns all valid joint solutions directly. No seed position is required. Pass includeDuals: true (C#) or include_duals=True (Python) to also include the dual configurations defined by the CRX kinematics.

using UnderAutomation.Fanuc.Common;
using UnderAutomation.Fanuc.Kinematics;
using UnderAutomation.Fanuc.Kinematics.Crx;

public class KinematicsIK
{
    static void Main()
    {
        
        // OPW industrial robot
        var dh = DhParameters.FromArmKinematicModel(ArmKinematicModels.ARCMate120iD);
        var target = new CartesianPosition { X = 800, Y = 0, Z = 450, W = 180, P = 0, R = 90 };
        JointsPosition[] solutions = KinematicsUtils.InverseKinematics(target, dh);

        // CRX cobot with dual solutions
        var dhCrx = DhParameters.FromArmKinematicModel(ArmKinematicModels.CRX10iAL);
        var targetCrx = new CartesianPosition { X = 400, Y = 250, Z = 650, W = 0, P = 90, R = 0 };
        JointsPosition[] crxSolutions = CrxKinematicsUtils.InverseKinematics(
            targetCrx, dhCrx,
            includeDuals: true
        );
        
    }
}

Build DH parameters from multiple sources

• Built-in catalog: DhParameters.FromArmKinematicModel(ArmKinematicModels model) gives the geometry of many Fanuc arms and cobots.
• ROBOGUIDE library: DhParameters.FromDefFile(path) parses robot definitions in ProgramData/FANUC/ROBOGUIDE/Robot Library.
• Controller variables: DhParameters.FromSymotnFile and DhParameters.FromMrrGrp convert live $MRR_GRP or symotn.va data to reusable DH structures.
• OPW data: DhParameters.FromOpwParameters maps OPW parameters (meters) to Fanuc-style DH while keeping the kinematics category consistent.

Tips

• Offline: the solvers need no controller and no connection.
• Pose normalization: OpwKinematicsUtils.InverseKinematics normalizes angles to (-180, 180] to match Fanuc expectations.
• CRX dual solutions: Pass includeDuals: true to CrxKinematicsUtils.InverseKinematics to include the additional configurations defined by the CRX kinematics model.
• Matrix helpers: KinematicsUtils.Mul multiplies 2D matrices if you need to compose transforms manually.

Kinematics on the controller

With a connection, the controller can compute the kinematics, without DH parameters. The controller keeps the joint and the Cartesian form of every position register. Write a position in one form with SNPX, then read the same register back to get the other form.

Forward kinematics using SNPX position registers

Write joint angles and read back the Cartesian pose:

FanucRobot _robot = new FanucRobot();
_robot.Connect("192.168.0.1");
// Forward kinematics via SNPX: joints → Cartesian
JointsPosition jointsPosition = new JointsPosition(10, 12, 50, 20, 12, 16);
_robot.Snpx.PositionRegisters.Write(1, jointsPosition);
CartesianPosition cartesianPosition = _robot.Snpx.PositionRegisters.Read(1).CartesianPosition;

// Inverse kinematics via SNPX: Cartesian → joints
CartesianPosition targetPosition = new CartesianPosition() { X = 100, Y = 100, Z = 100 };
targetPosition.Configuration.WristFlip = WristFlip.Flip;
targetPosition.Configuration.ArmUpDown = ArmUpDown.Down;
targetPosition.Configuration.ArmLeftRight = ArmLeftRight.Left;
_robot.Snpx.PositionRegisters.Write(1, targetPosition);
JointsPosition resultJoints = _robot.Snpx.PositionRegisters.Read(1).JointsPosition;
}
}

Inverse kinematics using SNPX position registers

Write a Cartesian pose and read back the joint angles. There is only one solution, because the Cartesian position contains the configuration.

Demonstration

Online 3D tool

fanuc-kinematics.underautomation.com is a 3D page to try the forward and inverse kinematics of the FANUC arms and cobots.

Demo application

Everything on this page can be tried without writing code, in the Forward & Invert Kinematics page of the demo application.

The demo application is open source. The C# source of this page is KinematicsControl.cs.

Reference