Inverse Kinematics (FABRIK)

Forward And Backward Reaching Inverse Kinematics solver operating on Actor.Bone chains.

File: ai4animation/IK/FABRIK.py

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Overview

FABRIK is an iterative IK algorithm that solves for joint positions along a bone chain to reach a target position and rotation. It works by alternating forward and backward passes along the chain, adjusting joint positions to satisfy distance constraints.

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API

Constructor

from ai4animation import FABRIK

ik = FABRIK(source_bone, target_bone)

Parameter	Type	Description
source_bone	Actor.Bone	Start of the bone chain (e.g., shoulder)
target_bone	Actor.Bone	End of the bone chain (e.g., wrist)

The constructor automatically builds the bone chain between the source and target bones.

Solve

ik.Solve(position, rotation, max_iterations=10, threshold=0.001)

Parameter	Type	Description
position	ndarray [3]	Target world position
rotation	ndarray [3, 3]	Target world rotation
max_iterations	int	Maximum solver iterations
threshold	float	Convergence distance threshold

Properties

Property	Type	Description
Bones	List[Actor.Bone]	The bone chain from source to target

Internal Methods

Method	Description
_backward_pass()	Adjusts positions from end-effector to root
_forward_pass()	Adjusts positions from root to end-effector
_assign()	Writes solved transforms back to bones

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Algorithm

1. Backward pass: Start at the target position, move each joint toward its parent while preserving bone lengths
2. Forward pass: Start at the root (fixed), move each joint toward its child while preserving bone lengths
3. Repeat until the end-effector is within the threshold distance of the target, or max iterations reached
4. Assign: Write the solved positions and rotations back to the actor's bones

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Example

From Demos/InverseKinematics/Program.py:

import os
from ai4animation import Actor, AI4Animation, FABRIK, Vector3


class Program:
    def Start(self):
        actor = AI4Animation.Scene.AddEntity("Actor")
        self.Actor = actor.AddComponent(
            Actor, os.path.join(ASSETS_PATH, "Model.glb"), bone_names
        )

        self.IK = FABRIK(
            self.Actor.GetBone("LeftShoulder"),
            self.Actor.GetBone("LeftWrist"),
        )

        self.Target = AI4Animation.Scene.AddEntity("Target")
        self.Target.SetPosition(
            self.Actor.GetBone("LeftWrist").GetPosition()
        )

        self.Pose = self.Actor.GetTransforms()

    def Update(self):
        self.Actor.SetTransforms(self.Pose)
        self.IK.Solve(
            self.Target.GetPosition(),
            self.Target.GetRotation(),
            max_iterations=10,
            threshold=0.001,
        )
        self.Actor.SyncToScene(self.IK.Bones)

    def GUI(self):
        self.Target.DrawHandle()


if __name__ == "__main__":
    AI4Animation(Program(), mode=AI4Animation.Mode.STANDALONE)

This creates a draggable target handle — moving it drives the left arm via IK in real-time.