(It uses Processing for the implementation.)
\u2615 Support my Work:) \/ Coffee Supplier on Patreon<\/a><\/strong><\/p>\n\n\n\n
Understanding FABRIK<\/strong><\/h2>\n\n\n\nFABRIK (Forward And Backward Reaching Inverse Kinematics) was proposed in 2011 by Andreas Aristidou and Joan Lasenby as a more intuitive and efficient alternative to traditional inverse kinematics methods. Instead of calculating joint angles, FABRIK moves each segment based on its distance to the target while maintaining segment lengths.<\/p>\n\n\n\n
How FABRIK Works<\/strong><\/h3>\n\n\n\n\n- Forward Reaching:<\/strong>
1. Move the end effector towards the target position.
2. Adjust each joint sequentially while preserving segment lengths.<\/li>\n\n\n\n- Backward Reaching:<\/strong>
1. Fix the root position.
2. Adjust the joints in reverse order to maintain segment lengths and refine alignment.<\/li>\n<\/ul>\n\n\n\nThese steps repeat until the end effector is close enough to the target.<\/p>\n\n\n\n
Comparison with Other Methods<\/strong><\/h3>\n\n\n\n\n- CCD (Cyclic Coordinate Descent):<\/strong> Adjusts each joint individually to get closer to the target. It\u2019s simple and fast but doesn\u2019t always guarantee smooth movement.<\/li>\n\n\n\n
- Jacobian Inverse Methods:<\/strong> Uses matrices to determine optimal movements. While effective, they require complex calculations and can be computationally expensive.<\/li>\n\n\n\n
- FABRIK:<\/strong> Intuitive, fast, and avoids complex matrix operations, making it ideal for real-time applications.<\/li>\n<\/ul>\n\n\n\n
Implementing FABRIK in Processing<\/strong><\/h2>\n\n\n\nHere\u2019s how to implement FABRIK in Processing step by step.<\/p>\n\n\n\n
1. Define the EndEffector Class<\/strong><\/h3>\n\n\n\nEach end effector represents a joint in the kinematic chain. It has a position and a fixed length, which ensures that movements adhere to the constraints of the system.<\/p>\n\n\n\n
\nclass EndEffector {\n\u00a0\u00a0\u00a0\u00a0\u00a0PVector pos;\n\u00a0\u00a0\u00a0\u00a0\u00a0float leng;\n\u00a0\u00a0\u00a0\u00a0\u00a0EndEffector(float x, float y, float len) {\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0pos = new PVector(x, y);\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0leng = len;\n\u00a0\u00a0\u00a0\u00a0\u00a0}\n}\n<\/code><\/pre>\n\n\n\n2. Initialize the End Effectors<\/strong><\/h3>\n\n\n\nWe create a list of end effectors, defining a chain of connected joints. The number of end effectors determines the flexibility of the system.<\/p>\n\n\n\n
\nArrayList effectors = new ArrayList<>();\nint numEffectors = 10;\n<\/code><\/pre>\n\n\n\n3. Forward Reaching<\/strong><\/h3>\n\n\n\nThe forward reaching step moves the end effector toward the target while keeping all segment lengths fixed.<\/p>\n\n\n\n
3-1. Set the end effector’s position to the target<\/strong>
Since the end effector is the last joint, we move it directly to the target position.<\/p>\n\n\n\n\nEndEffector endEffector = effectors.get(effectors.size() - 1);\nendEffector.pos = target.copy();\n<\/code><\/pre>\n\n\n\n![\"\"](\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\")
<\/figure>\n\n\n\n3-2. Move each joint toward the next one<\/strong>
We iterate backward from the second-to-last joint to the first. Each joint moves toward the next joint (closer to the target) while preserving its length.<\/p>\n\n\n\n\nfor (int i = effectors.size() - 2; i >= 0; i--) {\n EndEffector current = effectors.get(i);\n PVector direction = PVector.sub(endEffector.pos, current.pos); \/\/ Calculate direction\n direction.setMag(current.leng); \/\/ Set vector magnitude to match segment length\n current.pos = PVector.sub(endEffector.pos, direction); \/\/ Move joint to new position\n endEffector = current;\n}\n<\/code><\/pre>\n\n\n\nThe setMag(current.length)<\/a> method scales the vector to ensure that the joint moves exactly<\/strong> the correct distance while maintaining constraints.<\/p>\n\n\n\n4. Backward Reaching<\/strong><\/h3>\n\n\n\nAfter the forward reaching step, the root position may have moved. The backward reaching step restores the root to its original position while preserving segment lengths.<\/p>\n\n\n\n
4-1. Fix the root position<\/strong>
The root (first joint) remains fixed at its initial position.<\/p>\n\n\n\n\nEndEffector previous = effectors.get(0);\nprevious.pos = root;\n<\/code><\/pre>\n\n\n\n<\/figure>\n\n\n\n4-2. Move each joint forward<\/strong>
We iterate through the chain from the root toward the end effector, adjusting each joint while keeping segment lengths fixed.<\/p>\n\n\n\n\nfor (int i = 1; i < effectors.size(); i++) {\n\u00a0\u00a0\u00a0\u00a0\u00a0EndEffector current = effectors.get(i);\n\u00a0\u00a0\u00a0\u00a0\u00a0PVector direction = PVector.sub(current.pos, previous.pos); \/\/ Calculate direction\n\u00a0\u00a0\u00a0\u00a0\u00a0direction.setMag(previous.leng); \/\/ Maintain segment length\n\u00a0\u00a0\u00a0\u00a0\u00a0current.pos = PVector.add(previous.pos, direction); \/\/ Move joint to new position\n\u00a0\u00a0\u00a0\u00a0\u00a0previous = current;\n}\n<\/code><\/pre>\n\n\n\nThis step ensures that the chain remains connected and respects length constraints while aligning properly with the root.<\/p>\n\n\n\n
5. Visualizing the End Effectors<\/strong><\/p>\n\n\n\nWe draw lines between end effectors to visualize the kinematic chain and observe its movement in real-time.<\/p>\n\n\n\n
\nfor (int i = 0; i < effectors.size() - 1; i++) {\n\u00a0\u00a0\u00a0\u00a0\u00a0PVector current = effectors.get(i).pos;\n\u00a0\u00a0\u00a0\u00a0\u00a0PVector next = effectors.get(i + 1).pos;\n\u00a0\u00a0\u00a0\u00a0\u00a0line(current.x, current.y, next.x, next.y);\n}\n<\/code><\/pre>\n\n\n\nFinal Thoughts<\/strong><\/h3>\n\n\n\nFABRIK is a simple yet efficient algorithm for inverse kinematics, making it a great choice for real-time applications. You can extend this implementation by adding constraints for joint rotation or adapting it to work in 3D.<\/p>\n\n\n\n
\n- If you need the complete code, it is available for download in the attached file on Patreon<\/a>.<\/strong><\/li>\n\n\n\n
- For a deeper dive into the theory behind FABRIK, check out the research paper \"FABRIK: A fast, iterative solver for the Inverse Kinematics problem\" by Andreas Aristidou and Joan Lasenby.<\/strong><\/li>\n<\/ul>\n\n\n\n
<\/p>\n\n\n\n
Recommended Book<\/em><\/h2>\n\n\n\n
- \n
- Forward Reaching:<\/strong>
1. Move the end effector towards the target position.
2. Adjust each joint sequentially while preserving segment lengths.<\/li>\n\n\n\n- Backward Reaching:<\/strong>
1. Fix the root position.
2. Adjust the joints in reverse order to maintain segment lengths and refine alignment.<\/li>\n<\/ul>\n\n\n\nThese steps repeat until the end effector is close enough to the target.<\/p>\n\n\n\n
Comparison with Other Methods<\/strong><\/h3>\n\n\n\n
- \n
- CCD (Cyclic Coordinate Descent):<\/strong> Adjusts each joint individually to get closer to the target. It\u2019s simple and fast but doesn\u2019t always guarantee smooth movement.<\/li>\n\n\n\n
- Jacobian Inverse Methods:<\/strong> Uses matrices to determine optimal movements. While effective, they require complex calculations and can be computationally expensive.<\/li>\n\n\n\n
- FABRIK:<\/strong> Intuitive, fast, and avoids complex matrix operations, making it ideal for real-time applications.<\/li>\n<\/ul>\n\n\n\n
Implementing FABRIK in Processing<\/strong><\/h2>\n\n\n\n
Here\u2019s how to implement FABRIK in Processing step by step.<\/p>\n\n\n\n
1. Define the EndEffector Class<\/strong><\/h3>\n\n\n\n
Each end effector represents a joint in the kinematic chain. It has a position and a fixed length, which ensures that movements adhere to the constraints of the system.<\/p>\n\n\n\n
\nclass EndEffector {\n\u00a0\u00a0\u00a0\u00a0\u00a0PVector pos;\n\u00a0\u00a0\u00a0\u00a0\u00a0float leng;\n\u00a0\u00a0\u00a0\u00a0\u00a0EndEffector(float x, float y, float len) {\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0pos = new PVector(x, y);\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0leng = len;\n\u00a0\u00a0\u00a0\u00a0\u00a0}\n}\n<\/code><\/pre>\n\n\n\n2. Initialize the End Effectors<\/strong><\/h3>\n\n\n\n
We create a list of end effectors, defining a chain of connected joints. The number of end effectors determines the flexibility of the system.<\/p>\n\n\n\n
\nArrayListeffectors = new ArrayList<>();\nint numEffectors = 10;\n<\/code><\/pre>\n\n\n\n 3. Forward Reaching<\/strong><\/h3>\n\n\n\n
The forward reaching step moves the end effector toward the target while keeping all segment lengths fixed.<\/p>\n\n\n\n
3-1. Set the end effector’s position to the target<\/strong>
Since the end effector is the last joint, we move it directly to the target position.<\/p>\n\n\n\n\nEndEffector endEffector = effectors.get(effectors.size() - 1);\nendEffector.pos = target.copy();\n<\/code><\/pre>\n\n\n\n<\/figure>\n\n\n\n3-2. Move each joint toward the next one<\/strong>
We iterate backward from the second-to-last joint to the first. Each joint moves toward the next joint (closer to the target) while preserving its length.<\/p>\n\n\n\n\nfor (int i = effectors.size() - 2; i >= 0; i--) {\n EndEffector current = effectors.get(i);\n PVector direction = PVector.sub(endEffector.pos, current.pos); \/\/ Calculate direction\n direction.setMag(current.leng); \/\/ Set vector magnitude to match segment length\n current.pos = PVector.sub(endEffector.pos, direction); \/\/ Move joint to new position\n endEffector = current;\n}\n<\/code><\/pre>\n\n\n\nThe setMag(current.length)<\/a> method scales the vector to ensure that the joint moves exactly<\/strong> the correct distance while maintaining constraints.<\/p>\n\n\n\n
4. Backward Reaching<\/strong><\/h3>\n\n\n\n
After the forward reaching step, the root position may have moved. The backward reaching step restores the root to its original position while preserving segment lengths.<\/p>\n\n\n\n
4-1. Fix the root position<\/strong>
The root (first joint) remains fixed at its initial position.<\/p>\n\n\n\n\nEndEffector previous = effectors.get(0);\nprevious.pos = root;\n<\/code><\/pre>\n\n\n\n<\/figure>\n\n\n\n4-2. Move each joint forward<\/strong>
We iterate through the chain from the root toward the end effector, adjusting each joint while keeping segment lengths fixed.<\/p>\n\n\n\n\nfor (int i = 1; i < effectors.size(); i++) {\n\u00a0\u00a0\u00a0\u00a0\u00a0EndEffector current = effectors.get(i);\n\u00a0\u00a0\u00a0\u00a0\u00a0PVector direction = PVector.sub(current.pos, previous.pos); \/\/ Calculate direction\n\u00a0\u00a0\u00a0\u00a0\u00a0direction.setMag(previous.leng); \/\/ Maintain segment length\n\u00a0\u00a0\u00a0\u00a0\u00a0current.pos = PVector.add(previous.pos, direction); \/\/ Move joint to new position\n\u00a0\u00a0\u00a0\u00a0\u00a0previous = current;\n}\n<\/code><\/pre>\n\n\n\nThis step ensures that the chain remains connected and respects length constraints while aligning properly with the root.<\/p>\n\n\n\n
5. Visualizing the End Effectors<\/strong><\/p>\n\n\n\n
We draw lines between end effectors to visualize the kinematic chain and observe its movement in real-time.<\/p>\n\n\n\n
\nfor (int i = 0; i < effectors.size() - 1; i++) {\n\u00a0\u00a0\u00a0\u00a0\u00a0PVector current = effectors.get(i).pos;\n\u00a0\u00a0\u00a0\u00a0\u00a0PVector next = effectors.get(i + 1).pos;\n\u00a0\u00a0\u00a0\u00a0\u00a0line(current.x, current.y, next.x, next.y);\n}\n<\/code><\/pre>\n\n\n\nFinal Thoughts<\/strong><\/h3>\n\n\n\n
FABRIK is a simple yet efficient algorithm for inverse kinematics, making it a great choice for real-time applications. You can extend this implementation by adding constraints for joint rotation or adapting it to work in 3D.<\/p>\n\n\n\n
- \n
- If you need the complete code, it is available for download in the attached file on Patreon<\/a>.<\/strong><\/li>\n\n\n\n
- For a deeper dive into the theory behind FABRIK, check out the research paper \"FABRIK: A fast, iterative solver for the Inverse Kinematics problem\" by Andreas Aristidou and Joan Lasenby.<\/strong><\/li>\n<\/ul>\n\n\n\n
<\/p>\n\n\n\n
Recommended Book<\/em><\/h2>\n\n\n\n
- For a deeper dive into the theory behind FABRIK, check out the research paper \"FABRIK: A fast, iterative solver for the Inverse Kinematics problem\" by Andreas Aristidou and Joan Lasenby.<\/strong><\/li>\n<\/ul>\n\n\n\n
- Jacobian Inverse Methods:<\/strong> Uses matrices to determine optimal movements. While effective, they require complex calculations and can be computationally expensive.<\/li>\n\n\n\n
- Backward Reaching:<\/strong>
![\"\"](\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2025\/03\/01Forward.webp\")
<\/figure>\n\n\n\n![\"\"](\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2025\/03\/02Backward.webp\")
<\/figure>\n\n\n\n![\"Grid-Systems-Raster-Systeme\"](\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2023\/06\/Grid-Systems-Raster-Systeme.webp\")
<\/figure>\n\n\n\n![\"\"](\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/07\/240801_bandcamp-top-BGD_SOUNDS.webp\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"