Closed Chain Inverse Kinematics

A generalized inverse kinematics solver that supports closed chains for parallel kinematics systems, dynamic reconfiguration, and arbitrary joint configuration based on damped least squares error minimization techniques. Supports all variety of joints including combinations of rotation and translation degrees of freedom and is agnostic to visualization framework. Inspired by Marty Vona's MSim research work and using techniques outlined in this 2009 paper by Samuel Buss. Developed with some aid and advice from Marty Vona.

Solver being used on JPL's ATHLETE robot for full body IK

Examples

Hexapod demo here!

ATHLETE and Robonaut demo here!

Rover mobility settling demo here!

VR demo here!

Partial degrees of freedom Goal demo here!

Model License Information

Robitics models used in the project are for demonstration purposes only and subject to the licenses of their respective projects.

ATHLETE

Robonaut

Curiosity

Perseverance

Staubli

PI Hexapod

Use

Simple 2 DoF System

import { Solver, Joint, Link, Goal, DOF } from 'closed-chain-ik';

// Create links and joints
const link1 = new Link();

const joint1 = new Joint();
joint.setDoF( DOF.EZ );
joint.setPosition( 0, 1, 0 );
joint.setDoFValues( Math.PI / 4 );

const link2 = new Link();

const joint2 = new Joint();
joint.setDoF( DOF.EX );
joint.setPosition( 0, 1, 0 );
joint.setDoFValues( Math.PI / 4 );

const link3 = new Link();
link3.setPosition( 0, 1, 0 );

// Create the goal
const goal = new Goal();
link3.getWorldPosition( goal.position );
link3.getWorldQuaternion( goal.quaternion );

// Create structure
link1.addChild( joint1 );
joint1.addChild( link2 );
link2.addChild( joint2 );
joint2.addChild( link3 );

goal.makeClosure( link3 );

// create solver
const solver = new Solver( link1 );

// ...

// move the goal around and solve
solver.solve();

Using a WebWorker Solver

import { WorkerSolve, Joint, Link, Goal, DOF } from 'closed-chain-ik';

// ... instantiate kinematic system...

const solver = new WorkerSolver( link1 );

// ...

// move the goal around and solve asynchronously
solver.solve();

Caveats

• The web worker implementation uses ShareArrayBuffers which are not available on some platforms (Safari, Chrome for Android). See issue #44.

• Smoothing out 3DoF non closure ball joint behavior is in progress. See issue #22.

• Enabling SVD on the Solver can cause divergence on solvable systems and stutter. See #76.

API

Constants

DOF

Enumerated fields representing different degrees of freedom for Joints.

// Translation DoF
DOF.X, DOF.Y, DOF.Z,

// Euler Rotation DoF
DOF.EX, DOF.EY, DOF.EZ,

DOF_NAMES

An array of strings representing the names of the above degrees of freedom.

SOLVE_STATUS

Enumerated fields representing the state of a solve result.

// Error for all goals are within
// the threshold.
SOLVE_STATUS.CONVERGED,

// Error for the goals has begun
// to diverge.
SOLVE_STATUS.DIVERGED,

// Resulting angles has not changed
// significantly enough to reach the
// stall threshold.
SOLVE_STATUS.STALLED,

// The solve has reached the maximum
// number of allowed iterations.
SOLVE_STATUS.TIMEOUT,

SOLVE_STATUS_NAMES

An array of strings representing the names of the above solve statuses.

Functions

Set of utility functions including some for creating an ik system from and working with results from URDFLoader.

findRoots

findRoots( frames : Array<Frame> ) : Array<Frame>

Takes an array of frames to traverse including the closure joints and links and finds a set of unique nodes to treat as the roots of the connected trees for use in solving.

urdfRobotToIKRoot

urdfRobotToIKRoot( robot : URDFRobot, trimUnused : Boolean = false ) : Joint

Generates an IK three based on the provided URDFRobot with the root joint having a all 6 degrees of freedom set. Returns the root joint. If trimUnused is true then any dangling links that do not connect to non-fixed joints will be removed from the system.

setUrdfFromIK

setUrdfFromIK( robot : URDFRobot, ikRoot : Joint ) : void

Copies the joint values from robot onto ikRoot based on joint names.

setIKFromUrdf

setIKFromUrdf( ikRoot : Joint, robot : URDFRobot ) : void

Copies the joint values from ikRoot onto robot based on joint names.

Frame

A base class for Link, Joint, and Goal representing a frame defined by a position and rotation in space.

.position

position : Float32Array[ 3 ]

The position of the frame. If this is modified directly setMatrixNeedsUpdate() must be called.

.quaternion

quaternion : Float32Array[ 4 ]

The orientation of the frame. If this is modified directly setMatrixNeedsUpdate() must be called.

.matrix

readonly matrix : Float32Array[ 16 ]

The local transform matrix composed from the position and quaternion.

.matrixWorld

readonly matrixWorld : Float32Array[ 16 ]

The world transform matrix computed based on the parent matrixWorld and this local matrix.

.parent

readonly parent : Frame

The parent frame this frame is a child of.

.children

readonly children : Array<Frame>

The set of child frames this frame is a parent of.

.setPosition

setPosition( x : Number, y : Number, z : Number ) : void

Sets the position of the frame.

.setWorldPosition

setWorldPosition( x : Number, y : Number, z : Number ) : void

Sets the positon of the frame in world space. Automatically computes the local position relative to the parent.

.getWorldPosition

getWorldPosition( target : FloatArray[ 3 ] ) : void

Gets the position of the frame in the world in the target argument.

.setQuaternion

setQuaternion( x : Number, y : Number, z : Number, w : Number ) : void

Sets the orientation of the frame.

.setWorldQuaternion

setWorldQuaternion( x : Number, y : Number, z : Number, w : Number ) : void

Sets the orientation of the frame in world space. Automatically computes the local orientation relative to the parent.

.getWorldQuaternion

getWorldQuaternion( target : FloatArray[ 4 ] ) : void

Gets the quaternion of the frame in the world in the target argument.

.traverseParents

traverseParents( callback : ( parent : Frame ) => Boolean ) : void

Fires the given callback for every parent starting with the closest. If callback returns true then the traversal is stopped.

.traverse

traverse( callback : ( child : Frame ) => Boolean ) : void

Fires the given callback for every child recursively in breadth first order. If callback returns true then the traversal is stopped.

.addChild

addChild( child : Frame ) : void

Adds a child to this frame and sets the childs parent to this frame. Throws an error if the child already has a parent.

.removeChild

removeChild( child : Frame ) : void

Removes the given child from this frame. Throws an error if the given frame is not a child of this frame.

.attachChild

attachChild( child : Frame ) : void

Adds the given frame as a child of this frame while preserving the world position of the child.

.detachChild

detachChild( child : Frame ) : void

Removes the given frame as a child of this frame while preserving the world position of the child.

.updateMatrix

updateMatrix() : void

Updates the local .matrix field if it needs to be updated.

.updateMatrixWorld

updateMatrixWorld( includeChildren : Boolean = false ) : void

Updates the local .matrix and .worldMatrix fields if they need to be updated. Ensures parent matrices are up to date.

.setMatrixNeedsUpdate

setMatrixNeedsUpdate() : void

Flags this frame as needing a matrix and matrix world update.

.setMatrixWorldNeedsUpdate

setMatrixNeedsUpdate() : void

Flags this frame and all its children as needing a matrix world update.

Link

extends Frame

A Frame modeling a fixed connection between two Joints. Only Joints may be added as children.

.closureJoints

closureJoints : Array<Joint>

The set of joints that are connected to this indirectly via Joint.makeClosure.

Joint

extends Frame

A dynamic Frame representing a kinematic joint arbitrarily defineable degrees of freedom. A degree of freedom indicates an offset value can be set. Only Links may be added as children and a Joint may only have a single child.

.child

readonly child : Link = null

Reference to the joint child.

.isClosure

readonly isClosure : Boolean = false

Whether or not the child relationship is a closure or not.

.dof

readonly dof : Array<DOF>

A list of all the free degrees of freedom.

.dofFlags

readonly dofFlags : Uint8Array[6]

A list of 0 and 1 flags with 1 corresonding to a field in dof.

.dofValues

readonly dofValues : Float32Array[6]

The current joint values for all joint degrees of freedom.

.dofTarget

readonly dofTarget : Float32Array[6]

The joint value targets for each degree of freedom. Solver will attempt to solve for these targets if targetSet is true.

.dofRestPose

readonly dofRestPose : Float32Array[6]

The rest pose for each joint degree of freedom. Solver will attempt to move the joint towards this position when it does not compromise solving for the other goals and when restPoseSet is true.

.minDoFLimit

readonly minDoFLimit : Float32Array[6]

The minimum value limits for each joint degree of freeom.

.maxDoFLimit

readonly maxDoFLimit : Float32Array[6]

The maximum value limits for each joint degree of freeom.

.matrixDoF

readonly matrixDoF : Float32Array[16]

The matrix representing the transformation offset due to the current joint values.

.targetSet

targetSet : Boolean = false

When set to true Solver will try to move this joints dofValues towards the target values.

.restPoseSet

restPoseSet : Boolean = false

When set to true Solver will try to move this joints dofValues towards the rest pose values without compromising the other goals.

.setDoF

setDoF( ...dof : Array<DOF> ) : void

Sets the degrees of freedom of the joint. Arguments must be passed in X, Y, Z, EX, EY, EZ order without duplicate values. All relatd degree of freedom values are reset.

.clearDoF

clearDoF() : void

Clears all degrees of freedom.

.set[ * ]Values

setDoFValues( ...values : Array<Number> ) : void;
setRestPoseValues( ...values : Array<Number> ) : void;
setTargetValues( ...values : Array<Number> ) : void;
setMinLimits( ...values : Array<Number> ) : void;
setMaxLimits( ...values : Array<Number> ) : void;

The number of arguments must match the number of degrees of freedom of the joint.

.set[ * ]Value

setDoFValue( dof : DOF, value : Number ) : Boolean
setRestPoseValue( dof : DOF, value : Number ) : Boolean
setTargetValue( dof : DOF, value : Number ) : Boolean
setMinLimit( dof : DOF, value : Number ) : Boolean
setMaxLimit( dof : DOF, value : Number ) : Boolean

.get[ * ]Value

getDoFValue( dof : DOF ) : Number
getRestPoseValue( dof : DOF ) : Number
getTargetValue( dof : DOF ) : Number
getMinLimit( dof : DOF ) : Number
getMaxLimit( dof : DOF ) : Number

.makeClosure

makeClosure( child : Link ) : void

Declares the relationship between this joint and the given child link is a closure meaning there is no direct parent child relationship but the Solver will treat the closure link as a target for this joint to keep them closed.

Note that when making a closure connection between a Joint and a Link the link will not be added to the Joints children array and instead will only be available on the child field. The Joint will be appended to the Links closureJoints array.

Goal

extends Joint

A Frame representing a goal to achieve for a connected Link. Set degrees of freedom represent fixed goals for a link to achieve as opposed to moveable degrees of freedom defined for Joints. A goal cannot have children and only be used to make a closure.

Solver

Class for solving the closure and target joint constraints of a sytem. As well as the listed fields a set of "options" are set on the object which are listed here:

// Whether or not to use the SVD when calculating the pseudo inverse of the jacobian
// which can result in a more numerically stable calculation. If the SVD cannot be calculated
// then the transpose method is used.
useSVD = true;

// The max amount of iterations to try to solve for. The solve will terminate
// with SOLVE_STATUS.TIMEOUT if this limit is exceeded.
maxIterations = 5;

// The threshold under which a joint is not considered to have really moved. If
// no joint is moved more than this threshold then the solve will terminate with
// SOLVE_STATUS.STALLED.
stallThreshold = 1e-4;

// The threshold for comparing how much error has changed between solve iterations.
// If the error has grown by more than this threshold then the solve will terminate
// with SOLVE_STATUS.DIVERGED.
divergeThreshold = 0.01;

// The fixed damping factor to use in the DLS calculation.
dampingFactor = 0.001;

// The factor with which to move the joints towards the rest pose if set.
restPoseFactor = 0.01;

// The thresholds with which to compute whether or not the translation or rotation
// goals have been met. If the error between target and goal is under these
// thresholds then the solve will terminate with SOLVE_STATUS.CONVERGED.
translationConvergeThreshold = 1e-3;
rotationConvergeThreshold = 1e-5;

// Factors to apply to the translation and rotation error in the error vector.
// Useful for weighting rotation higher than translation if they do not seem to
// be solved "evenly". Values are expected to be in the range [ 0, 1 ].
translationFactor = 1;
rotationFactor = 1;

// The amount to move a joint when calculating the change in error a joint has
// for a jacobian.
translationStep = 1e-3;
rotationStep = 1e-3;

// The step to take towards the IK goals when solving. Setting this to a larger value
// may solve more quickly but may lead also lead to divergence.
translationErrorClamp = 0.1;
rotationErrorClamp = 0.1;

.roots

roots : Array<Frame>

The list of roots that should be accounted for in a solve. When .updateStructure is called the series of roots are traversed including closure joints to find all connected link hierarchies to use in the solve.

.constructor

constructor( roots : Array<Frame> )

Constructor takes a list of roots to solve for.

.solve

solve() : Array<SOLVE_STATUS>

Traverses the given set of roots to find joint chains to solve for and attempts to solve for the error in the system goals. A result is returned for each independent chain found in the system.

.updateStructure

updateStructure() : void

Must be called whenever parent child relationships and structural changes related to the tree change or .roots is modified.

WorkerSolver

Implements the interface defined by Solver but runs the solve asynchronously on in a WebWorker. Results are automatically copied to the joint system being solved for.

⚠️ When SharedArrayBuffers are not available new copies of ArrayBuffer are created every update and from the worker.

.results

results : Array<Solve_STATUS>

The list of the last results from the solve copied over from the WebWorker.

.updateSolverSettings

updateSolverSettings( settings : Object ) : void

Sets the solver settings in the WebWorker to the values in the given object. Valid "options" values are listed in the Solver docs.

.updateFrameState

updateFrameState( ...jointsToUpdate : Array<Joint> = [] ) : void

Copies the joint settings for the given joints to the WebWorker for a solve. "Joint settings" include everything except for joint values (that the solver would be solving for) and parent child relationships. If joint values or parent child relationhips change then updateStructure must be called.

.solve

solve() : void

Starts a solve in the WebWorker if one is not active. The solve will terminate automatically if none of the results are SOLVE_STATUS.TIMEOUT.

.stop

stop() : void

Terminate any active solve in the WebWorker.

.dispose

dispose() : void

Terminates the WebWorker and sets members to null.

IKRootsHelper

extends THREE.Group

A helper class for rendering the joints and links in a three.js scene. Renders frame relationships as lines and joints degrees of freedom with indicators based on the joint type.

.roots

roots : Array<Frame>

Set of roots to render in the helper visualization. If this is changed then .updateStructure must be called.

.constructor

constructor( roots : Array<Frame> )

Takes the set of roots to visualize.

.setJointScale

setJointScale( scale : Number ) : this

Sets the scale of the joint indicators.

.setColor

setColor( color : Color | String | Number ) : this

Sets the color of the helper.

.setDrawThrough

setDrawThrough( drawThrough : Boolean ) : this

Sets whether the helper will draw through the environment.

.setResolution

setResolution( width : Number, height : Number ) : this

Sets the resolution of the renderer so the 2d lines can be rendered at the appropriate thickness.

.updateStructure

updateStructure() : void

Must be called if the structure of the IK system being visualized has changed.

.dispose

dispose() : void

Calls dispose on all created materials and geometry in the tree.