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UnilateralLagrangianConstraint

This component belongs to the category of Constraint Laws used for the Lagrange constraint resolution and inherits from the PairInteractionConstraint. The UnilateralLagrangianConstraint defines an non-holonomic constraint law between a pair of simulated body, i.e. the constraint defined between the pair of objects must have an inequality form:

\[ \Psi(x_1,x_2...)~\geq~0 \]

Such a constraint are used for friction-less and friction contact modeling (it can even be used as a starting point for puncture modeling). For a UnilateralLagrangianConstraint, the constraint matrix \(\mathbf{H}\) (derivative of the constraint law) corresponds to:

  • \(\mathbf{H}_1 = \begin{bmatrix} \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_0 & ... & \vec{n}_i & ... & \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_{N_1}\\ \end{bmatrix}\) for object 1
  • \(\mathbf{H}_1 = \begin{bmatrix} \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_0 & ... & \vec{n}_j & ... & \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_{N_2} \\ \end{bmatrix}\) for object 2

We can see from these matrices that the UnilateralLagrangianConstraint is a transformation towards the constraint space, by building a projection of any field against the contact direction (normal here, and possibly tangential directions as well if friction is defined).

As all constraint laws, the UnilateralLagrangianConstraint will be called in the following functions and for the following steps:

  • getConstraintViolation(): project the free velocity in the constraint space and compute the free interpenetration \(\dot{\delta}_1^{free}=\mathbf{H}_1v_1^{free}\)
  • buildConstraintMatrix(): build the compliance made up of \(dt\mathbf{H}_1\mathbf{A}_1^{-1}\mathbf{H}_1^T\) and \(dt\mathbf{H}_2\mathbf{A}_2^{-1}\mathbf{H}_2^T\)

Usage

The UnilateralLagrangianConstraint can only be used in the context of Lagrange constraint resolution. The scene must therefore contain:

  • a FreeMotionAnimationLoop
  • a ConstraintSolver

Moreover, each constrained object must define in its node a ConstraintCorrection so that the corrective motion can be applied. Unlike other constraints, the UnilateralLagrangianConstraint is mostly used in SOFA for contact modeling. UnilateralLagrangianConstraint are therefore dynamically and automatically created within the scene graph when two objects are colliding: when the CollisionPipeline defines new DetectionOutput with ContactResponse using Lagrange multipliers, each DetectionOutput generates a new UnilateralLagrangianConstraint.

Lagrangian-based inequality constraint

Vec3d

Templates:

  • Vec3d

Target: Sofa.Component.Constraint.Lagrangian.Model

namespace: sofa::component::constraint::lagrangian::model

parents:

  • PairInteractionConstraint

Data

Name Description Default value
name object name unnamed
printLog if true, emits extra messages at runtime. 0
tags list of the subsets the object belongs to
bbox this object bounding box
componentState The state of the component among (Dirty, Valid, Undefined, Loading, Invalid). Undefined
listening if true, handle the events, otherwise ignore the events 0
group ID of the group containing this constraint. This ID is used to specify which constraints are solved by which solver, by specifying in each solver which groups of constraints it should handle. 0
constraintIndex Constraint index (first index in the right hand term resolution vector) 0
endTime The constraint stops acting after the given value. Use a negative value for infinite constraints -1
Name Description Destination type name
context Graph Node containing this object (or BaseContext::getDefault() if no graph is used) BaseContext
slaves Sub-objects used internally by this object BaseObject
master nullptr for regular objects, or master object for which this object is one sub-objects BaseObject
mechanicalStates List of mechanical states to which this component is associated BaseMechanicalState
object1 First object associated to this component MechanicalState<Vec3d>
object2 Second object associated to this component MechanicalState<Vec3d>