Namespaces
	benchmarks

	constraint

	hydroelastics

	test

	test_utilities

Classes
struct	AddMultibodyPlantSceneGraphResult
	Temporary result from `AddMultibodyPlantSceneGraph`. More...

class	AngleBetweenVectorsConstraint
	Constrains that the angle between a vector `a` and another vector `b` is between [θ_lower, θ_upper]. More...

class	ArticulatedBodyInertia
	Articulated Body Inertia is the inertia that a body appears to have when it is the base (or root) of a rigid-body system, also referred to as Articulated Body in the context of articulated body algorithms. More...

class	BallRpyJoint
	This Joint allows two bodies to rotate freely relative to one another. More...

class	Body
	Body provides the general abstraction of a body with an API that makes no assumption about whether a body is rigid or deformable and neither does it make any assumptions about the underlying physical model or approximation. More...

class	BodyFrame
	A BodyFrame is a material Frame that serves as the unique reference frame for a Body. More...

class	ContactResults
	A container class storing the contact results information for each contact pair for a given state of the simulation. More...

class	ContactResultsToLcmSystem
	A System that encodes ContactResults into a lcmt_contact_results_for_viz message. More...

struct	ContactWrench
	Stores the contact wrench (spatial force) from Body A to Body B applied at point Cb. More...

class	ContactWrenchEvaluator

class	ContactWrenchFromForceInWorldFrameEvaluator
	The contact wrench is τ_AB_W = 0, f_AB_W = λ Namely we assume that λ is the contact force from A to B, applied directly at B's witness point. More...

class	CoulombFriction
	Parameters for Coulomb's Law of Friction, namely: More...

class	DistanceConstraint
	Constrains the distance between a pair of geometries to be within a range [distance_lower, distance_upper]. More...

class	DoorHinge
	This ForceElement models a revolute DoorHinge joint that could exhibit different force/torque characteristics at different states due to the existence of different type of torques on the joint. More...

struct	DoorHingeConfig
	Configuration structure for the DoorHinge. More...

struct	ExternallyAppliedSpatialForce

class	FixedOffsetFrame
	FixedOffsetFrame represents a material frame F whose pose is fixed with respect to a parent material frame P. More...

class	ForceElement
	A ForceElement allows modeling state and time dependent forces in a MultibodyTree model. More...

class	Frame
	Frame is an abstract class representing a material frame (also called a physical frame), meaning that it is associated with a material point of a Body. More...

class	FrameBase
	FrameBase is an abstract representation of the concept of a frame in multibody dynamics. More...

class	GaussianTriangleQuadratureRule

class	GazeTargetConstraint
	Constrains a target point T to be within a cone K. More...

class	HydroelasticContactInfo
	A class containing information regarding contact and contact response between two geometries attached to a pair of bodies. More...

struct	HydroelasticQuadraturePointData
	Results from intermediate calculations used during the quadrature routine. More...

class	InverseKinematics
	Solves an inverse kinematics (IK) problem on a MultibodyPlant, to find the postures of the robot satisfying certain constraints. More...

class	Joint
	A Joint models the kinematical relationship which characterizes the possible relative motion between two bodies. More...

class	JointActuator
	The JointActuator class is mostly a simple bookkeeping structure to represent an actuator acting on a given Joint. More...

class	LinearBushingRollPitchYaw
	This ForceElement models a massless flexible bushing that connects a frame A of a link (body) L0 to a frame C of a link (body) L1. More...

class	LinearSpringDamper
	This ForceElement models a spring-damper attached between two points on two different bodies. More...

class	ManipulatorEquationConstraint
	A Constraint to impose the manipulator equation: 0 = (Buₙ₊₁ + ∑ᵢ (Jᵢ_WBᵀ(qₙ₊₁)ᵀ * Fᵢ_AB_W(λᵢ,ₙ₊₁)) More...

class	MinimumDistanceConstraint
	Constrain the signed distance between all candidate pairs of geometries (according to the logic of SceneGraphInspector::GetCollisionCandidates()) to be no smaller than a specified minimum distance. More...

class	MultibodyElement
	A class representing an element (subcomponent) of a MultibodyPlant or (internally) a MultibodyTree. More...

class	MultibodyForces
	A class to hold a set of forces applied to a MultibodyTree system. More...

class	MultibodyPlant
	MultibodyPlant is a Drake system framework representation (see systems::System) for the model of a physical system consisting of a collection of interconnected bodies. More...

class	MultibodyPlantTester

class	OrientationConstraint
	Constrains that the angle difference θ between the orientation of frame A and the orientation of frame B to satisfy θ ≤ θ_bound. More...

class	PackageMap
	Maps ROS package names to their full path on the local file system. More...

class	Parser
	Parses SDF and URDF input files into a MultibodyPlant and (optionally) a SceneGraph. More...

class	PointPairContactInfo
	A class containing information regarding contact response between two bodies including: More...

class	PointToPointDistanceConstraint
	Constrain that the distance between a point P1 on frame B1 and another point P2 on frame B2 is within a range [distance_lower, distance_upper]. More...

class	PositionConstraint
	Constrains the position of a point Q, rigidly attached to a frame B, to be within a bounding box measured and expressed in frame A. More...

class	PrismaticJoint
	This Joint allows two bodies to translate relative to one another along a common axis. More...

class	Propeller
	A System that connects to the MultibodyPlant in order to model the effects of one or more controlled propellers acting on a Body. More...

struct	PropellerInfo
	Parameters that describe the kinematic frame and force-production properties of a single propeller. More...

class	RevoluteJoint
	This Joint allows two bodies to rotate relatively to one another around a common axis. More...

class	RevoluteSpring
	This ForceElement models a torsional spring attached to a RevoluteJoint and applies a torque to that joint. More...

class	RigidBody
	The term rigid body implies that the deformations of the body under consideration are so small that they have no significant effect on the overall motions of the body and therefore deformations can be neglected. More...

class	RotationalInertia
	This class describes the mass distribution (inertia properties) of a body or composite body about a particular point. More...

struct	SignedDistanceWithTimeDerivative
	The struct containing the signed distance and its time derivative between a pair of geometries. More...

class	SpatialAcceleration
	This class is used to represent a spatial acceleration that combines rotational (angular acceleration) and translational (linear acceleration) components. More...

class	SpatialForce
	This class is used to represent a spatial force (also called a wrench) that combines both rotational (torque) and translational force components. More...

class	SpatialInertia
	This class represents the physical concept of a Spatial Inertia. More...

class	SpatialMomentum
	This class is used to represent the spatial momentum of a particle, system of particles or body (whether rigid or soft.) The linear momentum `l_NS` of a system of particles S in a reference frame N is defined by: More...

class	SpatialVector
	This class is used to represent physical quantities that correspond to spatial vectors such as spatial velocities, spatial accelerations and spatial forces. More...

class	SpatialVelocity
	This class is used to represent a spatial velocity (also called a twist) that combines rotational (angular) and translational (linear) velocity components. More...

class	StaticEquilibriumConstraint
	Impose the static equilibrium constraint 0 = τ_g + Bu + ∑J_WBᵀ(q) * Fapp_B_W. More...

class	StaticEquilibriumProblem
	Finds the static equilibrium pose of a multibody system through optimization. More...

class	StaticFrictionConeConstraint
	Formulates the nonlinear friction cone constraint \|fₜ\| ≤ μ*fₙ, where fₜ is the tangential contact force, fₙ is the normal contact force, and μ is the friction coefficient. More...

class	TamsiSolver

struct	TamsiSolverIterationStats
	Struct used to store information about the iteration process performed by TamsiSolver. More...

struct	TamsiSolverParameters
	These are the parameters controlling the iteration process of the TamsiSolver solver. More...

class	TriangleQuadrature
	A class for integrating a function using numerical quadrature over triangular domains. More...

class	TriangleQuadratureRule
	A "rule" (weights and quadrature points) for computing quadrature over triangular domains. More...

class	UniformGravityFieldElement
	This ForceElement allows modeling the effect of a uniform gravity field as felt by bodies on the surface of the Earth. More...

class	UnitInertia
	This class is used to represent rotational inertias for unit mass bodies. More...

class	UniversalJoint
	This joint models a universal joint allowing two bodies to rotate relative to one another with two degrees of freedom. More...

class	WeldJoint
	This Joint fixes the relative pose between two frames as if "welding" them together. More...

Typedefs
using	MinimumDistancePenaltyFunction = solvers::MinimumValuePenaltyFunction
	Computes the penalty function φ(x) and its derivatives dφ(x)/dx. More...

using	FrameIndex = TypeSafeIndex< class FrameTag >
	Type used to identify frames by index in a multibody tree system. More...

using	BodyIndex = TypeSafeIndex< class BodyTag >
	Type used to identify bodies by index in a multibody tree system. More...

using	ForceElementIndex = TypeSafeIndex< class ForceElementTag >
	Type used to identify force elements by index within a multibody tree system. More...

using	JointIndex = TypeSafeIndex< class JointElementTag >
	Type used to identify joints by index within a multibody tree system. More...

using	JointActuatorIndex = TypeSafeIndex< class JointActuatorElementTag >
	Type used to identify actuators by index within a multibody tree system. More...

using	ModelInstanceIndex = TypeSafeIndex< class ModelInstanceTag >
	Type used to identify model instances by index within a multibody tree system. More...

Enumerations
enum	ContactModel { kHydroelasticsOnly, kPointContactOnly, kHydroelasticWithFallback }
	Enumeration for contact model options. More...

enum	TamsiSolverResult { kSuccess = 0, kMaxIterationsReached = 1, kLinearSolverFailed = 2 }
	The result from TamsiSolver::SolveWithGuess() used to report the success or failure of the solver. More...

enum	JacobianWrtVariable { kQDot, kV }
	Enumeration that indicates whether the Jacobian is partial differentiation with respect to q̇ (time-derivatives of generalized positions) or with respect to v (generalized velocities). More...

Functions
std::pair< solvers::Binding< internal::SlidingFrictionComplementarityNonlinearConstraint >, solvers::Binding< StaticFrictionConeConstraint > >	AddSlidingFrictionComplementarityExplicitContactConstraint (const ContactWrenchEvaluator contact_wrench_evaluator, double complementarity_tolerance, const Eigen::Ref< const VectorX< symbolic::Variable >> &q_vars, const Eigen::Ref< const VectorX< symbolic::Variable >> &v_vars, const Eigen::Ref< const VectorX< symbolic::Variable >> &lambda_vars, solvers::MathematicalProgram prog)
	For a pair of geometries in explicit contact, adds the sliding friction complementarity constraint explained in sliding_friction_complementarity_constraint to an optimization program. More...

std::pair< solvers::Binding< internal::SlidingFrictionComplementarityNonlinearConstraint >, solvers::Binding< internal::StaticFrictionConeComplementarityNonlinearConstraint > >	AddSlidingFrictionComplementarityImplicitContactConstraint (const ContactWrenchEvaluator contact_wrench_evaluator, double complementarity_tolerance, const Eigen::Ref< const VectorX< symbolic::Variable >> &q_vars, const Eigen::Ref< const VectorX< symbolic::Variable >> &v_vars, const Eigen::Ref< const VectorX< symbolic::Variable >> &lambda_vars, solvers::MathematicalProgram prog)
	For a pair of geometries in implicit contact (they may or may not be in contact, adds the sliding friction complementarity constraint explained in sliding_friction_complementarity_constraint. More...

solvers::Binding< internal::StaticFrictionConeComplementarityNonlinearConstraint >	AddStaticFrictionConeComplementarityConstraint (const ContactWrenchEvaluator contact_wrench_evaluator, double complementarity_tolerance, const Eigen::Ref< const VectorX< symbolic::Variable >> &q_vars, const Eigen::Ref< const VectorX< symbolic::Variable >> &lambda_vars, solvers::MathematicalProgram prog)
	Adds the complementarity constraint on the static friction force between a pair of contacts \|ft_W\| <= μ * n_Wᵀ * f_W (static friction force in the friction cone). More...

SignedDistanceWithTimeDerivative	CalcDistanceAndTimeDerivative (const multibody::MultibodyPlant< double > &plant, const SortedPair< geometry::GeometryId > &geometry_pair, const systems::Context< double > &context)
	Given a pair of geometries and the generalized position/velocity of the plant, compute the signed distance between the pair of geometries and the time derivative of the signed distance. More...

systems::lcm::LcmPublisherSystem *	ConnectContactResultsToDrakeVisualizer (systems::DiagramBuilder< double > builder, const MultibodyPlant< double > &multibody_plant, lcm::DrakeLcmInterface lcm=nullptr)
	Extends a Diagram with the required components to publish contact results to drake_visualizer. More...

systems::lcm::LcmPublisherSystem *	ConnectContactResultsToDrakeVisualizer (systems::DiagramBuilder< double > builder, const MultibodyPlant< double > &multibody_plant, const systems::OutputPort< double > &contact_results_port, lcm::DrakeLcmInterface lcm=nullptr)
	Implements ConnectContactResultsToDrakeVisualizer, but using explicitly specified `contact_results_port` and `geometry_input_port` arguments. More...

template<typename T >
CoulombFriction< T >	CalcContactFrictionFromSurfaceProperties (const CoulombFriction< T > &surface_properties1, const CoulombFriction< T > &surface_properties2)
	Given the surface properties of two different surfaces, this method computes the Coulomb's law coefficients of friction characterizing the interaction by friction of the given surface pair. More...

template<typename T >
bool	operator== (const HydroelasticQuadraturePointData< T > &data1, const HydroelasticQuadraturePointData< T > &data2)
	Returns `true` if all of the corresponding individual fields of `data1` and `data2` are equal (i.e., using their corresponding `operator==()` functions). More...

BodyIndex	world_index ()
	For every MultibodyTree the world body always has this unique index and it is always zero. More...

ModelInstanceIndex	world_model_instance ()
	Returns the model instance containing the world body. More...

ModelInstanceIndex	default_model_instance ()
	Returns the model instance which contains all tree elements with no explicit model instance specified. More...

Typedef Documentation

◆ BodyIndex

using BodyIndex = TypeSafeIndex<class BodyTag>

Type used to identify bodies by index in a multibody tree system.

◆ ForceElementIndex

using ForceElementIndex = TypeSafeIndex<class ForceElementTag>

Type used to identify force elements by index within a multibody tree system.

◆ FrameIndex

using FrameIndex = TypeSafeIndex<class FrameTag>

Type used to identify frames by index in a multibody tree system.

◆ JointActuatorIndex

using JointActuatorIndex = TypeSafeIndex<class JointActuatorElementTag>

Type used to identify actuators by index within a multibody tree system.

◆ JointIndex

using JointIndex = TypeSafeIndex<class JointElementTag>

Type used to identify joints by index within a multibody tree system.

◆ MinimumDistancePenaltyFunction

using MinimumDistancePenaltyFunction = solvers::MinimumValuePenaltyFunction

Computes the penalty function φ(x) and its derivatives dφ(x)/dx.

Valid penalty functions must meet the following criteria:

φ(x) ≥ 0 ∀ x ∈ ℝ.
dφ(x)/dx ≤ 0 ∀ x ∈ ℝ.
φ(x) = 0 ∀ x ≥ 0.
dφ(x)/dx < 0 ∀ x < 0.

◆ ModelInstanceIndex

using ModelInstanceIndex = TypeSafeIndex<class ModelInstanceTag>

Type used to identify model instances by index within a multibody tree system.

Enumeration Type Documentation

◆ ContactModel

enum ContactModel

strong

Enumeration for contact model options.

Enumerator

kHydroelasticsOnly

Contact forces are computed using the Hydroelastic model.

Conctact between unsupported geometries will cause a runtime exception.

kPointContactOnly

Contact forces are computed using a point contact model, see Numerical Approximation of Point Contact.

kHydroelasticWithFallback

Contact forces are computed using the hydroelastic model, where possible.

For most other unsupported colliding pairs, the point model from kPointContactOnly is used. See geometry::QueryObject:ComputeContactSurfacesWithFallback for more details.

◆ JacobianWrtVariable

enum JacobianWrtVariable

strong

Enumeration that indicates whether the Jacobian is partial differentiation with respect to q̇ (time-derivatives of generalized positions) or with respect to v (generalized velocities).

Enumerator
kQDot	J = ∂V/∂q̇
kV	J = ∂V/∂v.

◆ TamsiSolverResult

enum TamsiSolverResult

strong

The result from TamsiSolver::SolveWithGuess() used to report the success or failure of the solver.

Enumerator

kSuccess

Successful computation.

kMaxIterationsReached

The maximum number of iterations was reached.

kLinearSolverFailed

The linear solver used within the Newton-Raphson loop failed.

This might be caused by a divergent iteration that led to an invalid Jacobian matrix.

Function Documentation

◆ AddSlidingFrictionComplementarityExplicitContactConstraint()

std::pair<solvers::Binding< internal::SlidingFrictionComplementarityNonlinearConstraint>, solvers::Binding<StaticFrictionConeConstraint> > drake::multibody::AddSlidingFrictionComplementarityExplicitContactConstraint	(	const ContactWrenchEvaluator *	contact_wrench_evaluator,
		double	complementarity_tolerance,
		const Eigen::Ref< const VectorX< symbolic::Variable >> &	q_vars,
		const Eigen::Ref< const VectorX< symbolic::Variable >> &	v_vars,
		const Eigen::Ref< const VectorX< symbolic::Variable >> &	lambda_vars,
		solvers::MathematicalProgram *	prog
	)

For a pair of geometries in explicit contact, adds the sliding friction complementarity constraint explained in sliding_friction_complementarity_constraint to an optimization program.

This function adds the slack variables (f_static, f_sliding, c), and impose all the constraints in sliding_friction_complementarity_constraint.

Parameters

contact_wrench_evaluator	Evaluates the contact wrench between a pair of geometries.
complementarity_tolerance	The tolerance on the complementarity constraint.
q_vars	The variable for the generalized position q in `prog`.
v_vars	The variable for the generalized velocity v in `prog`.
lambda_vars	The variables to parameterize the contact wrench between this pair of geometry.
prog	The optimization program to which the sliding friction complementarity constraint is imposed.

Returns: (sliding_friction_complementarity_constraint, static_friction_cone_constraint), the pair of constraint that imposes (1)-(4) and (6) in sliding_friction_complementarity_constraint.

◆ AddSlidingFrictionComplementarityImplicitContactConstraint()

std::pair<solvers::Binding< internal::SlidingFrictionComplementarityNonlinearConstraint>, solvers::Binding< internal::StaticFrictionConeComplementarityNonlinearConstraint> > drake::multibody::AddSlidingFrictionComplementarityImplicitContactConstraint	(	const ContactWrenchEvaluator *	contact_wrench_evaluator,
		double	complementarity_tolerance,
		const Eigen::Ref< const VectorX< symbolic::Variable >> &	q_vars,
		const Eigen::Ref< const VectorX< symbolic::Variable >> &	v_vars,
		const Eigen::Ref< const VectorX< symbolic::Variable >> &	lambda_vars,
		solvers::MathematicalProgram *	prog
	)

For a pair of geometries in implicit contact (they may or may not be in contact, adds the sliding friction complementarity constraint explained in sliding_friction_complementarity_constraint.

The input arguments are the same as those in AddSlidingFrictionComplementarityExplicitContactConstraint(). The difference is that the returned argument includes the nonlinear complementarity binding 0 ≤ φ(q) ⊥ fₙ≥ 0, which imposes the constraint for implicit contact.

◆ AddStaticFrictionConeComplementarityConstraint()

solvers::Binding<internal::StaticFrictionConeComplementarityNonlinearConstraint> drake::multibody::AddStaticFrictionConeComplementarityConstraint	(	const ContactWrenchEvaluator *	contact_wrench_evaluator,
		double	complementarity_tolerance,
		const Eigen::Ref< const VectorX< symbolic::Variable >> &	q_vars,
		const Eigen::Ref< const VectorX< symbolic::Variable >> &	lambda_vars,
		solvers::MathematicalProgram *	prog
	)

Adds the complementarity constraint on the static friction force between a pair of contacts |ft_W| <= μ * n_Wᵀ * f_W (static friction force in the friction cone).

fn_W * sdf = 0 (complementarity condition) sdf >= 0 (no penetration) where sdf stands for signed distance function, ft_W stands for the tangential friction force expressed in the world frame.

Mathematically, we add the following constraints to the optimization program

f_Wᵀ * ((μ² + 1)* n_W * n_Wᵀ - I) * f_W ≥ 0                    (1)
n_Wᵀ * f_W = α                                                 (2)
sdf(q) = β                                                     (3)
0 ≤ α * β ≤ ε                                                  (4)
α ≥ 0                                                          (5)
β ≥ 0                                                          (6)

the slack variables α and β are added to the optimization program as well.

Parameters

	contact_wrench_evaluator	The evaluator to compute the contact wrench expressed in the world frame.
	complementarity_tolerance	ε in the documentation above.
	q_vars	The decision variable for the generalized configuration q.
	lambda_vars	The decision variable to parameterize the contact wrench.
[in,out]	prog	The optimization program to which the constraint is added.

Returns: binding The binding containing the nonlinear constraints (1)-(4).

Precondition: Both q_vars and lambda_vars have been added to prog before calling this function.

◆ CalcContactFrictionFromSurfaceProperties()

CoulombFriction<T> drake::multibody::CalcContactFrictionFromSurfaceProperties	(	const CoulombFriction< T > &	surface_properties1,
		const CoulombFriction< T > &	surface_properties2
	)

Given the surface properties of two different surfaces, this method computes the Coulomb's law coefficients of friction characterizing the interaction by friction of the given surface pair.

The surface properties are specified by individual Coulomb's law coefficients of friction. As outlined in the class's documentation for CoulombFriction, friction coefficients characterize a surface pair and not individual surfaces. However, we find it useful in practice to associate the abstract idea of friction coefficients to a single surface. Please refer to the documentation for CoulombFriction for details on this topic.

More specifically, this method computes the contact coefficients for the given surface pair as:

  μ = 2μₘμₙ/(μₘ + μₙ)

where the operation above is performed separately on the static and dynamic friction coefficients.

Parameters

[in]	surface_properties1	Surface properties for surface 1. Specified as an individual set of Coulomb's law coefficients of friction.
[in]	surface_properties2	Surface properties for surface 2. Specified as an individual set of Coulomb's law coefficients of friction.

Returns: the combined friction coefficients for the interacting surfaces.

◆ CalcDistanceAndTimeDerivative()

SignedDistanceWithTimeDerivative drake::multibody::CalcDistanceAndTimeDerivative	(	const multibody::MultibodyPlant< double > &	plant,
		const SortedPair< geometry::GeometryId > &	geometry_pair,
		const systems::Context< double > &	context
	)

Given a pair of geometries and the generalized position/velocity of the plant, compute the signed distance between the pair of geometries and the time derivative of the signed distance.

This function is similar to QueryObject::ComputeSignedDistancePairClosestPoints(), but it also provides the time derivative of the signed distance.

Parameters

	plant	The plant on which the geometries are attached. This plant must have been connected to a SceneGraph.
	geometry_pair	The pair of geometries whose distance and time derivative are computed.
	context	The context of the plant. This must store both q and v. This context must have been extracted from the diagram context which contains both MultibodyPlant and SceneGraph contexts.
[out]	distance	The signed distance between the pair of geometry.
[out]	distance_time_derivative	The time derivative of the signed distance.

◆ default_model_instance()

ModelInstanceIndex drake::multibody::default_model_instance ( )

Returns the model instance which contains all tree elements with no explicit model instance specified.

◆ operator==()

bool drake::multibody::operator==	(	const HydroelasticQuadraturePointData< T > &	data1,
		const HydroelasticQuadraturePointData< T > &	data2
	)

Returns true if all of the corresponding individual fields of data1 and data2 are equal (i.e., using their corresponding operator==() functions).

◆ world_index()

BodyIndex drake::multibody::world_index ( )

For every MultibodyTree the world body always has this unique index and it is always zero.

◆ world_model_instance()

ModelInstanceIndex drake::multibody::world_model_instance ( )

Returns the model instance containing the world body.

For every MultibodyTree the world body always has this unique model instance and it is always zero (as described in #3088).

Namespaces

Classes

Typedefs

Enumerations

Functions

Typedef Documentation

◆ BodyIndex

◆ ForceElementIndex

◆ FrameIndex

◆ JointActuatorIndex

◆ JointIndex

◆ MinimumDistancePenaltyFunction

◆ ModelInstanceIndex

Enumeration Type Documentation

◆ ContactModel

◆ JacobianWrtVariable

◆ TamsiSolverResult

Function Documentation

◆ AddSlidingFrictionComplementarityExplicitContactConstraint()

◆ AddSlidingFrictionComplementarityImplicitContactConstraint()

◆ AddStaticFrictionConeComplementarityConstraint()

◆ CalcContactFrictionFromSurfaceProperties()

◆ CalcDistanceAndTimeDerivative()

◆ default_model_instance()

◆ operator==()

◆ world_index()

◆ world_model_instance()