Detailed Description

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

The angle difference between frame A's orientation R_WA and B's orientation R_WB is θ (θ ∈ [0, π]), if there exists a rotation axis a, such that rotating frame A by angle θ about axis a aligns it with frame B. Namely R_AB = I + sinθ â + (1-cosθ)â² (1) where R_AB is the orientation of frame B expressed in frame A. â is the skew symmetric matrix of the rotation axis a. Equation (1) is the Rodrigues formula that computes the rotation matrix froma rotation axis a and an angle θ, https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula If the users want frame A and frame B to align perfectly, they can set θ_bound = 0. Mathematically, this constraint is imposed as trace(R_AB) ≥ 2cos(θ_bound) + 1 (1) To derive (1), using Rodrigues formula R_AB = I + sinθ â + (1-cosθ)â² where trace(R_AB) = 2cos(θ) + 1 ≥ 2cos(θ_bound) + 1

#include <drake/multibody/inverse_kinematics/orientation_constraint.h>

Public Member Functions
	OrientationConstraint (const MultibodyPlant< double > const plant, const Frame< double > &frameAbar, const math::RotationMatrix< double > &R_AbarA, const Frame< double > &frameBbar, const math::RotationMatrix< double > &R_BbarB, double theta_bound, systems::Context< double > plant_context)
	Constructs an OrientationConstraint object. More...

	OrientationConstraint (const MultibodyPlant< AutoDiffXd > const plant, const Frame< AutoDiffXd > &frameAbar, const math::RotationMatrix< double > &R_AbarA, const Frame< AutoDiffXd > &frameBbar, const math::RotationMatrix< double > &R_BbarB, double theta_bound, systems::Context< AutoDiffXd > plant_context)
	Overloaded constructor. More...

	~OrientationConstraint () override

Does not allow copy, move, or assignment
	OrientationConstraint (const OrientationConstraint &)=delete

OrientationConstraint &	operator= (const OrientationConstraint &)=delete

	OrientationConstraint (OrientationConstraint &&)=delete

OrientationConstraint &	operator= (OrientationConstraint &&)=delete

Public Member Functions inherited from Constraint
template<typename DerivedLB , typename DerivedUB >
	Constraint (int num_constraints, int num_vars, const Eigen::MatrixBase< DerivedLB > &lb, const Eigen::MatrixBase< DerivedUB > &ub, const std::string &description="")
	Constructs a constraint which has `num_constraints` rows, with an input `num_vars` x 1 vector. More...

	Constraint (int num_constraints, int num_vars)
	Constructs a constraint which has `num_constraints` rows, with an input `num_vars` x 1 vector, with no bounds. More...

bool	CheckSatisfied (const Eigen::Ref< const Eigen::VectorXd > &x, double tol=1E-6) const
	Return whether this constraint is satisfied by the given value, `x`. More...

bool	CheckSatisfied (const Eigen::Ref< const AutoDiffVecXd > &x, double tol=1E-6) const

symbolic::Formula	CheckSatisfied (const Eigen::Ref< const VectorX< symbolic::Variable >> &x) const

const Eigen::VectorXd &	lower_bound () const

const Eigen::VectorXd &	upper_bound () const

int	num_constraints () const
	Number of rows in the output constraint. More...

	Constraint (const Constraint &)=delete

Constraint &	operator= (const Constraint &)=delete

	Constraint (Constraint &&)=delete

Constraint &	operator= (Constraint &&)=delete

Public Member Functions inherited from EvaluatorBase
virtual	~EvaluatorBase ()

void	Eval (const Eigen::Ref< const Eigen::VectorXd > &x, Eigen::VectorXd *y) const
	Evaluates the expression. More...

void	Eval (const Eigen::Ref< const AutoDiffVecXd > &x, AutoDiffVecXd *y) const
	Evaluates the expression. More...

void	Eval (const Eigen::Ref< const VectorX< symbolic::Variable >> &x, VectorX< symbolic::Expression > *y) const
	Evaluates the expression. More...

void	set_description (const std::string &description)
	Set a human-friendly description for the evaluator. More...

const std::string &	get_description () const
	Getter for a human-friendly description for the evaluator. More...

std::ostream &	Display (std::ostream &os, const VectorX< symbolic::Variable > &vars) const
	Formats this evaluator into the given stream using `vars` for the bound decision variable names. More...

std::ostream &	Display (std::ostream &os) const
	Formats this evaluator into the given stream, without displaying the decision variables it is bound to. More...

std::string	ToLatex (const VectorX< symbolic::Variable > &vars, int precision=3) const
	Returns a LaTeX string describing this evaluator. More...

int	num_vars () const
	Getter for the number of variables, namely the number of rows in x, as used in Eval(x, y). More...

int	num_outputs () const
	Getter for the number of outputs, namely the number of rows in y, as used in Eval(x, y). More...

void	SetGradientSparsityPattern (const std::vector< std::pair< int, int >> &gradient_sparsity_pattern)
	Set the sparsity pattern of the gradient matrix ∂y/∂x (the gradient of y value in Eval, w.r.t x in Eval) . More...

const std::optional< std::vector< std::pair< int, int > > > &	gradient_sparsity_pattern () const
	Returns the vector of (row_index, col_index) that contains all the entries in the gradient of Eval function (∂y/∂x) whose value could be non-zero, namely if ∂yᵢ/∂xⱼ could be non-zero, then the pair (i, j) is in gradient_sparsity_pattern. More...

	EvaluatorBase (const EvaluatorBase &)=delete

EvaluatorBase &	operator= (const EvaluatorBase &)=delete

	EvaluatorBase (EvaluatorBase &&)=delete

EvaluatorBase &	operator= (EvaluatorBase &&)=delete

Additional Inherited Members
Protected Member Functions inherited from Constraint
void	UpdateLowerBound (const Eigen::Ref< const Eigen::VectorXd > &new_lb)
	Updates the lower bound. More...

void	UpdateUpperBound (const Eigen::Ref< const Eigen::VectorXd > &new_ub)
	Updates the upper bound. More...

void	set_bounds (const Eigen::Ref< const Eigen::VectorXd > &new_lb, const Eigen::Ref< const Eigen::VectorXd > &new_ub)
	Set the upper and lower bounds of the constraint. More...

virtual bool	DoCheckSatisfied (const Eigen::Ref< const Eigen::VectorXd > &x, const double tol) const

virtual bool	DoCheckSatisfied (const Eigen::Ref< const AutoDiffVecXd > &x, const double tol) const

virtual symbolic::Formula	DoCheckSatisfied (const Eigen::Ref< const VectorX< symbolic::Variable >> &x) const

Protected Member Functions inherited from EvaluatorBase
	EvaluatorBase (int num_outputs, int num_vars, const std::string &description="")
	Constructs a evaluator. More...

virtual std::ostream &	DoDisplay (std::ostream &os, const VectorX< symbolic::Variable > &vars) const
	NVI implementation of Display. More...

virtual std::string	DoToLatex (const VectorX< symbolic::Variable > &vars, int precision) const

void	set_num_outputs (int num_outputs)

Constructor & Destructor Documentation

◆ OrientationConstraint() [1/4]

OrientationConstraint ( const OrientationConstraint & )

delete

◆ OrientationConstraint() [2/4]

OrientationConstraint ( OrientationConstraint && )

delete

◆ OrientationConstraint() [3/4]

OrientationConstraint	(	const MultibodyPlant< double > *const	plant,
		const Frame< double > &	frameAbar,
		const math::RotationMatrix< double > &	R_AbarA,
		const Frame< double > &	frameBbar,
		const math::RotationMatrix< double > &	R_BbarB,
		double	theta_bound,
		systems::Context< double > *	plant_context
	)

Constructs an OrientationConstraint object.

The frame A is fixed to a frame A̅, with orientatation R_AbarA measured in frame A̅. The frame B is fixed to a frame B̅, with orientation R_BbarB measured in frame B. We constrain the angle between frame A and B to be less than theta_bound.

Parameters

plant	The MultibodyPlant on which the constraint is imposed. `plant` should be alive during the lifetime of this constraint.
frameAbar	The frame A̅ in the model to which frame A is fixed.
R_AbarA	The orientation of frame A measured in frame A̅.
frameBbar	The frame B̅ in the model to which frame B is fixed.
R_BbarB	The orientation of frame B measured in frame B̅.
theta_bound	The bound on the angle difference between frame A's orientation and frame B's orientation. It is denoted as θ_bound in the class documentation. `theta_bound` is in radians.
plant_context	The Context that has been allocated for this `plant`. We will update the context when evaluating the constraint. `plant_context` should be alive during the lifetime of this constraint.

Exceptions

std::exception	if `plant` is nullptr.
std::exception	if `frameAbar` or `frameBbar` does not belong to `plant`.
std::exception	if angle_bound < 0.
std::exception	if `plant_context` is nullptr.

◆ OrientationConstraint() [4/4]

OrientationConstraint	(	const MultibodyPlant< AutoDiffXd > *const	plant,
		const Frame< AutoDiffXd > &	frameAbar,
		const math::RotationMatrix< double > &	R_AbarA,
		const Frame< AutoDiffXd > &	frameBbar,
		const math::RotationMatrix< double > &	R_BbarB,
		double	theta_bound,
		systems::Context< AutoDiffXd > *	plant_context
	)

Overloaded constructor.

Constructs the constraint using MultibodyPlant<AutoDiffXd>

◆ ~OrientationConstraint()

~OrientationConstraint ( )

override

Member Function Documentation

◆ operator=() [1/2]

OrientationConstraint& operator= ( const OrientationConstraint & )

delete

◆ operator=() [2/2]

OrientationConstraint& operator= ( OrientationConstraint && )

delete

The documentation for this class was generated from the following file:

drake/multibody/inverse_kinematics/orientation_constraint.h

Detailed Description

Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ OrientationConstraint() [1/4]

◆ OrientationConstraint() [2/4]

◆ OrientationConstraint() [3/4]

◆ OrientationConstraint() [4/4]

◆ ~OrientationConstraint()

Member Function Documentation

◆ operator=() [1/2]

◆ operator=() [2/2]