Drake
OrientationConstraint Class Reference

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)

~OrientationConstraint () override

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

OrientationConstraintoperator= (const OrientationConstraint &)=delete

OrientationConstraint (OrientationConstraint &&)=delete

OrientationConstraintoperator= (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

Constraintoperator= (const Constraint &)=delete

Constraint (Constraint &&)=delete

Constraintoperator= (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...

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 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

EvaluatorBaseoperator= (const EvaluatorBase &)=delete

EvaluatorBase (EvaluatorBase &&)=delete

EvaluatorBaseoperator= (EvaluatorBase &&)=delete 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 > &lower_bound, const Eigen::Ref< const Eigen::VectorXd > &upper_bound)
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...

void set_num_outputs (int num_outputs)

◆ 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 tree. We will update the context when evaluating the constraint. plant_context should be alive during the lifetime of this constraint.
Exceptions
 std::invalid_argument if plant is nullptr. std::logic_error if frameAbar or frameBbar does not belong to plant. std::invalid_argument if angle_bound < 0. std::invalid_argument 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 )

Constructs the constraint using MultibodyPlant<AutoDiffXd>

◆ ~OrientationConstraint()

 ~OrientationConstraint ( )
override

◆ 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 files: