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
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| | 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...
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| | 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...
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| | ~OrientationConstraint () override |
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| | OrientationConstraint (const OrientationConstraint &)=delete |
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| OrientationConstraint & | operator= (const OrientationConstraint &)=delete |
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| | OrientationConstraint (OrientationConstraint &&)=delete |
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| OrientationConstraint & | operator= (OrientationConstraint &&)=delete |
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| 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...
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| | 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...
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| 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...
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| bool | CheckSatisfied (const Eigen::Ref< const AutoDiffVecXd > &x, double tol=1E-6) const |
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| symbolic::Formula | CheckSatisfied (const Eigen::Ref< const VectorX< symbolic::Variable >> &x) const |
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| const Eigen::VectorXd & | lower_bound () const |
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| const Eigen::VectorXd & | upper_bound () const |
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| int | num_constraints () const |
| | Number of rows in the output constraint. More...
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| | Constraint (const Constraint &)=delete |
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| Constraint & | operator= (const Constraint &)=delete |
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| | Constraint (Constraint &&)=delete |
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| Constraint & | operator= (Constraint &&)=delete |
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| virtual | ~EvaluatorBase () |
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| void | Eval (const Eigen::Ref< const Eigen::VectorXd > &x, Eigen::VectorXd *y) const |
| | Evaluates the expression. More...
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| void | Eval (const Eigen::Ref< const AutoDiffVecXd > &x, AutoDiffVecXd *y) const |
| | Evaluates the expression. More...
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| void | Eval (const Eigen::Ref< const VectorX< symbolic::Variable >> &x, VectorX< symbolic::Expression > *y) const |
| | Evaluates the expression. More...
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| void | set_description (const std::string &description) |
| | Set a human-friendly description for the evaluator. More...
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| const std::string & | get_description () const |
| | Getter for a human-friendly description for the evaluator. More...
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| 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...
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| std::ostream & | Display (std::ostream &os) const |
| | Formats this evaluator into the given stream, without displaying the decision variables it is bound to. More...
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| std::string | ToLatex (const VectorX< symbolic::Variable > &vars, int precision=3) const |
| | Returns a LaTeX string describing this evaluator. More...
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| int | num_vars () const |
| | Getter for the number of variables, namely the number of rows in x, as used in Eval(x, y). More...
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| int | num_outputs () const |
| | Getter for the number of outputs, namely the number of rows in y, as used in Eval(x, y). More...
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| 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...
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| 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...
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| bool | is_thread_safe () const |
| | Returns whether it is safe to call Eval in parallel. More...
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| | EvaluatorBase (const EvaluatorBase &)=delete |
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| EvaluatorBase & | operator= (const EvaluatorBase &)=delete |
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| | EvaluatorBase (EvaluatorBase &&)=delete |
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| EvaluatorBase & | operator= (EvaluatorBase &&)=delete |
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Public Member Functions inherited from Constraint