Constrain min(d) >= lb, namely 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 lb.
This constraint should be bound to decision variables corresponding to the configuration vector, q, of the associated MultibodyPlant.
The formulation of the constraint is
SmoothOverMax( φ((dᵢ(q) - d_influence)/(d_influence - lb)) / φ(-1) ) ≤ 1
where dᵢ(q) is the signed distance of the i-th pair, lb is the minimum allowable distance, d_influence is the "influence distance" (the distance below which a pair of geometries influences the constraint), φ is a solvers::MinimumValuePenaltyFunction. SmoothOverMax(d) is smooth over approximation of max(d). We require that lb < d_influence. The input scaling (dᵢ(q) - d_influence)/(d_influence - lb) ensures that at the boundary of the feasible set (when dᵢ(q) == lb), we evaluate the penalty function at -1, where it is required to have a non-zero gradient.
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| | MinimumDistanceLowerBoundConstraint (const multibody::MultibodyPlant< double > *const plant, double bound, systems::Context< double > *plant_context, solvers::MinimumValuePenaltyFunction penalty_function={}, double influence_distance_offset=0.01) |
| | Constructs a MinimumDistanceLowerBoundConstraint.
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| | MinimumDistanceLowerBoundConstraint (const multibody::MultibodyPlant< AutoDiffXd > *const plant, double bound, systems::Context< AutoDiffXd > *plant_context, solvers::MinimumValuePenaltyFunction penalty_function={}, double influence_distance_offset=0.01) |
| | Overloaded constructor.
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| | MinimumDistanceLowerBoundConstraint (const planning::CollisionChecker *collision_checker, double bound, planning::CollisionCheckerContext *collision_checker_context, solvers::MinimumValuePenaltyFunction penalty_function={}, double influence_distance_offset=0.01) |
| | Overloaded constructor.
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| | ~MinimumDistanceLowerBoundConstraint () override |
| double | distance_bound () const |
| | Getter for the lower bound of the minimum distance.
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| double | influence_distance () const |
| | Getter for the influence distance.
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| | MinimumDistanceLowerBoundConstraint (const MinimumDistanceLowerBoundConstraint &)=delete |
| MinimumDistanceLowerBoundConstraint & | operator= (const MinimumDistanceLowerBoundConstraint &)=delete |
| | MinimumDistanceLowerBoundConstraint (MinimumDistanceLowerBoundConstraint &&)=delete |
| MinimumDistanceLowerBoundConstraint & | operator= (MinimumDistanceLowerBoundConstraint &&)=delete |
| 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.
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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.
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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.
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| 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.
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| | Constraint (const Constraint &)=delete |
| Constraint & | operator= (const Constraint &)=delete |
| | Constraint (Constraint &&)=delete |
| Constraint & | operator= (Constraint &&)=delete |
| virtual | ~EvaluatorBase () |
| void | Eval (const Eigen::Ref< const Eigen::VectorXd > &x, Eigen::VectorXd *y) const |
| | Evaluates the expression.
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| void | Eval (const Eigen::Ref< const AutoDiffVecXd > &x, AutoDiffVecXd *y) const |
| | Evaluates the expression.
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| void | Eval (const Eigen::Ref< const VectorX< symbolic::Variable > > &x, VectorX< symbolic::Expression > *y) const |
| | Evaluates the expression.
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| void | set_description (const std::string &description) |
| | Set a human-friendly description for the evaluator.
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| const std::string & | get_description () const |
| | Getter for a human-friendly description for the evaluator.
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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.
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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.
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| std::string | ToLatex (const VectorX< symbolic::Variable > &vars, int precision=3) const |
| | Returns a LaTeX string describing this evaluator.
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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).
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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).
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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) .
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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.
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| bool | is_thread_safe () const |
| | Returns whether it is safe to call Eval in parallel.
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| | EvaluatorBase (const EvaluatorBase &)=delete |
| EvaluatorBase & | operator= (const EvaluatorBase &)=delete |
| | EvaluatorBase (EvaluatorBase &&)=delete |
| EvaluatorBase & | operator= (EvaluatorBase &&)=delete |
