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Drake
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Drake
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Constrain min(v) <= ub where v=f(x).
Namely at least one element of the vector v returned by the user-provided function f(x) to be no larger than a specified value ub.
The formulation of the constraint is
SmoothUnderMax( φ((vᵢ - v_influence)/(v_influence - ub)) / φ(-1) ) ≥ 1
where vᵢ is the i-th value returned by the user-provided function, ub is the upper bound for the min(v). (Note that ub is NOT the upper bound of v). v_influence is the "influence value" (the value below which an element influences the constraint or, conversely, the value above which an element is ignored), φ is a solvers::MinimumValuePenaltyFunction. SmoothUnderMax(x) is a smooth, under approximation of max(v) (i.e. SmoothUnderMax(v) <= max(v) for all v). We require that ub < v_influence. The input scaling (vᵢ - v_influence)/(v_influence - ub) ensures that at the boundary of the feasible set (when vᵢ == ub), we evaluate the penalty function at -1, where it is required to have a non-zero gradient. The user-provided function may return a vector with up to max_num_values elements. If it returns a vector with fewer than max_num_values elements, the remaining elements are assumed to be greater than the "influence value".
#include <drake/solvers/minimum_value_constraint.h>
Public Member Functions | |
| MinimumValueUpperBoundConstraint (int num_vars, double minimum_value_upper, double influence_value_offset, int max_num_values, std::function< AutoDiffVecXd(const Eigen::Ref< const AutoDiffVecXd > &, double)> value_function, std::function< VectorX< double >(const Eigen::Ref< const VectorX< double >> &, double)> value_function_double={}) | |
| Constructs a MinimumValueUpperBoundConstraint. More... | |
| ~MinimumValueUpperBoundConstraint () override | |
| double | minimum_value_upper () const |
| Getter for the upper bound on the minimum value. More... | |
| double | influence_value () const |
| Getter for the influence value. More... | |
| int | max_num_values () const |
| Getter for maximum number of values expected from value_function. More... | |
| void | set_penalty_function (MinimumValuePenaltyFunction new_penalty_function) |
| Setter for the penalty function. More... | |
 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) |
| MinimumValueUpperBoundConstraint | ( | int | num_vars, |
| double | minimum_value_upper, | ||
| double | influence_value_offset, | ||
| int | max_num_values, | ||
| std::function< AutoDiffVecXd(const Eigen::Ref< const AutoDiffVecXd > &, double)> | value_function | ||
| ) |
Constructs a MinimumValueUpperBoundConstraint.
min(v) <= ub
| num_vars | The number of inputs to value_function |
| minimum_value_upper | The upper bound on the minimum allowed value for all elements of the vector returned by value_function, namely min(value_function(x)) <= minimum_value_upper |
| influence_value_offset | The difference between the influence value, v_influence, and minimum_value_upper. This value must be finite and strictly positive, as it is used to scale the values returned by value_function. Larger values may increase the possibility of finding a solution to the constraint. With a small v_influence, the value_function will ignore the entries with value less than v_influence. While it is possible that by changing x, that value (that currently been ignored) can decrease to below ub with a different x, by using a small v_influence, the gradient of that entry is never considered if the entry is ignored. We strongly suggest using a larger v_influence compared to the one used in MinimumValueConstraint when constraining min(v) >= lb. |
| max_num_values | The maximum number of elements in the vector returned by value_function. |
| value_function | User-provided function that takes a num_vars-element vector and the influence distance as inputs and returns a vector with up to max_num_values elements. The function can omit from the return vector any elements larger than the provided influence distance. |
| value_function_double | Optional user-provide function that computes the same values as value_function but for double rather than AutoDiffXd. If omitted, value_function will be called (and the gradients discarded) when this constraint is evaluated for doubles. |
value_function_double(ExtractValue(x), v_influence) == ExtractValue(value_function(x, v_influence)) for all x. value_function(x).size() <= max_num_values for all x. | std::exception | if influence_value_offset = ∞. |
| std::exception | if influence_value_offset ≤ 0. |
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override |
| double influence_value | ( | ) | const |
Getter for the influence value.
| int max_num_values | ( | ) | const |
Getter for maximum number of values expected from value_function.
| double minimum_value_upper | ( | ) | const |
Getter for the upper bound on the minimum value.
| void set_penalty_function | ( | MinimumValuePenaltyFunction | new_penalty_function | ) |
Setter for the penalty function.