Drake
Drake C++ Documentation MinimumDistanceConstraint Class Referencefinal

## Detailed Description

Constrain lb <= min(d) <= ub, 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, and the minimal distance is no larger than a specified ub.

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
SmoothUnderMax( φ((dᵢ(q) - d_influence)/(d_influence - ub)) / 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) and SmoothUnderMax(d) is smooth over and under 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.

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

## Public Member Functions

MinimumDistanceConstraint (const multibody::MultibodyPlant< double > *const plant, double minimum_distance, systems::Context< double > *plant_context, solvers::MinimumValuePenaltyFunction penalty_function={}, double influence_distance_offset=1)
Constructs a MinimumDistanceConstraint. More...

MinimumDistanceConstraint (const multibody::MultibodyPlant< double > *const plant, double minimum_distance_lower, double minimum_distance_upper, systems::Context< double > *plant_context, solvers::MinimumValuePenaltyFunction penalty_function, double influence_distance)

MinimumDistanceConstraint (const multibody::MultibodyPlant< AutoDiffXd > *const plant, double minimum_distance, systems::Context< AutoDiffXd > *plant_context, solvers::MinimumValuePenaltyFunction penalty_function={}, double influence_distance_offset=1)

MinimumDistanceConstraint (const multibody::MultibodyPlant< AutoDiffXd > *const plant, double minimum_distance_lower, double minimum_distance_upper, systems::Context< AutoDiffXd > *plant_context, solvers::MinimumValuePenaltyFunction penalty_function, double influence_distance)

MinimumDistanceConstraint (const planning::CollisionChecker *collision_checker, double minimum_distance, planning::CollisionCheckerContext *collision_checker_context, solvers::MinimumValuePenaltyFunction penalty_function={}, double influence_distance_offset=1)

MinimumDistanceConstraint (const planning::CollisionChecker *collision_checker, double minimum_distance_lower, double minimum_distance_upper, planning::CollisionCheckerContext *collision_checker_context, solvers::MinimumValuePenaltyFunction penalty_function, double influence_distance)

~MinimumDistanceConstraint () override

double minimum_distance_lower () const
Getter for the lower bound of the minimum distance. More...

double minimum_distance_upper () const
Getter for the upper bound of the minimum distance. More...

double influence_distance () const
Getter for the influence distance. More...

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

MinimumDistanceConstraintoperator= (const MinimumDistanceConstraint &)=delete

MinimumDistanceConstraint (MinimumDistanceConstraint &&)=delete

MinimumDistanceConstraintoperator= (MinimumDistanceConstraint &&)=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...

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...

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

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)

void UpdateUpperBound (const Eigen::Ref< const Eigen::VectorXd > &new_ub)

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)

## ◆ MinimumDistanceConstraint() [1/8]

 MinimumDistanceConstraint ( const MinimumDistanceConstraint & )
delete

## ◆ MinimumDistanceConstraint() [2/8]

 MinimumDistanceConstraint ( MinimumDistanceConstraint && )
delete

## ◆ MinimumDistanceConstraint() [3/8]

 MinimumDistanceConstraint ( const multibody::MultibodyPlant< double > *const plant, double minimum_distance, systems::Context< double > * plant_context, solvers::MinimumValuePenaltyFunction penalty_function = {}, double influence_distance_offset = 1 )

Constructs a MinimumDistanceConstraint.

Parameters
 plant The multibody system on which the constraint will be evaluated. minimum_distance The minimum allowed value, lb, of the signed distance between any candidate pair of geometries. penalty_function The penalty function formulation. Default: QuadraticallySmoothedHinge influence_distance_offset The difference (in meters) between the influence distance, d_influence, and the minimum distance, lb (see class documentation), namely influence_distance = minimum_distance_lower + influence_distance_offset. This value must be finite and strictly positive, as it is used to scale the signed distances between pairs of geometries. Smaller values may improve performance, as fewer pairs of geometries need to be considered in each constraint evaluation. Default: 1 meter. The chosen influence_distance_offset can significantly affect the runtime and optimization performance of using this constraint. Larger values result in more expensive collision checks (since more potential collision candidates must be considered) and may result in worse optimization performance (the optimizer may not be able to find a configuration that satisfies the constraint). In work at TRI, we have used much lower values (e.g. 1e-6) for influence_distance_offset with good results.
Exceptions
 std::exception if plant has not registered its geometry with a SceneGraph object. std::exception if influence_distance_offset = ∞. std::exception if influence_distance_offset ≤ 0.

## ◆ MinimumDistanceConstraint() [4/8]

 MinimumDistanceConstraint ( const multibody::MultibodyPlant< double > *const plant, double minimum_distance_lower, double minimum_distance_upper, systems::Context< double > * plant_context, solvers::MinimumValuePenaltyFunction penalty_function, double influence_distance )

lower <= min(distance) <= upper.

Parameters
 minimum_distance_lower The lower bound of the minimum distance. lower <= min(distance). minimum_distance_upper The upper bound of the minimum distance. min(distance) <= upper. If minimum_distance_upper is finite, then it must be smaller than influence_distance_offset.

## ◆ MinimumDistanceConstraint() [5/8]

 MinimumDistanceConstraint ( const multibody::MultibodyPlant< AutoDiffXd > *const plant, double minimum_distance, systems::Context< AutoDiffXd > * plant_context, solvers::MinimumValuePenaltyFunction penalty_function = {}, double influence_distance_offset = 1 )

Constructs the constraint using MultibodyPlant<AutoDiffXd>.

## ◆ MinimumDistanceConstraint() [6/8]

 MinimumDistanceConstraint ( const multibody::MultibodyPlant< AutoDiffXd > *const plant, double minimum_distance_lower, double minimum_distance_upper, systems::Context< AutoDiffXd > * plant_context, solvers::MinimumValuePenaltyFunction penalty_function, double influence_distance )

Constructs the constraint using MultibodyPlant<AutoDiffXd>. lower <= min(distance) <= upper.

Parameters
 minimum_distance_lower The lower bound of the minimum distance. lower <= min(distance). We must have minimum_distance_lower <= influence_distance. minimum_distance_upper The upper bound of the minimum distance. min(distance) <= upper. If minimum_distance_upper is finite, then it must be smaller than influence_distance. collision_checker_context The context for the collision checker.

## ◆ MinimumDistanceConstraint() [7/8]

 MinimumDistanceConstraint ( const planning::CollisionChecker * collision_checker, double minimum_distance, planning::CollisionCheckerContext * collision_checker_context, solvers::MinimumValuePenaltyFunction penalty_function = {}, double influence_distance_offset = 1 )

Constructs the constraint with CollisionChecker instead of MultibodyPlant.

Parameters
 collision_checker collision_checker must outlive this constraint. collision_checker_context The context for the collision checker. See CollisionChecker class for more details.

## ◆ MinimumDistanceConstraint() [8/8]

 MinimumDistanceConstraint ( const planning::CollisionChecker * collision_checker, double minimum_distance_lower, double minimum_distance_upper, planning::CollisionCheckerContext * collision_checker_context, solvers::MinimumValuePenaltyFunction penalty_function, double influence_distance )

Constructs the constraint with CollisionChecker instead of MultibodyPlant.

Parameters
 collision_checker collision_checker must outlive this constraint. collision_checker_context The context for the collision checker. See CollisionChecker class for more details.

## ◆ ~MinimumDistanceConstraint()

 ~MinimumDistanceConstraint ( )
override

## ◆ influence_distance()

 double influence_distance ( ) const

Getter for the influence distance.

## ◆ minimum_distance_lower()

 double minimum_distance_lower ( ) const

Getter for the lower bound of the minimum distance.

## ◆ minimum_distance_upper()

 double minimum_distance_upper ( ) const

Getter for the upper bound of the minimum distance.

## ◆ operator=() [1/2]

 MinimumDistanceConstraint& operator= ( const MinimumDistanceConstraint & )
delete

## ◆ operator=() [2/2]

 MinimumDistanceConstraint& operator= ( MinimumDistanceConstraint && )
delete

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