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point_to_line_distance_constraint.h
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point_to_line_distance_constraint.h
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#pragma once
#include <memory>
#include "drake/multibody/plant/multibody_plant.h"
#include "drake/solvers/constraint.h"
#include "drake/systems/framework/context.h"
namespace drake {
namespace multibody {
/**
Constrain that the distance between a point P on frame B1 and another line L on
frame B2 is within a range [distance_lower, distance_upper].
@ingroup solver_evaluators
*/
class PointToLineDistanceConstraint : public solvers::Constraint {
public:
DRAKE_NO_COPY_NO_MOVE_NO_ASSIGN(PointToLineDistanceConstraint)
/**
Constrain the distance between a point P attached to frame_point (denoted as
B1) and the line L attached to frame_line (denoted as B2) is within the range
[distance_lower, distance_upper].
Mathematically, we impose the constraint
distance_lower² <= distance(P, L)² <= distance_upper².
We impose the constraint on the distance square instead of distance
directly, because the gradient of distance is not well defined at
distance=0; on the other hand, the gradient of the distance square is well
defined everywhere.
We parameterize the line using a point Q on the line, and a directional
vector n along the line.
@param plant The MultibodyPlant on which the constraint is imposed. `plant`
must be alive during the lifetime of this constraint.
@param frame_point The frame B1 to which the point P is attached.
@param p_B1P The position of point P measured and expressed in B1.
@param frame_line The frame B2 to which the line is attached.
@param p_B2Q Q is a point on the line, p_B2Q is the position of this point Q
measured and expressed in B2.
@param n_B2 n is the directional vector of the line, n_B2 is this vector
measured and expressed in B2.
@param distance_lower The lower bound on the distance, must be
non-negative.
@param distance_upper The upper bound on the distance, must be
non-negative.
@param plant_context The Context that has been allocated for this
`plant`. We will update the context when evaluating the constraint.
`plant_context` must be alive during the lifetime of this constraint.
@pydrake_mkdoc_identifier{double}
*/
PointToLineDistanceConstraint(const MultibodyPlant<double>* plant,
const Frame<double>& frame_point,
const Eigen::Ref<const Eigen::Vector3d>& p_B1P,
const Frame<double>& frame_line,
const Eigen::Ref<const Eigen::Vector3d>& p_B2Q,
const Eigen::Ref<const Eigen::Vector3d>& n_B2,
double distance_lower, double distance_upper,
systems::Context<double>* plant_context);
/**
Overloaded constructor. Same as the constructor with the double version
(using MultibodyPlant<double> and Context<double>), except the gradient of
the constraint is computed from autodiff.
@pydrake_mkdoc_identifier{autodiff}
*/
PointToLineDistanceConstraint(const MultibodyPlant<AutoDiffXd>* plant,
const Frame<AutoDiffXd>& frame_point,
const Eigen::Ref<const Eigen::Vector3d>& p_B1P,
const Frame<AutoDiffXd>& frame_line,
const Eigen::Ref<const Eigen::Vector3d>& p_B2Q,
const Eigen::Ref<const Eigen::Vector3d>& n_B2,
double distance_lower, double distance_upper,
systems::Context<AutoDiffXd>* plant_context);
~PointToLineDistanceConstraint() override {}
private:
void DoEval(const Eigen::Ref<const Eigen::VectorXd>& x,
Eigen::VectorXd* y) const override;
void DoEval(const Eigen::Ref<const AutoDiffVecXd>& x,
AutoDiffVecXd* y) const override;
void DoEval(const Eigen::Ref<const VectorX<symbolic::Variable>>&,
VectorX<symbolic::Expression>*) const override {
throw std::logic_error(
"PointToLineDistanceConstraint::DoEval() does not work for symbolic "
"variables.");
}
bool use_autodiff() const { return plant_autodiff_; }
const MultibodyPlant<double>* const plant_double_;
const FrameIndex frame_point_index_;
const FrameIndex frame_line_index_;
const Eigen::Vector3d p_B1P_;
const Eigen::Vector3d p_B2Q_;
const Eigen::Vector3d n_B2_normalized_;
// project_matrix = I - nnᵀ where n = n_B2_normalized_
const Eigen::Matrix3d project_matrix_;
systems::Context<double>* const context_double_;
const MultibodyPlant<AutoDiffXd>* const plant_autodiff_;
systems::Context<AutoDiffXd>* const context_autodiff_;
};
} // namespace multibody
} // namespace drake