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gaze_target_constraint.cc
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gaze_target_constraint.cc
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#include "drake/multibody/inverse_kinematics/gaze_target_constraint.h"
#include <limits>
#include "drake/math/autodiff_gradient.h"
#include "drake/multibody/inverse_kinematics/kinematic_evaluator_utilities.h"
using drake::multibody::internal::NormalizeVector;
using drake::multibody::internal::RefFromPtrOrThrow;
using drake::multibody::internal::UpdateContextConfiguration;
namespace drake {
namespace multibody {
GazeTargetConstraint::GazeTargetConstraint(
const MultibodyPlant<double>* const plant, const Frame<double>& frameA,
const Eigen::Ref<const Eigen::Vector3d>& p_AS,
const Eigen::Ref<const Eigen::Vector3d>& n_A, const Frame<double>& frameB,
const Eigen::Ref<const Eigen::Vector3d>& p_BT, double cone_half_angle,
systems::Context<double>* plant_context)
: solvers::Constraint(
2, RefFromPtrOrThrow(plant).num_positions(), Eigen::Vector2d::Zero(),
Eigen::Vector2d::Constant(std::numeric_limits<double>::infinity())),
plant_double_{plant},
frameA_index_{frameA.index()},
frameB_index_{frameB.index()},
p_AS_{p_AS},
n_A_{NormalizeVector(n_A)},
p_BT_{p_BT},
cone_half_angle_{cone_half_angle},
cos_cone_half_angle_{std::cos(cone_half_angle_)},
context_double_{plant_context},
plant_autodiff_{nullptr},
context_autodiff_{nullptr} {
if (plant_context == nullptr)
throw std::invalid_argument("plant_context is nullptr.");
if (cone_half_angle < 0 || cone_half_angle > M_PI_2) {
throw std::invalid_argument(
"GazeTargetConstraint: cone_half_angle should be within [0, pi/2]");
}
}
GazeTargetConstraint::GazeTargetConstraint(
const MultibodyPlant<AutoDiffXd>* const plant,
const Frame<AutoDiffXd>& frameA,
const Eigen::Ref<const Eigen::Vector3d>& p_AS,
const Eigen::Ref<const Eigen::Vector3d>& n_A,
const Frame<AutoDiffXd>& frameB,
const Eigen::Ref<const Eigen::Vector3d>& p_BT, double cone_half_angle,
systems::Context<AutoDiffXd>* plant_context)
: solvers::Constraint(
2, RefFromPtrOrThrow(plant).num_positions(), Eigen::Vector2d::Zero(),
Eigen::Vector2d::Constant(std::numeric_limits<double>::infinity())),
plant_double_{nullptr},
frameA_index_{frameA.index()},
frameB_index_{frameB.index()},
p_AS_{p_AS},
n_A_{NormalizeVector(n_A)},
p_BT_{p_BT},
cone_half_angle_{cone_half_angle},
cos_cone_half_angle_{std::cos(cone_half_angle_)},
context_double_{nullptr},
plant_autodiff_{plant},
context_autodiff_{plant_context} {
if (plant_context == nullptr)
throw std::invalid_argument("plant_context is nullptr.");
if (cone_half_angle < 0 || cone_half_angle > M_PI_2) {
throw std::invalid_argument(
"GazeTargetConstraint: cone_half_angle should be within [0, pi/2]");
}
}
void EvalConstraintGradient(
const systems::Context<double>& context,
const MultibodyPlant<double>& plant, const Frame<double>& frameA,
const Frame<double>& frameB, const Eigen::Vector3d& p_BT,
const Eigen::Vector3d& n_A,
const Eigen::Vector3d& cos_cone_half_angle_squared_times_p,
const double& p_dot_n, const Eigen::Vector2d& g,
const Eigen::Ref<const AutoDiffVecXd>& x, AutoDiffVecXd* y) {
// The constraint values are
// g(q) = ⎡ p · n_unit_A ⎤
// ⎣(p · n_unit_A)² - (cosθ)²p · p⎦
// where p is an abbreviation for p_ST_A(q). The partial derivative of g,
// ∂g/∂q, is therefore given by
// ∂g/∂q = ⎡n_unit_Aᵀ ⎤ ∂p/∂q,
// ⎣2 [(p · n_unit_A) n_unit_A - (cosθ)²p]ᵀ⎦
// Position of target point T measured and expressed in A frame.
Eigen::MatrixXd Jq_V_ABt(6, plant.num_positions());
plant.CalcJacobianSpatialVelocity(context, JacobianWrtVariable::kQDot, frameB,
p_BT, frameA, frameA, &Jq_V_ABt);
// Jq_p = Jq_v_ABt = ∂p/∂q.
const Matrix3X<double> Jq_p = Jq_V_ABt.bottomRows<3>();
// J_g_p = ∂g/∂p.
const Eigen::Matrix<double, 2, 3> Jp_g =
(Eigen::Matrix<double, 2, 3>() << n_A.transpose(),
2 * (p_dot_n * n_A - cos_cone_half_angle_squared_times_p).transpose())
.finished();
*y = math::InitializeAutoDiff(g, Jp_g * Jq_p * math::ExtractGradient(x));
}
template <typename T, typename S>
void DoEvalGeneric(const MultibodyPlant<T>& plant, systems::Context<T>* context,
const FrameIndex frameA_index, const FrameIndex frameB_index,
const Eigen::Vector3d& p_AS, const Eigen::Vector3d& n_A,
const Eigen::Vector3d p_BT, double cos_cone_half_angle,
const Eigen::Ref<const VectorX<S>>& x, VectorX<S>* y) {
UpdateContextConfiguration(context, plant, x);
const Frame<T>& frameA = plant.get_frame(frameA_index);
const Frame<T>& frameB = plant.get_frame(frameB_index);
// Position of target point T measured and expressed in A frame.
Vector3<T> p_AT;
plant.CalcPointsPositions(*context, frameB, p_BT.cast<T>(), frameA, &p_AT);
const Vector3<T> p_ST_A = p_AT - p_AS;
const T p_dot_n = p_ST_A.dot(n_A);
const Vector3<T> cos_cone_half_angle_squared_times_p =
std::pow(cos_cone_half_angle, 2) * p_ST_A;
// Constraint values, g.
const Vector2<T> g{
p_dot_n,
p_dot_n * p_dot_n - cos_cone_half_angle_squared_times_p.dot(p_ST_A)};
if constexpr (std::is_same_v<T, S>) {
*y = g;
} else {
EvalConstraintGradient(*context, plant, frameA, frameB, p_BT, n_A,
cos_cone_half_angle_squared_times_p, p_dot_n, g, x,
y);
}
}
void GazeTargetConstraint::DoEval(const Eigen::Ref<const Eigen::VectorXd>& x,
Eigen::VectorXd* y) const {
if (use_autodiff()) {
AutoDiffVecXd y_t;
Eval(x.cast<AutoDiffXd>(), &y_t);
*y = math::ExtractValue(y_t);
} else {
DoEvalGeneric(*plant_double_, context_double_, frameA_index_, frameB_index_,
p_AS_, n_A_, p_BT_, cos_cone_half_angle_, x, y);
}
}
void GazeTargetConstraint::DoEval(const Eigen::Ref<const AutoDiffVecXd>& x,
AutoDiffVecXd* y) const {
if (use_autodiff()) {
DoEvalGeneric(*plant_autodiff_, context_autodiff_, frameA_index_,
frameB_index_, p_AS_, n_A_, p_BT_, cos_cone_half_angle_, x,
y);
} else {
DoEvalGeneric(*plant_double_, context_double_, frameA_index_, frameB_index_,
p_AS_, n_A_, p_BT_, cos_cone_half_angle_, x, y);
}
}
} // namespace multibody
} // namespace drake