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gaze_target_constraint_test.cc
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gaze_target_constraint_test.cc
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#include "drake/multibody/inverse_kinematics/gaze_target_constraint.h"
#include <gtest/gtest.h>
#include "drake/multibody/inverse_kinematics/test/inverse_kinematics_test_utilities.h"
using drake::systems::Context;
namespace drake {
namespace multibody {
namespace {
AutoDiffVecXd EvalGazeTargetConstraintAutoDiff(
const MultibodyPlant<AutoDiffXd>& plant, const Frame<AutoDiffXd>& frameA,
const Vector3<double>& p_AS, const Vector3<double>& n_A,
const Frame<AutoDiffXd>& frameB, const Vector3<double>& p_BT,
double cone_half_angle, const Context<AutoDiffXd>& context) {
Vector3<AutoDiffXd> p_AT;
plant.CalcPointsPositions(context, frameB, p_BT.cast<AutoDiffXd>(), frameA,
&p_AT);
const Vector3<AutoDiffXd> p_ST_A = p_AT - p_AS;
Vector2<AutoDiffXd> y_autodiff;
const Vector3<double> n_A_normalized = n_A.normalized();
y_autodiff(0) = p_ST_A.dot(n_A_normalized);
y_autodiff(1) = pow(p_ST_A.dot(n_A_normalized), 2) -
std::pow(std::cos(cone_half_angle), 2) * p_ST_A.squaredNorm();
return y_autodiff;
}
TEST_F(IiwaKinematicConstraintTest, GazeTargetConstraint) {
const auto frameA_index = plant_->GetFrameByName("iiwa_link_7").index();
const auto frameB_index = plant_->GetFrameByName("iiwa_link_3").index();
const Frame<double>& frameA = plant_->get_frame(frameA_index);
const Frame<double>& frameB = plant_->get_frame(frameB_index);
const Eigen::Vector3d p_AS(0.1, 0.2, 0.3);
const Eigen::Vector3d n_A(-0.1, 0.3, 0.4);
const Eigen::Vector3d p_BT(0.4, 0.2, -0.3);
const double cone_half_angle{0.1 * M_PI};
GazeTargetConstraint constraint(plant_, frameA, p_AS, n_A, frameB, p_BT,
cone_half_angle, plant_context_);
EXPECT_EQ(constraint.num_constraints(), 2);
EXPECT_EQ(constraint.num_vars(), plant_autodiff_->num_positions());
EXPECT_TRUE(
CompareMatrices(constraint.lower_bound(), Eigen::Vector2d::Zero()));
EXPECT_TRUE(CompareMatrices(
constraint.upper_bound(),
Eigen::Vector2d::Constant(std::numeric_limits<double>::infinity())));
Eigen::VectorXd q(plant_autodiff_->num_positions());
// arbitrary joint configuration.
q << 0.1, 0.2, -0.3, 0.5, -0.2, -0.05, 0.34;
AutoDiffVecXd q_autodiff = math::InitializeAutoDiff(q);
AutoDiffVecXd y_autodiff;
constraint.Eval(q_autodiff, &y_autodiff);
plant_autodiff_->SetPositions(plant_context_autodiff_.get(), q_autodiff);
Vector2<AutoDiffXd> y_autodiff_expected = EvalGazeTargetConstraintAutoDiff(
*plant_autodiff_,
plant_autodiff_->GetFrameByName(frameA.name()), p_AS, n_A,
plant_autodiff_->GetFrameByName(frameB.name()), p_BT,
cone_half_angle, *plant_context_autodiff_);
CompareAutoDiffVectors(y_autodiff, y_autodiff_expected, 1E-12);
// Test with non-identity gradient for q_autodiff.
q_autodiff = math::InitializeAutoDiff(q, MatrixX<double>::Ones(q.size(), 2));
plant_autodiff_->SetPositions(plant_context_autodiff_.get(), q_autodiff);
constraint.Eval(q_autodiff, &y_autodiff);
y_autodiff_expected = EvalGazeTargetConstraintAutoDiff(
*plant_autodiff_,
plant_autodiff_->GetFrameByName(frameA.name()), p_AS, n_A,
plant_autodiff_->GetFrameByName(frameB.name()), p_BT,
cone_half_angle, *plant_context_autodiff_);
CompareAutoDiffVectors(y_autodiff, y_autodiff_expected, 1E-12);
// Checks if the constraint constructed from MBP<ADS> gives the same result
// as from MBP<double>.
const GazeTargetConstraint constraint_from_autodiff(
plant_autodiff_.get(), plant_autodiff_->get_frame(frameA_index), p_AS,
n_A, plant_autodiff_->get_frame(frameB_index), p_BT, cone_half_angle,
plant_context_autodiff_.get());
// Set dq to arbitrary value.
Eigen::Matrix<double, 7, 2> dq;
for (int i = 0; i < 7; ++i) {
dq(i, 0) = i * 2 + 1;
dq(i, 1) = std::sin(i + 0.2);
}
/* tolerance for checking numerical gradient vs analytical gradient. The
* numerical gradient is only accurate up to 1E-6 */
const double gradient_tol = 1E-6;
TestKinematicConstraintEval(constraint, constraint_from_autodiff, q, dq,
gradient_tol);
}
TEST_F(TwoFreeBodiesConstraintTest, GazeTargetConstraint) {
// All the numbers are chosen arbitrarily.
const Eigen::Vector3d p_AS(0.2, -0.1, 0.3);
const Eigen::Vector3d n_A(0.4, -0.3, 0.9);
const Eigen::Vector3d p_BT(-0.02, 0.5, 1.3);
const Eigen::Quaterniond body1_quaternion(Eigen::AngleAxisd(
0.1 * M_PI, Eigen::Vector3d(0.2, -.9, 1.3).normalized()));
const Eigen::Vector3d body1_position(0.5, 1.6, 2.3);
const Eigen::Quaterniond body2_quaternion(Eigen::AngleAxisd(
0.3 * M_PI, Eigen::Vector3d(0.1, -1.5, 2.4).normalized()));
const Eigen::Vector3d body2_position(0.1, -2.3, 10.2);
Eigen::Matrix<double, 14, 1> q;
q << QuaternionToVectorWxyz(body1_quaternion), body1_position,
QuaternionToVectorWxyz(body2_quaternion), body2_position;
// Compute the angle between the vector p_ST and n_A;
const Eigen::Vector3d p_AT =
body1_quaternion.inverse() *
(body2_quaternion * p_BT + body2_position - body1_position);
const Eigen::Vector3d p_ST_A = p_AT - p_AS;
const double angle =
std::acos(p_ST_A.dot(n_A) / (p_ST_A.norm() * n_A.norm()));
{
GazeTargetConstraint good_constraint(
plant_, plant_->get_frame(body1_index_), p_AS, n_A,
plant_->get_frame(body2_index_), p_BT, angle + 0.01 * M_PI,
plant_context_);
EXPECT_TRUE(good_constraint.CheckSatisfied(q));
}
{
GazeTargetConstraint bad_constraint(
plant_, plant_->get_frame(body1_index_), p_AS, n_A,
plant_->get_frame(body2_index_), p_BT, angle - 0.01 * M_PI,
plant_context_);
EXPECT_FALSE(bad_constraint.CheckSatisfied(q));
}
}
TEST_F(IiwaKinematicConstraintTest, GazeTargetConstraintConstructorError) {
// Check if the constructor for GazeTargetConstraint will throw errors if the
// inputs are incorrect.
const Eigen::Vector3d p_AS(1, 2, 3);
const Eigen::Vector3d p_BT(2, 3, 4);
const Frame<double>& frameA = plant_->GetFrameByName("iiwa_link_3");
const Frame<double>& frameB = plant_->GetFrameByName("iiwa_link_4");
// zero n_A
EXPECT_THROW(
GazeTargetConstraint(plant_, frameA, p_AS, Eigen::Vector3d::Zero(),
frameB, p_BT, 0.1, plant_context_),
std::invalid_argument);
// cone_half_angle < 0
EXPECT_THROW(
GazeTargetConstraint(plant_, frameA, p_AS, Eigen::Vector3d::Ones(),
frameB, p_BT, -0.1, plant_context_),
std::invalid_argument);
// cone_half_angle > π/2
EXPECT_THROW(
GazeTargetConstraint(plant_, frameA, p_AS, Eigen::Vector3d::Ones(),
frameB, p_BT, 1.6, plant_context_),
std::invalid_argument);
}
} // namespace
} // namespace multibody
} // namespace drake