Use ceres solver for extrinsics calibration
Using auto differentiation to solve for camera mount angle and imu bias.
Change-Id: I434f5bc7ac97acb5d18f09ec9174d79e6f5bbb06
Signed-off-by: milind-u <milind.upadhyay@gmail.com>
Signed-off-by: Austin Schuh <austin.linux@gmail.com>
diff --git a/frc971/control_loops/BUILD b/frc971/control_loops/BUILD
index 644346a..c7a5dd7 100644
--- a/frc971/control_loops/BUILD
+++ b/frc971/control_loops/BUILD
@@ -99,7 +99,9 @@
],
target_compatible_with = ["@platforms//os:linux"],
deps = [
+ ":jacobian",
":quaternion_utils",
+ ":runge_kutta",
"//aos/testing:googletest",
"//aos/testing:random_seed",
"@com_github_google_glog//:glog",
diff --git a/frc971/control_loops/drivetrain/improved_down_estimator.h b/frc971/control_loops/drivetrain/improved_down_estimator.h
index 548dba8..ddbf0bb 100644
--- a/frc971/control_loops/drivetrain/improved_down_estimator.h
+++ b/frc971/control_loops/drivetrain/improved_down_estimator.h
@@ -8,6 +8,7 @@
#include "aos/time/time.h"
#include "frc971/control_loops/drivetrain/drivetrain_config.h"
#include "frc971/control_loops/drivetrain/drivetrain_status_generated.h"
+#include "frc971/control_loops/quaternion_utils.h"
#include "frc971/control_loops/runge_kutta.h"
#include "glog/logging.h"
@@ -216,22 +217,9 @@
// A good reference for angular velocity vectors with quaternions is at
// http://www.euclideanspace.com/physics/kinematics/angularvelocity/
- // Creates a rotational velocity vector to be integrated.
- //
- // omega is the rotational velocity vector in body coordinates.
- // q is a matrix with the compononents of the quaternion in it.
- //
- // Returns dq / dt
static Eigen::Vector4d QuaternionDerivative(Eigen::Vector3d omega,
const Eigen::Vector4d &q_matrix) {
- Eigen::Quaternion<double> q(q_matrix);
-
- Eigen::Quaternion<double> omega_q;
- omega_q.w() = 0.0;
- omega_q.vec() = 0.5 * (q * omega);
-
- Eigen::Quaternion<double> deriv = omega_q * q;
- return deriv.coeffs();
+ return frc971::controls::QuaternionDerivative(omega, q_matrix);
}
// Moves the robot by the provided rotation vector (U).
diff --git a/frc971/control_loops/drivetrain/improved_down_estimator_test.cc b/frc971/control_loops/drivetrain/improved_down_estimator_test.cc
index 4dcfe60..3312030 100644
--- a/frc971/control_loops/drivetrain/improved_down_estimator_test.cc
+++ b/frc971/control_loops/drivetrain/improved_down_estimator_test.cc
@@ -27,71 +27,6 @@
}
} // namespace
-// Do a known transformation to see if quaternion integration is working
-// correctly.
-TEST(DownEstimatorTest, QuaternionIntegral) {
- Eigen::Vector3d ux = Eigen::Vector3d::UnitX();
- Eigen::Vector3d uy = Eigen::Vector3d::UnitY();
- Eigen::Vector3d uz = Eigen::Vector3d::UnitZ();
-
- Eigen::Quaternion<double> q(
- Eigen::AngleAxis<double>(0.5 * M_PI, Eigen::Vector3d::UnitY()));
-
- Eigen::Quaternion<double> q0(
- Eigen::AngleAxis<double>(0, Eigen::Vector3d::UnitY()));
-
- auto qux = q * ux;
-
- VLOG(1) << "Q is w: " << q.w() << " vec: " << q.vec();
- VLOG(1) << "ux is " << ux;
- VLOG(1) << "qux is " << qux;
-
- // Start by rotating around the X body vector for pi/2
- Eigen::Quaternion<double> integral1(
- RungeKutta(std::bind(&drivetrain::DrivetrainUkf::QuaternionDerivative, ux,
- std::placeholders::_1),
- q0.coeffs(), 0.5 * M_PI));
-
- VLOG(1) << "integral1 * uz => " << integral1 * uz;
-
- // Then rotate around the Y body vector for pi/2
- Eigen::Quaternion<double> integral2(
- RungeKutta(std::bind(&drivetrain::DrivetrainUkf::QuaternionDerivative, uy,
- std::placeholders::_1),
- integral1.normalized().coeffs(), 0.5 * M_PI));
-
- VLOG(1) << "integral2 * uz => " << integral2 * uz;
-
- // Then rotate around the X body vector for -pi/2
- Eigen::Quaternion<double> integral3(
- RungeKutta(std::bind(&drivetrain::DrivetrainUkf::QuaternionDerivative,
- -ux, std::placeholders::_1),
- integral2.normalized().coeffs(), 0.5 * M_PI));
-
- integral1.normalize();
- integral2.normalize();
- integral3.normalize();
-
- VLOG(1) << "Integral is w: " << integral1.w() << " vec: " << integral1.vec()
- << " norm " << integral1.norm();
-
- VLOG(1) << "Integral is w: " << integral3.w() << " vec: " << integral3.vec()
- << " norm " << integral3.norm();
-
- VLOG(1) << "ux => " << integral3 * ux;
- EXPECT_NEAR(0.0, (ux - integral1 * ux).norm(), 5e-2);
- EXPECT_NEAR(0.0, (uz - integral1 * uy).norm(), 5e-2);
- EXPECT_NEAR(0.0, (-uy - integral1 * uz).norm(), 5e-2);
-
- EXPECT_NEAR(0.0, (uy - integral2 * ux).norm(), 5e-2);
- EXPECT_NEAR(0.0, (uz - integral2 * uy).norm(), 5e-2);
- EXPECT_NEAR(0.0, (ux - integral2 * uz).norm(), 5e-2);
-
- EXPECT_NEAR(0.0, (uy - integral3 * ux).norm(), 5e-2);
- EXPECT_NEAR(0.0, (-ux - integral3 * uy).norm(), 5e-2);
- EXPECT_NEAR(0.0, (uz - integral3 * uz).norm(), 5e-2);
-}
-
TEST(DownEstimatorTest, UkfConstantRotation) {
drivetrain::DrivetrainUkf dtukf(
drivetrain::testing::GetTestDrivetrainConfig());
diff --git a/frc971/control_loops/quaternion_utils.cc b/frc971/control_loops/quaternion_utils.cc
index 0226e6d..bce78d0 100644
--- a/frc971/control_loops/quaternion_utils.cc
+++ b/frc971/control_loops/quaternion_utils.cc
@@ -5,52 +5,48 @@
namespace frc971 {
namespace controls {
+namespace {
-Eigen::Matrix<double, 4, 1> ToQuaternionFromRotationVector(
- const Eigen::Matrix<double, 3, 1> &X, const double max_angle_cap) {
- const double unclipped_angle = X.norm();
- const double angle_scalar =
- (unclipped_angle > max_angle_cap) ? max_angle_cap / unclipped_angle : 1.0;
- const double angle = unclipped_angle * angle_scalar;
- const double half_angle = angle * 0.5;
-
- const double half_angle_squared = half_angle * half_angle;
+double SinXoverX(double x) {
+ const double xsquared = x * x;
// sin(x)/x = 1
double sinx_x = 1.0;
// - x^2/3!
- double value = half_angle_squared / 6.0;
+ double value = xsquared / 6.0;
sinx_x -= value;
// + x^4/5!
- value = value * half_angle_squared / 20.0;
+ value = value * xsquared / 20.0;
sinx_x += value;
// - x^6/7!
- value = value * half_angle_squared / (6.0 * 7.0);
+ value = value * xsquared / (6.0 * 7.0);
sinx_x -= value;
// + x^8/9!
- value = value * half_angle_squared / (8.0 * 9.0);
+ value = value * xsquared / (8.0 * 9.0);
sinx_x += value;
// - x^10/11!
- value = value * half_angle_squared / (10.0 * 11.0);
+ value = value * xsquared / (10.0 * 11.0);
sinx_x -= value;
// + x^12/13!
- value = value * half_angle_squared / (12.0 * 13.0);
+ value = value * xsquared / (12.0 * 13.0);
sinx_x += value;
// - x^14/15!
- value = value * half_angle_squared / (14.0 * 15.0);
+ value = value * xsquared / (14.0 * 15.0);
sinx_x -= value;
// + x^16/17!
- value = value * half_angle_squared / (16.0 * 17.0);
+ value = value * xsquared / (16.0 * 17.0);
sinx_x += value;
+ return sinx_x;
+
// To plot the residual in matplotlib, run:
// import numpy
// import scipy
@@ -65,15 +61,10 @@
// x ** 14 / scipy.misc.factorial(15) +
// x ** 16 / scipy.misc.factorial(17) -
// numpy.sin(x) / x)
-
- const double scalar = sinx_x * 0.5;
-
- Eigen::Matrix<double, 4, 1> result;
- result.block<3, 1>(0, 0) = X * scalar * angle_scalar;
- result(3, 0) = std::cos(half_angle);
- return result;
}
+} // namespace
+
inline Eigen::Matrix<double, 4, 1> MaybeFlipX(
const Eigen::Matrix<double, 4, 1> &X) {
if (X(3, 0) < 0.0) {
@@ -83,6 +74,24 @@
}
}
+Eigen::Matrix<double, 4, 1> ToQuaternionFromRotationVector(
+ const Eigen::Matrix<double, 3, 1> &X, const double max_angle_cap) {
+ const double unclipped_angle = X.norm();
+ const double angle_scalar =
+ (unclipped_angle > max_angle_cap) ? max_angle_cap / unclipped_angle : 1.0;
+ const double angle = unclipped_angle * angle_scalar;
+ const double half_angle = angle * 0.5;
+
+ const double scalar = SinXoverX(half_angle) * 0.5;
+
+ Eigen::Matrix<double, 4, 1> result;
+ result.block<3, 1>(0, 0) = X * scalar * angle_scalar;
+ result(3, 0) = std::cos(half_angle);
+ return result;
+}
+
+// q = cos(a/2) + i ( x * sin(a/2)) + j (y * sin(a/2)) + k ( z * sin(a/2))
+
Eigen::Matrix<double, 3, 1> ToRotationVectorFromQuaternion(
const Eigen::Matrix<double, 4, 1> &X) {
// TODO(austin): Verify we still need it.
@@ -90,50 +99,38 @@
const double half_angle =
std::atan2(corrected_X.block<3, 1>(0, 0).norm(), corrected_X(3, 0));
- const double half_angle_squared = half_angle * half_angle;
-
- // TODO(austin): We are doing a division at the end of this. Do the taylor
- // series expansion of x/sin(x) instead to avoid this.
-
- // sin(x)/x = 1
- double sinx_x = 1.0;
-
- // - x^2/3!
- double value = half_angle_squared / 6.0;
- sinx_x -= value;
-
- // + x^4/5!
- value = value * half_angle_squared / 20.0;
- sinx_x += value;
-
- // - x^6/7!
- value = value * half_angle_squared / (6.0 * 7.0);
- sinx_x -= value;
-
- // + x^8/9!
- value = value * half_angle_squared / (8.0 * 9.0);
- sinx_x += value;
-
- // - x^10/11!
- value = value * half_angle_squared / (10.0 * 11.0);
- sinx_x -= value;
-
- // + x^12/13!
- value = value * half_angle_squared / (12.0 * 13.0);
- sinx_x += value;
-
- // - x^14/15!
- value = value * half_angle_squared / (14.0 * 15.0);
- sinx_x -= value;
-
- // + x^16/17!
- value = value * half_angle_squared / (16.0 * 17.0);
- sinx_x += value;
-
- const double scalar = 2.0 / sinx_x;
+ const double scalar = 2.0 / SinXoverX(half_angle);
return corrected_X.block<3, 1>(0, 0) * scalar;
}
+Eigen::Matrix<double, 4, 3> QuaternionDerivativeDerivitive(
+ const Eigen::Vector4d &q_matrix) {
+ // qa * qb = (a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
+ // a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
+ // a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x(),
+ // a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z())
+ //
+ // We want q * omega_q = result * omega.
+ Eigen::Matrix<double, 4, 3> result;
+ result(3, 0) = -q_matrix.x() * 0.5;
+ result(3, 1) = -q_matrix.y() * 0.5;
+ result(3, 2) = -q_matrix.z() * 0.5;
+
+ result(0, 0) = q_matrix.w() * 0.5;
+ result(0, 1) = -q_matrix.z() * 0.5;
+ result(0, 2) = q_matrix.y() * 0.5;
+
+ result(1, 0) = q_matrix.z() * 0.5;
+ result(1, 1) = q_matrix.w() * 0.5;
+ result(1, 2) = -q_matrix.x() * 0.5;
+
+ result(2, 0) = -q_matrix.y() * 0.5;
+ result(2, 1) = q_matrix.x() * 0.5;
+ result(2, 2) = q_matrix.w() * 0.5;
+
+ return result;
+}
+
} // namespace controls
} // namespace frc971
diff --git a/frc971/control_loops/quaternion_utils.h b/frc971/control_loops/quaternion_utils.h
index 25ffa91..e97935c 100644
--- a/frc971/control_loops/quaternion_utils.h
+++ b/frc971/control_loops/quaternion_utils.h
@@ -65,6 +65,34 @@
const Eigen::Matrix<double, 3, 1> &X,
const double max_angle_cap = std::numeric_limits<double>::infinity());
+// Creates a rotational velocity vector to be integrated.
+//
+// omega is the rotational velocity vector in body coordinates.
+// q is a matrix with the compononents of the quaternion in it.
+//
+// Returns dq / dt
+inline Eigen::Vector4d QuaternionDerivative(Eigen::Vector3d omega,
+ const Eigen::Vector4d &q_matrix) {
+ // See https://www.ashwinnarayan.com/post/how-to-integrate-quaternions/ for
+ // another resource on quaternion integration and derivitives.
+ Eigen::Quaternion<double> q(q_matrix);
+
+ Eigen::Quaternion<double> omega_q;
+ omega_q.w() = 0.0;
+ omega_q.vec() = 0.5 * omega;
+
+ Eigen::Quaternion<double> deriv = q * omega_q;
+ return deriv.coeffs();
+}
+
+// d QuaternionDerivative / d omega
+Eigen::Matrix<double, 4, 3> QuaternionDerivativeDerivitive(
+ const Eigen::Vector4d &q_matrix);
+inline Eigen::Matrix<double, 4, 3> QuaternionDerivativeDerivitive(
+ const Eigen::Quaternion<double> &q) {
+ return QuaternionDerivativeDerivitive(q.coeffs());
+}
+
} // namespace controls
} // namespace frc971
diff --git a/frc971/control_loops/quaternion_utils_test.cc b/frc971/control_loops/quaternion_utils_test.cc
index f472a46..ada5e60 100644
--- a/frc971/control_loops/quaternion_utils_test.cc
+++ b/frc971/control_loops/quaternion_utils_test.cc
@@ -2,8 +2,10 @@
#include <random>
-#include "frc971/control_loops/quaternion_utils.h"
#include "aos/testing/random_seed.h"
+#include "frc971/control_loops/jacobian.h"
+#include "frc971/control_loops/quaternion_utils.h"
+#include "frc971/control_loops/runge_kutta.h"
#include "glog/logging.h"
#include "gtest/gtest.h"
@@ -147,6 +149,68 @@
}
}
+// Do a known transformation to see if quaternion integration is working
+// correctly.
+TEST(DownEstimatorTest, QuaternionIntegral) {
+ Eigen::Vector3d ux = Eigen::Vector3d::UnitX();
+ Eigen::Vector3d uy = Eigen::Vector3d::UnitY();
+ Eigen::Vector3d uz = Eigen::Vector3d::UnitZ();
+
+ Eigen::Quaternion<double> q(
+ Eigen::AngleAxis<double>(0.5 * M_PI, Eigen::Vector3d::UnitY()));
+
+ Eigen::Quaternion<double> q0(
+ Eigen::AngleAxis<double>(0, Eigen::Vector3d::UnitY()));
+
+ auto qux = q * ux;
+
+ VLOG(1) << "Q is w: " << q.w() << " vec: " << q.vec();
+ VLOG(1) << "ux is " << ux;
+ VLOG(1) << "qux is " << qux;
+
+ // Start by rotating around the X body vector for pi/2
+ Eigen::Quaternion<double> integral1(control_loops::RungeKutta(
+ std::bind(&QuaternionDerivative, ux, std::placeholders::_1), q0.coeffs(),
+ 0.5 * M_PI));
+
+ VLOG(1) << "integral1 * uz => " << integral1 * uz;
+
+ // Then rotate around the Y body vector for pi/2
+ Eigen::Quaternion<double> integral2(control_loops::RungeKutta(
+ std::bind(&QuaternionDerivative, uy, std::placeholders::_1),
+ integral1.normalized().coeffs(), 0.5 * M_PI));
+
+ VLOG(1) << "integral2 * uz => " << integral2 * uz;
+
+ // Then rotate around the X body vector for -pi/2
+ Eigen::Quaternion<double> integral3(control_loops::RungeKutta(
+ std::bind(&QuaternionDerivative, -ux, std::placeholders::_1),
+ integral2.normalized().coeffs(), 0.5 * M_PI));
+
+ integral1.normalize();
+ integral2.normalize();
+ integral3.normalize();
+
+ VLOG(1) << "Integral is w: " << integral1.w() << " vec: " << integral1.vec()
+ << " norm " << integral1.norm();
+
+ VLOG(1) << "Integral is w: " << integral3.w() << " vec: " << integral3.vec()
+ << " norm " << integral3.norm();
+
+ VLOG(1) << "ux => " << integral3 * ux;
+ EXPECT_NEAR(0.0, (ux - integral1 * ux).norm(), 5e-2);
+ EXPECT_NEAR(0.0, (uz - integral1 * uy).norm(), 5e-2);
+ EXPECT_NEAR(0.0, (-uy - integral1 * uz).norm(), 5e-2);
+
+ EXPECT_NEAR(0.0, (uy - integral2 * ux).norm(), 5e-2);
+ EXPECT_NEAR(0.0, (uz - integral2 * uy).norm(), 5e-2);
+ EXPECT_NEAR(0.0, (ux - integral2 * uz).norm(), 5e-2);
+
+ EXPECT_NEAR(0.0, (uy - integral3 * ux).norm(), 5e-2);
+ EXPECT_NEAR(0.0, (-ux - integral3 * uy).norm(), 5e-2);
+ EXPECT_NEAR(0.0, (uz - integral3 * uz).norm(), 5e-2);
+}
+
} // namespace testing
} // namespace controls
} // namespace frc971
diff --git a/frc971/control_loops/runge_kutta.h b/frc971/control_loops/runge_kutta.h
index 61d674e..963f463 100644
--- a/frc971/control_loops/runge_kutta.h
+++ b/frc971/control_loops/runge_kutta.h
@@ -19,6 +19,18 @@
return X + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4);
}
+// Implements Runge Kutta integration (4th order) split up into steps steps. fn
+// is the function to integrate. It must take 1 argument of type T. The
+// integration starts at an initial value X, and integrates for dt.
+template <typename F, typename T>
+T RungeKuttaSteps(const F &fn, T X, double dt, int steps) {
+ dt = dt / steps;
+ for (int i = 0; i < steps; ++i) {
+ X = RungeKutta(fn, X, dt);
+ }
+ return X;
+}
+
// Implements Runge Kutta integration (4th order). This integrates dy/dt = fn(t,
// y). It must have the call signature of fn(double t, T y). The
// integration starts at an initial value y, and integrates for dt.