diff --git a/wpimath/src/main/java/edu/wpi/first/math/StateSpaceUtil.java b/wpimath/src/main/java/edu/wpi/first/math/StateSpaceUtil.java
index 35bac8a0e9..8baf401a4b 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/StateSpaceUtil.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/StateSpaceUtil.java
@@ -87,9 +87,9 @@ public final class StateSpaceUtil {
/**
* Returns true if (A, B) is a stabilizable pair.
*
- *
(A,B) is stabilizable if and only if the uncontrollable eigenvalues of A, if any, have
+ *
(A, B) is stabilizable if and only if the uncontrollable eigenvalues of A, if any, have
* absolute values less than one, where an eigenvalue is uncontrollable if rank(λI - A, B) %3C n
- * where n is number of states.
+ * where n is the number of states.
*
* @param Num representing the size of A.
* @param Num representing the columns of B.
@@ -103,6 +103,26 @@ public final class StateSpaceUtil {
return WPIMathJNI.isStabilizable(A.getNumRows(), B.getNumCols(), A.getData(), B.getData());
}
+ /**
+ * Returns true if (A, C) is a detectable pair.
+ *
+ * (A, C) is detectable if and only if the unobservable eigenvalues of A, if any, have absolute
+ * values less than one, where an eigenvalue is unobservable if rank(λI - A; C) %3C n where n is
+ * the number of states.
+ *
+ * @param Num representing the size of A.
+ * @param Num representing the rows of C.
+ * @param A System matrix.
+ * @param C Output matrix.
+ * @return If the system is detectable.
+ */
+ @SuppressWarnings("MethodTypeParameterName")
+ public static boolean isDetectable(
+ Matrix A, Matrix C) {
+ return WPIMathJNI.isStabilizable(
+ A.getNumRows(), C.getNumRows(), A.transpose().getData(), C.transpose().getData());
+ }
+
/**
* Convert a {@link Pose2d} to a vector of [x, y, theta], where theta is in radians.
*
diff --git a/wpimath/src/main/java/edu/wpi/first/math/WPIMathJNI.java b/wpimath/src/main/java/edu/wpi/first/math/WPIMathJNI.java
index 1e2ccaf4e6..54445d3600 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/WPIMathJNI.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/WPIMathJNI.java
@@ -79,9 +79,9 @@ public final class WPIMathJNI {
/**
* Returns true if (A, B) is a stabilizable pair.
*
- * (A,B) is stabilizable if and only if the uncontrollable eigenvalues of A, if any, have
+ *
(A, B) is stabilizable if and only if the uncontrollable eigenvalues of A, if any, have
* absolute values less than one, where an eigenvalue is uncontrollable if rank(lambda * I - A, B)
- * < n where n is number of states.
+ * < n where n is the number of states.
*
* @param states the number of states of the system.
* @param inputs the number of inputs to the system.
diff --git a/wpimath/src/main/java/edu/wpi/first/math/controller/LinearQuadraticRegulator.java b/wpimath/src/main/java/edu/wpi/first/math/controller/LinearQuadraticRegulator.java
index 1c957b7069..cf4b26dea8 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/controller/LinearQuadraticRegulator.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/controller/LinearQuadraticRegulator.java
@@ -5,6 +5,7 @@
package edu.wpi.first.math.controller;
import edu.wpi.first.math.Drake;
+import edu.wpi.first.math.MathSharedStore;
import edu.wpi.first.math.Matrix;
import edu.wpi.first.math.Nat;
import edu.wpi.first.math.Num;
@@ -90,7 +91,7 @@ public class LinearQuadraticRegulator A,
Matrix B,
@@ -101,6 +102,18 @@ public class LinearQuadraticRegulator& A,
const Eigen::Ref& B) {
- // This function checks if (A,B) is a stabilizable pair.
- // (A,B) is stabilizable if and only if the uncontrollable eigenvalues of
- // A, if any, have absolute values less than one, where an eigenvalue is
- // uncontrollable if Rank[lambda * I - A, B] < n.
- int n = B.rows(), m = B.cols();
- Eigen::EigenSolver es(A);
- for (int i = 0; i < n; i++) {
+ int states = B.rows();
+ int inputs = B.cols();
+ Eigen::EigenSolver es{A};
+ for (int i = 0; i < states; ++i) {
if (es.eigenvalues()[i].real() * es.eigenvalues()[i].real() +
es.eigenvalues()[i].imag() * es.eigenvalues()[i].imag() <
1) {
continue;
}
- Eigen::MatrixXcd E(n, n + m);
- E << es.eigenvalues()[i] * Eigen::MatrixXcd::Identity(n, n) - A, B;
- Eigen::ColPivHouseholderQR qr(E);
- if (qr.rank() != n) {
+ Eigen::MatrixXcd E{states, states + inputs};
+ E << es.eigenvalues()[i] * Eigen::MatrixXcd::Identity(states, states) - A,
+ B;
+ Eigen::ColPivHouseholderQR qr{E};
+ if (qr.rank() < states) {
return false;
}
}
@@ -196,7 +204,7 @@ Java_edu_wpi_first_math_WPIMathJNI_isStabilizable
Eigen::Matrix>
B{nativeB, states, inputs};
- bool isStabilizable = check_stabilizable(A, B); // NOLINT
+ bool isStabilizable = check_stabilizable(A, B);
env->ReleaseDoubleArrayElements(aSrc, nativeA, 0);
env->ReleaseDoubleArrayElements(bSrc, nativeB, 0);
diff --git a/wpimath/src/main/native/include/frc/StateSpaceUtil.h b/wpimath/src/main/native/include/frc/StateSpaceUtil.h
index 2d41915169..3300a48ea0 100644
--- a/wpimath/src/main/native/include/frc/StateSpaceUtil.h
+++ b/wpimath/src/main/native/include/frc/StateSpaceUtil.h
@@ -78,7 +78,7 @@ bool IsStabilizableImpl(const Eigen::Matrix& A,
Eigen::ColPivHouseholderQR<
Eigen::Matrix, States, States + Inputs>>
- qr(E);
+ qr{E};
if (qr.rank() < States) {
return false;
}
@@ -258,9 +258,9 @@ Eigen::Vector PoseTo4dVector(const Pose2d& pose);
/**
* Returns true if (A, B) is a stabilizable pair.
*
- * (A,B) is stabilizable if and only if the uncontrollable eigenvalues of A, if
+ * (A, B) is stabilizable if and only if the uncontrollable eigenvalues of A, if
* any, have absolute values less than one, where an eigenvalue is
- * uncontrollable if rank(λI - A, B) < n where n is number of states.
+ * uncontrollable if rank(λI - A, B) < n where n is the number of states.
*
* @param A System matrix.
* @param B Input matrix.
@@ -271,6 +271,23 @@ bool IsStabilizable(const Eigen::Matrix& A,
return detail::IsStabilizableImpl(A, B);
}
+/**
+ * Returns true if (A, C) is a detectable pair.
+ *
+ * (A, C) is detectable if and only if the unobservable eigenvalues of A, if
+ * any, have absolute values less than one, where an eigenvalue is unobservable
+ * if rank(λI - A; C) < n where n is the number of states.
+ *
+ * @param A System matrix.
+ * @param C Output matrix.
+ */
+template
+bool IsDetectable(const Eigen::Matrix& A,
+ const Eigen::Matrix& C) {
+ return detail::IsStabilizableImpl(A.transpose(),
+ C.transpose());
+}
+
// Template specializations are used here to make common state-input pairs
// compile faster.
template <>
diff --git a/wpimath/src/main/native/include/frc/controller/LinearQuadraticRegulator.h b/wpimath/src/main/native/include/frc/controller/LinearQuadraticRegulator.h
index c324702b81..a10f1ee0ac 100644
--- a/wpimath/src/main/native/include/frc/controller/LinearQuadraticRegulator.h
+++ b/wpimath/src/main/native/include/frc/controller/LinearQuadraticRegulator.h
@@ -4,6 +4,10 @@
#pragma once
+#include
+
+#include
+
#include
#include
@@ -16,6 +20,7 @@
#include "frc/system/LinearSystem.h"
#include "units/time.h"
#include "unsupported/Eigen/MatrixFunctions"
+#include "wpimath/MathShared.h"
namespace frc {
namespace detail {
@@ -82,6 +87,16 @@ class LinearQuadraticRegulatorImpl {
Eigen::Matrix discB;
DiscretizeAB(A, B, dt, &discA, &discB);
+ if (!IsStabilizable(discA, discB)) {
+ std::string msg = fmt::format(
+ "The system passed to the LQR is uncontrollable!\n\nA =\n{}\nB "
+ "=\n{}\n",
+ discA, discB);
+
+ wpi::math::MathSharedStore::ReportError(msg);
+ throw std::invalid_argument(msg);
+ }
+
Eigen::Matrix S =
drake::math::DiscreteAlgebraicRiccatiEquation(discA, discB, Q, R);
diff --git a/wpimath/src/main/native/include/frc/estimator/ExtendedKalmanFilter.h b/wpimath/src/main/native/include/frc/estimator/ExtendedKalmanFilter.h
index 985f2c14d9..8191f82b25 100644
--- a/wpimath/src/main/native/include/frc/estimator/ExtendedKalmanFilter.h
+++ b/wpimath/src/main/native/include/frc/estimator/ExtendedKalmanFilter.h
@@ -71,10 +71,7 @@ class ExtendedKalmanFilter {
Eigen::Matrix discR =
DiscretizeR(m_contR, dt);
- // IsStabilizable(Aᵀ, Cᵀ) will tell us if the system is observable.
- bool isObservable =
- IsStabilizable(discA.transpose(), C.transpose());
- if (isObservable && Outputs <= States) {
+ if (IsDetectable(discA, C) && Outputs <= States) {
m_initP = drake::math::DiscreteAlgebraicRiccatiEquation(
discA.transpose(), C.transpose(), discQ, discR);
} else {
@@ -137,10 +134,7 @@ class ExtendedKalmanFilter {
Eigen::Matrix discR =
DiscretizeR(m_contR, dt);
- // IsStabilizable(Aᵀ, Cᵀ) will tell us if the system is observable.
- bool isObservable =
- IsStabilizable(discA.transpose(), C.transpose());
- if (isObservable && Outputs <= States) {
+ if (IsDetectable(discA, C) && Outputs <= States) {
m_initP = drake::math::DiscreteAlgebraicRiccatiEquation(
discA.transpose(), C.transpose(), discQ, discR);
} else {
diff --git a/wpimath/src/main/native/include/frc/estimator/KalmanFilter.h b/wpimath/src/main/native/include/frc/estimator/KalmanFilter.h
index 363753e5a3..437b76eb16 100644
--- a/wpimath/src/main/native/include/frc/estimator/KalmanFilter.h
+++ b/wpimath/src/main/native/include/frc/estimator/KalmanFilter.h
@@ -4,7 +4,10 @@
#pragma once
+#include
+
#include
+#include
#include
#include
@@ -65,14 +68,14 @@ class KalmanFilterImpl {
const auto& C = plant.C();
- // IsStabilizable(Aᵀ, Cᵀ) will tell us if the system is observable.
- bool isObservable =
- IsStabilizable(discA.transpose(), C.transpose());
- if (!isObservable) {
- wpi::math::MathSharedStore::ReportError(
- "The system passed to the Kalman filter is not observable!");
- throw std::invalid_argument(
- "The system passed to the Kalman filter is not observable!");
+ if (!IsDetectable(discA, C)) {
+ std::string msg = fmt::format(
+ "The system passed to the Kalman filter is "
+ "unobservable!\n\nA =\n{}\nC =\n{}\n",
+ discA, C);
+
+ wpi::math::MathSharedStore::ReportError(msg);
+ throw std::invalid_argument(msg);
}
Eigen::Matrix P =
diff --git a/wpimath/src/test/java/edu/wpi/first/math/StateSpaceUtilTest.java b/wpimath/src/test/java/edu/wpi/first/math/StateSpaceUtilTest.java
index 795e76aa9d..456506c70c 100644
--- a/wpimath/src/test/java/edu/wpi/first/math/StateSpaceUtilTest.java
+++ b/wpimath/src/test/java/edu/wpi/first/math/StateSpaceUtilTest.java
@@ -76,6 +76,33 @@ public class StateSpaceUtilTest {
assertTrue(StateSpaceUtil.isStabilizable(A, B));
}
+ @Test
+ @SuppressWarnings("LocalVariableName")
+ public void testIsDetectable() {
+ Matrix A;
+ Matrix C = Matrix.mat(Nat.N1(), Nat.N2()).fill(0, 1);
+
+ // First eigenvalue is unobservable and unstable.
+ // Second eigenvalue is observable and stable.
+ A = Matrix.mat(Nat.N2(), Nat.N2()).fill(1.2, 0, 0, 0.5);
+ assertFalse(StateSpaceUtil.isDetectable(A, C));
+
+ // First eigenvalue is unobservable and marginally stable.
+ // Second eigenvalue is observable and stable.
+ A = Matrix.mat(Nat.N2(), Nat.N2()).fill(1, 0, 0, 0.5);
+ assertFalse(StateSpaceUtil.isDetectable(A, C));
+
+ // First eigenvalue is unobservable and stable.
+ // Second eigenvalue is observable and stable.
+ A = Matrix.mat(Nat.N2(), Nat.N2()).fill(0.2, 0, 0, 0.5);
+ assertTrue(StateSpaceUtil.isDetectable(A, C));
+
+ // First eigenvalue is unobservable and stable.
+ // Second eigenvalue is observable and unstable.
+ A = Matrix.mat(Nat.N2(), Nat.N2()).fill(0.2, 0, 0, 1.2);
+ assertTrue(StateSpaceUtil.isDetectable(A, C));
+ }
+
@Test
public void testMakeWhiteNoiseVector() {
var firstData = new ArrayList();
diff --git a/wpimath/src/test/native/cpp/StateSpaceUtilTest.cpp b/wpimath/src/test/native/cpp/StateSpaceUtilTest.cpp
index 3710cffd6c..57b93bb42b 100644
--- a/wpimath/src/test/native/cpp/StateSpaceUtilTest.cpp
+++ b/wpimath/src/test/native/cpp/StateSpaceUtilTest.cpp
@@ -134,3 +134,27 @@ TEST(StateSpaceUtilTest, IsStabilizable) {
EXPECT_TRUE((frc::IsStabilizable<2, 1>(
Eigen::Matrix{{0.2, 0}, {0, 1.2}}, B)));
}
+
+TEST(StateSpaceUtilTest, IsDetectable) {
+ Eigen::Matrix C{0, 1};
+
+ // First eigenvalue is unobservable and unstable.
+ // Second eigenvalue is observable and stable.
+ EXPECT_FALSE((frc::IsDetectable<2, 1>(
+ Eigen::Matrix{{1.2, 0}, {0, 0.5}}, C)));
+
+ // First eigenvalue is unobservable and marginally stable.
+ // Second eigenvalue is observable and stable.
+ EXPECT_FALSE((frc::IsDetectable<2, 1>(
+ Eigen::Matrix{{1, 0}, {0, 0.5}}, C)));
+
+ // First eigenvalue is unobservable and stable.
+ // Second eigenvalue is observable and stable.
+ EXPECT_TRUE((frc::IsDetectable<2, 1>(
+ Eigen::Matrix{{0.2, 0}, {0, 0.5}}, C)));
+
+ // First eigenvalue is unobservable and stable.
+ // Second eigenvalue is observable and unstable.
+ EXPECT_TRUE((frc::IsDetectable<2, 1>(
+ Eigen::Matrix{{0.2, 0}, {0, 1.2}}, C)));
+}