[wpimath] Add ImplicitModelFollower (#4056)

wpimath/src/main/native/include/frc/controller/ImplicitModelFollower.h

@@ -0,0 +1,137 @@
+// Copyright (c) FIRST and other WPILib contributors.
+// Open Source Software; you can modify and/or share it under the terms of
+// the WPILib BSD license file in the root directory of this project.
+
+#pragma once
+
+#include <frc/system/Discretization.h>
+#include <frc/system/LinearSystem.h>
+
+#include "Eigen/Core"
+#include "Eigen/QR"
+#include "units/time.h"
+
+namespace frc {
+
+/**
+ * Contains the controller coefficients and logic for an implicit model
+ * follower.
+ *
+ * Implicit model following lets us design a feedback controller that erases the
+ * dynamics of our system and makes it behave like some other system. This can
+ * be used to make a drivetrain more controllable during teleop driving by
+ * making it behave like a slower or more benign drivetrain.
+ *
+ * For more on the underlying math, read appendix B.3 in
+ * https://file.tavsys.net/control/controls-engineering-in-frc.pdf.
+ */
+template <int States, int Inputs>
+class ImplicitModelFollower {
+ public:
+  /**
+   * Constructs a controller with the given coefficients and plant.
+   *
+   * @param plant    The plant being controlled.
+   * @param plantRef The plant whose dynamics should be followed.
+   * @param dt       Discretization timestep.
+   */
+  template <int Outputs>
+  ImplicitModelFollower(const LinearSystem<States, Inputs, Outputs>& plant,
+                        const LinearSystem<States, Inputs, Outputs>& plantRef,
+                        units::second_t dt)
+      : ImplicitModelFollower<States, Inputs>(plant.A(), plant.B(),
+                                              plantRef.A(), plantRef.B(), dt) {}
+
+  /**
+   * Constructs a controller with the given coefficients and plant.
+   *
+   * @param A      Continuous system matrix of the plant being controlled.
+   * @param B      Continuous input matrix of the plant being controlled.
+   * @param Aref   Continuous system matrix whose dynamics should be followed.
+   * @param Bref   Continuous input matrix whose dynamics should be followed.
+   * @param dt     Discretization timestep.
+   */
+  ImplicitModelFollower(const Eigen::Matrix<double, States, States>& A,
+                        const Eigen::Matrix<double, States, Inputs>& B,
+                        const Eigen::Matrix<double, States, States>& Aref,
+                        const Eigen::Matrix<double, States, Inputs>& Bref,
+                        units::second_t dt) {
+    // Discretize real dynamics
+    Eigen::Matrix<double, States, States> discA;
+    Eigen::Matrix<double, States, Inputs> discB;
+    frc::DiscretizeAB<States, Inputs>(A, B, dt, &discA, &discB);
+
+    // Discretize desired dynamics
+    Eigen::Matrix<double, States, States> discAref;
+    Eigen::Matrix<double, States, Inputs> discBref;
+    frc::DiscretizeAB<States, Inputs>(Aref, Bref, dt, &discAref, &discBref);
+
+    // Find u_imf that makes real model match reference model.
+    //
+    // x_k+1 = Ax_k + Bu_imf
+    // z_k+1 = Aref z_k + Bref u_k
+    //
+    // Let x_k = z_k.
+    //
+    // x_k+1 = z_k+1
+    // Ax_k + Bu_imf = Aref x_k + Bref u_k
+    // Bu_imf = Aref x_k - Ax_k + Bref u_k
+    // Bu_imf = (Aref - A)x_k + Bref u_k
+    // u_imf = B^+ ((Aref - A)x_k + Bref u_k)
+    // u_imf = -B^+ (A - Aref)x_k + B^+ Bref u_k
+
+    // The first term makes the open-loop poles that of the reference
+    // system, and the second term makes the input behave like that of the
+    // reference system.
+    m_A = -discB.householderQr().solve(discA - discAref);
+    m_B = discB.householderQr().solve(discBref);
+
+    Reset();
+  }
+
+  /**
+   * Returns the control input vector u.
+   *
+   * @return The control input.
+   */
+  const Eigen::Vector<double, Inputs>& U() const { return m_u; }
+
+  /**
+   * Returns an element of the control input vector u.
+   *
+   * @param i Row of u.
+   *
+   * @return The row of the control input vector.
+   */
+  double U(int i) const { return m_u(i); }
+
+  /**
+   * Resets the controller.
+   */
+  void Reset() { m_u.setZero(); }
+
+  /**
+   * Returns the next output of the controller.
+   *
+   * @param x The current state x.
+   * @param u The current input for the original model.
+   */
+  Eigen::Vector<double, Inputs> Calculate(
+      const Eigen::Vector<double, States>& x,
+      const Eigen::Vector<double, Inputs>& u) {
+    m_u = m_A * x + m_B * u;
+    return m_u;
+  }
+
+ private:
+  // Computed controller output
+  Eigen::Vector<double, Inputs> m_u;
+
+  // State space conversion gain
+  Eigen::Matrix<double, Inputs, States> m_A;
+
+  // Input space conversion gain
+  Eigen::Matrix<double, Inputs, Inputs> m_B;
+};
+
+}  // namespace frc