Package edu.wpi.first.math

Class StateSpaceUtil

java.lang.Object
edu.wpi.first.math.StateSpaceUtil
public final class StateSpaceUtil
extends Object
State-space utilities.

  • Method Details

    • makeCovarianceMatrix

      public static <States extends Num> Matrix<States,​States> makeCovarianceMatrix​(Nat<States> states, Matrix<States,​N1> stdDevs)
      Creates a covariance matrix from the given vector for use with Kalman filters.

      Each element is squared and placed on the covariance matrix diagonal.

      Type Parameters:
      States - Num representing the states of the system.
      Parameters:
      states - A Nat representing the states of the system.
      stdDevs - For a Q matrix, its elements are the standard deviations of each state from how the model behaves. For an R matrix, its elements are the standard deviations for each output measurement.
      Returns:
      Process noise or measurement noise covariance matrix.

    • makeWhiteNoiseVector

      public static <N extends Num> Matrix<N,​N1> makeWhiteNoiseVector​(Matrix<N,​N1> stdDevs)
      Creates a vector of normally distributed white noise with the given noise intensities for each element.
      Type Parameters:
      N - Num representing the dimensionality of the noise vector to create.
      Parameters:
      stdDevs - A matrix whose elements are the standard deviations of each element of the noise vector.
      Returns:
      White noise vector.

    • makeCostMatrix

      public static <Elements extends Num> Matrix<Elements,​Elements> makeCostMatrix​(Matrix<Elements,​N1> tolerances)
      Creates a cost matrix from the given vector for use with LQR.

      The cost matrix is constructed using Bryson's rule. The inverse square of each tolerance is placed on the cost matrix diagonal. If a tolerance is infinity, its cost matrix entry is set to zero.

      Type Parameters:
      Elements - Nat representing the number of system states or inputs.
      Parameters:
      tolerances - An array. For a Q matrix, its elements are the maximum allowed excursions of the states from the reference. For an R matrix, its elements are the maximum allowed excursions of the control inputs from no actuation.
      Returns:
      State excursion or control effort cost matrix.

    • isStabilizable

      public static <States extends Num,​ Inputs extends Num> boolean isStabilizable​(Matrix<States,​States> A, Matrix<States,​Inputs> B)
      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 absolute values less than one, where an eigenvalue is uncontrollable if rank([λI - A, B]) %3C n where n is the number of states.

      Type Parameters:
      States - Num representing the size of A.
      Inputs - Num representing the columns of B.
      Parameters:
      A - System matrix.
      B - Input matrix.
      Returns:
      If the system is stabilizable.

    • isDetectable

      public static <States extends Num,​ Outputs extends Num> boolean isDetectable​(Matrix<States,​States> A, Matrix<Outputs,​States> C)
      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.

      Type Parameters:
      States - Num representing the size of A.
      Outputs - Num representing the rows of C.
      Parameters:
      A - System matrix.
      C - Output matrix.
      Returns:
      If the system is detectable.

    • poseToVector

      public static Matrix<N3,​N1> poseToVector​(Pose2d pose)
      Convert a Pose2d to a vector of [x, y, theta], where theta is in radians.
      Parameters:
      pose - A pose to convert to a vector.
      Returns:
      The given pose in vector form, with the third element, theta, in radians.

    • clampInputMaxMagnitude

      public static <I extends Num> Matrix<I,​N1> clampInputMaxMagnitude​(Matrix<I,​N1> u, Matrix<I,​N1> umin, Matrix<I,​N1> umax)
      Clamp the input u to the min and max.
      Type Parameters:
      I - Number of inputs.
      Parameters:
      u - The input to clamp.
      umin - The minimum input magnitude.
      umax - The maximum input magnitude.
      Returns:
      The clamped input.

    • desaturateInputVector

      public static <I extends Num> Matrix<I,​N1> desaturateInputVector​(Matrix<I,​N1> u, double maxMagnitude)
      Renormalize all inputs if any exceeds the maximum magnitude. Useful for systems such as differential drivetrains.
      Type Parameters:
      I - Number of inputs.
      Parameters:
      u - The input vector.
      maxMagnitude - The maximum magnitude any input can have.
      Returns:
      The normalizedInput

    • poseTo4dVector

      public static Matrix<N4,​N1> poseTo4dVector​(Pose2d pose)
      Convert a Pose2d to a vector of [x, y, cos(theta), sin(theta)], where theta is in radians.
      Parameters:
      pose - A pose to convert to a vector.
      Returns:
      The given pose in as a 4x1 vector of x, y, cos(theta), and sin(theta).

    • poseTo3dVector

      public static Matrix<N3,​N1> poseTo3dVector​(Pose2d pose)
      Convert a Pose2d to a vector of [x, y, theta], where theta is in radians.
      Parameters:
      pose - A pose to convert to a vector.
      Returns:
      The given pose in vector form, with the third element, theta, in radians.