AttitudeFactor.h/AttitudeFactor.cpp

gravity相关
gtsam users group discussion

0、误差计算以SO3为例

  /** vector of errors */
Vector evaluateError(const Rot3& nRb, //nRb是优化初值
    boost::optional<Matrix&> H = boost::none) const override {
  return attitudeError(nRb, H);
Vector AttitudeFactor::attitudeError(const Rot3& nRb,
    OptionalJacobian<2, 3> H) const {
  if (H) {
    Matrix23 D_nRef_R;
    Matrix22 D_e_nRef;
    //bRef_是参考有defalt值(是一个vector,通常是重力方向默认(0,0,1))
    //下面是将bRef_通过nRb转到导航系下(world)(nRb是优化变量)
    Unit3 nRef = nRb.rotate(bRef_, D_nRef_R);
    //nz_是在导航系下的测量值
    //下面是测量值nZ_和上一步优化变量()计算误差，算Jacobian
    Vector e = nZ_.error(nRef, D_e_nRef);

    (*H) = D_e_nRef * D_nRef_R;
    return e;
  } else {
    Unit3 nRef = nRb * bRef_;
    return nZ_.error(nRef);
  }
}

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24

一、AttitudeFactor类

姿态的先验
在body frame的重力方向
reference是navigation frame中的重力方向
可是一般会进行设置body frame与navigation frame进行重合
如果nRb * bF == nG 因子将会输出零误差

nG==nRb * bF (body frame 转到navigation frame)

/**
 * Base class for prior on attitude
 * Example:
 * - measurement is direction of gravity in body frame bF
 * - reference is direction of gravity in navigation frame nG
 * This factor will give zero error if nRb * bF == nG
 * @addtogroup Navigation
 */
 class AttitudeFactor 
 {};
1
2
3
4
5
6
7
8
9
10

1.1 成员函数

都是protected作用域

protected:

  Unit3 nZ_, bRef_; ///< Position measurement in
1
2
3

1.2 构造函数

nZ是navigation frame的测量方向 bRef是在body frame中的参考方向 由系的转换的到旋转矩阵

nZ ->是在导航系中的测量
bRef ->body frame的参考方向

  /** default constructor - only use for serialization */
  AttitudeFactor() {
  }

  /**
   * @brief Constructor
   * @param nZ measured direction in navigation frame
   * @param bRef reference direction in body frame (default Z-axis in NED frame, i.e., [0; 0; 1])
   */
  AttitudeFactor(const Unit3& nZ, const Unit3& bRef = Unit3(0, 0, 1)) :
      nZ_(nZ), bRef_(bRef) {
  }
1
2
3
4
5
6
7
8
9
10
11
12

1.3 计算误差的

  /** vector of errors */
  Vector attitudeError(const Rot3& p,
      OptionalJacobian<2,3> H = boost::none) const;
1
2
3

重要的一个函数

//rotate 3D direction from rotated coordinate frame to world frame
gtsam::Unit3 gtsam::Rot3::rotate(const gtsam::Unit3 &p, gtsam::OptionalJacobian<2, 3> HR = boost::none, gtsam::OptionalJacobian<2, 2> Hp = boost::none) const
1
2

//nRb是body和navigation的变换关系
Vector AttitudeFactor::attitudeError(const Rot3& nRb,
    OptionalJacobian<2, 3> H) const {
  if (H) {
    Matrix23 D_nRef_R;
    Matrix22 D_e_nRef;
    Unit3 nRef = nRb.rotate(bRef_, D_nRef_R);//b -> world
    Vector e = nZ_.error(nRef, D_e_nRef);//nZ_测量，nRef计算得到，由于是单位向量所以D_e_nRef是2x2的矩阵

    (*H) = D_e_nRef * D_nRef_R;//链式求导//对变换关系的导数
    return e;
  } else {
    Unit3 nRef = nRb * bRef_;
    return nZ_.error(nRef);
  }
}
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16

1.4 其他

  const Unit3& nZ() const {
    return nZ_;
  }
  const Unit3& bRef() const {
    return bRef_;
  }

  /** Serialization function */
  friend class boost::serialization::access;
  template<class ARCHIVE>
  void serialize(ARCHIVE & ar, const unsigned int /*version*/) {
    ar & boost::serialization::make_nvp("nZ_",  nZ_);
    ar & boost::serialization::make_nvp("bRef_", bRef_);
  }
1
2
3
4
5
6
7
8
9
10
11
12
13
14

二、基于SO(3)的派生类

/**
 * Version of AttitudeFactor for Rot3
 * @addtogroup Navigation
 */
class GTSAM_EXPORT Rot3AttitudeFactor: public NoiseModelFactor1<Rot3>, public AttitudeFactor 
{};
1
2
3
4
5
6

2.1 一些定义

  typedef NoiseModelFactor1<Rot3> Base;

public:

  /// shorthand for a smart pointer to a factor
  typedef boost::shared_ptr<Rot3AttitudeFactor> shared_ptr;

  /// Typedef to this class
  typedef Rot3AttitudeFactor This;
1
2
3
4
5
6
7
8
9

2.2 有参构造

key ->value的key
nZ ->navigation frame中的测量方向
bRef ->body frame下的参考方向

  /**
   * @brief Constructor
   * @param key of the Rot3 variable that will be constrained
   * @param nZ measured direction in navigation frame
   * @param model Gaussian noise model
   * @param bRef reference direction in body frame (default Z-axis)
   */
  Rot3AttitudeFactor(Key key, const Unit3& nZ, const SharedNoiseModel& model,
      const Unit3& bRef = Unit3(0, 0, 1)) :
      Base(model, key), AttitudeFactor(nZ, bRef) {
  }
1
2
3
4
5
6
7
8
9
10
11

2.3 计算误差

见attitudeError

  /** vector of errors */
  Vector evaluateError(const Rot3& nRb, //
      boost::optional<Matrix&> H = boost::none) const override {
    return attitudeError(nRb, H);
  }
1
2
3
4
5

2.4 traits

三、基于SE(3)的派生类

class GTSAM_EXPORT Pose3AttitudeFactor: public NoiseModelFactor1<Pose3>, public AttitudeFactor 
{};
1
2

3.1 一些定义

  typedef NoiseModelFactor1<Pose3> Base;

public:

  /// shorthand for a smart pointer to a factor
  typedef boost::shared_ptr<Pose3AttitudeFactor> shared_ptr;

  /// Typedef to this class
  typedef Pose3AttitudeFactor This;
1
2
3
4
5
6
7
8
9

3.2 有参构造

key ->value的key
nZ ->navigation frame中的测量方向
bRef ->body frame下的参考方向

  /**
   * @brief Constructor
   * @param key of the Pose3 variable that will be constrained
   * @param nZ measured direction in navigation frame
   * @param model Gaussian noise model
   * @param bRef reference direction in body frame (default Z-axis)
   */
  Pose3AttitudeFactor(Key key, const Unit3& nZ, const SharedNoiseModel& model,
      const Unit3& bRef = Unit3(0, 0, 1)) :
      Base(model, key), AttitudeFactor(nZ, bRef) {
  }
1
2
3
4
5
6
7
8
9
10
11

3.3 误差函数

对Pose3的求导
对平移导数为0,只保留旋转的

  /** vector of errors */
  Vector evaluateError(const Pose3& nTb, //
      boost::optional<Matrix&> H = boost::none) const override {
    Vector e = attitudeError(nTb.rotation(), H);//对旋转求导
    if (H) {
      Matrix H23 = *H;
      *H = Matrix::Zero(2,6);
      H->block<2,3>(0,0) = H23;//对平移导数为0,只保留旋转的
    }
    return e;
  }
1
2
3
4
5
6
7
8
9
10
11

3.4 traits