1 基本资料

https://blog.csdn.net/heyijia0327/article/details/51773578

2推导公式

2-1 结论

2-2 slam14讲解推导

伴随性质利用

其中用到了近似

https://github.com/b51/CeresSim3Optimize

Jacobian Calculation of sim(3)

Derivation of $J a c o b i a n_{i}$

Same to $J a c o b i a n_{j}$

3代码

https://github.com/b51/CeresSim3Optimize

G2O代码

void EdgeSE3Expmap::computeError() {
  const VertexSE3Expmap* v1 = static_cast<const VertexSE3Expmap*>(_vertices[0]);
  const VertexSE3Expmap* v2 = static_cast<const VertexSE3Expmap*>(_vertices[1]);

  SE3Quat C(_measurement);
  SE3Quat error_ = v2->estimate().inverse() * C * v1->estimate();
  _error = error_.log();
}

void EdgeSE3Expmap::linearizeOplus() {
  VertexSE3Expmap* vi = static_cast<VertexSE3Expmap*>(_vertices[0]);
  SE3Quat Ti(vi->estimate());

  VertexSE3Expmap* vj = static_cast<VertexSE3Expmap*>(_vertices[1]);
  SE3Quat Tj(vj->estimate());

  const SE3Quat& Tij = _measurement;
  SE3Quat invTij = Tij.inverse();

  SE3Quat invTj_Tij = Tj.inverse() * Tij;
  SE3Quat infTi_invTij = Ti.inverse() * invTij;

  _jacobianOplusXi = invTj_Tij.adj();
  _jacobianOplusXj = -infTi_invTij.adj();
}