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SE3 with Gaussian Distribution Emanuele Ruffaldi, Scuola Superiore Sant'Anna 2014-2016

Overview

Representation: group = rotation and translation as full 4x4 matrix adjoint = adjoint 6x6 representation of the group for transforming parameters algebra as parametric = 6 values of angular and translational velocity gaussian group = group with gaussian as 6x6 covariance

Function organization for use in Simulink

Function Organization

Useful for Matlab Simulink code generation, all under matse3

  • representation: group: matrix 4x4 alg: vector 1x6 dist: flattened(16+36): matrix4x4 followed by covariance (6x6)
  • operations on group (se3_): conversion, mul, invert, exp, log, adj
  • operations on group distribution (se3d_): conversion/build, mul, invert, fuse, sample, build from data

Class Organization

Class se3d wrapping the above functions

TODO

  • There is still an outstanding bug
  • Finalize testing of non linear transformation using sigma points
  • More Examples

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SE3 Lie algebra and distribution over SE3 in Matlab as functions

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