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LEGO

LEGO is a Light wEight Graph-based Optimization library in C++. It is a graph-based non-linear optimization framework for learning and practicing which only depends on Eigen3. This graph-based optimization library is designed for a generic purpose, and it is primarily targeted at Bundle Adjustment optimization problems in the backend of visual or visual-inertial SLAM. Now, the optimization problem solving in LEGO mainly depends on Levenberg-Marquardt algorithm with two updating strategies in the iterations and it will include more algorithms and updating strategies in the future, such as Dog-leg. This version is only tested on Ubuntu 18.04.

Installation

Prerequisites

  • GCC and CMake

  • Eigen3

    On Ubuntu 18.04, we can install CMake and Eigen3 following:

    # cmake 
sudo apt-get install gcc cmake 
# Eigen3 
sudo apt-get install libeigen3-dev

Build and Install

We can build and install LEGO from this repository and follow:

git clone https://github.com/zha0ming1e/LEGO.git 
cd LEGO/ 
mkdir build/ 
cd build/ 
cmake .. && make -j6 
# if you want to install it 
sudo make install

Now we have already installed the LEGO and then we can test and use it.

Examples

There are two examples which are implemented by LEGO (one of non-linear data fitting and one of pose graph optimization on SE3/se3 with Lie group/algebra) under the lego/examples/ folder.

  • Non-linear Data Fitting

    • Default updating strategy

      Run

      ./bin/example_nonlinear_fitting 0

      Output

      Example: Non-linear Fitting start... 
==========LEGO OPTIMIZER==========
Iteration = 0,	Chi = 185454,	Lambda = 0.01
Iteration = 1,	Chi = 153661,	Lambda = 6990.51
Iteration = 2,	Chi = 62936.6,	Lambda = 18641.4
Iteration = 3,	Chi = 27640.5,	Lambda = 12427.6
Iteration = 4,	Chi = 1090.47,	Lambda = 4142.52
Iteration = 5,	Chi = 546.72,	Lambda = 1380.84
Iteration = 6,	Chi = 526.969,	Lambda = 460.28
Iteration = 7,	Chi = 505.841,	Lambda = 153.427
Iteration = 8,	Chi = 490.512,	Lambda = 51.1423
Iteration = 9,	Chi = 487.068,	Lambda = 17.0474
Iteration = 10,	Chi = 486.901,	Lambda = 5.68247
Iteration = 11,	Chi = 486.9,	Lambda = 1.89416

Stop the optimization: [last_chi_(486.9) - currentChi_(486.9) = 1.17714e-06] < 1e-5

Info: 
TimeCost(SolveProblem) = 8.30634 ms
TimeCost(BuildHessian) = 6.29361 ms

--------Estimates after optimization--------
a, b, c = 0.98179, 2.0277, 0.989624
--------Ground truth--------
a, b, c = 1.0, 2.0, 1.0

    • Strategy 1

      Run

      ./bin/example_nonlinear_fitting 1

      Output

      Example: Non-linear Fitting start... 
==========LEGO OPTIMIZER==========
Iteration = 0,	Chi = 185454,	Lambda = 1e-05
Iteration = 1,	Chi = 10190.1,	Lambda = 1.9684
Iteration = 2,	Chi = 5286.38,	Lambda = 0.218711
Iteration = 3,	Chi = 3595.03,	Lambda = 0.0243012
Iteration = 4,	Chi = 1142.98,	Lambda = 0.00270014
Iteration = 5,	Chi = 531.136,	Lambda = 0.000300015
Iteration = 6,	Chi = 491.046,	Lambda = 3.3335e-05
Iteration = 7,	Chi = 486.914,	Lambda = 3.70389e-06
Iteration = 8,	Chi = 486.9,	Lambda = 4.11544e-07

Stop the optimization: [last_chi_(486.9) - currentChi_(486.9) = 8.1672e-07] < 1e-5

Info: 
TimeCost(SolveProblem) = 6.86506 ms
TimeCost(BuildHessian) = 5.41139 ms

--------Estimates after optimization--------
a, b, c = 0.98179, 2.0277, 0.989624
--------Ground truth--------
a, b, c = 1.0, 2.0, 1.0

    • Result

      nonlinear_fitting

  • Pose Graph Optimization on SE3/se3

    (e.g. pose graph optimization on se3/Lie algebra with the default updating strategy)

    Run

    ./bin/example_pose_graph_lie_algebra ./lego/examples/pose_graph/sphere_with_noise.g2o 0

    Output

    Example: Pose Graph Optimization with Lie Algebra start...
Read Total:
VertexCount = 2500, EdgeCount = 9799
Optimizing...
==========LEGO OPTIMIZER==========
Iteration = 0,  Chi = 4.78072e+09,      Lambda = 20119.8
Iteration = 1,  Chi = 3.13329e+08,      Lambda = 6706.59
Iteration = 2,  Chi = 1.16618e+08,      Lambda = 2235.53
Iteration = 3,  Chi = 7.13149e+07,      Lambda = 745.176
Iteration = 4,  Chi = 4.21091e+07,      Lambda = 248.392
Iteration = 5,  Chi = 2.10751e+07,      Lambda = 82.7973
Iteration = 6,  Chi = 8.36379e+06,      Lambda = 27.5991
Iteration = 7,  Chi = 3.09541e+06,      Lambda = 9.19971
Iteration = 8,  Chi = 1.10012e+06,      Lambda = 3.06657
Iteration = 9,  Chi = 367621,   Lambda = 1.02219
Iteration = 10, Chi = 142505,   Lambda = 0.34073
Iteration = 11, Chi = 85654.1,  Lambda = 0.185811
Iteration = 12, Chi = 72762.7,  Lambda = 0.061937
Iteration = 13, Chi = 71210.5,  Lambda = 0.0206457
Iteration = 14, Chi = 68794.8,  Lambda = 0.00688189
Iteration = 15, Chi = 65649.9,  Lambda = 0.00229396
Iteration = 16, Chi = 64014.7,  Lambda = 0.000764654
Iteration = 17, Chi = 63794.2,  Lambda = 0.000254885
Iteration = 18, Chi = 63789.1,  Lambda = 8.49616e-05
Iteration = 19, Chi = 63789.1,  Lambda = 2.83205e-05

Stop the optimization: [last_chi_(63789.1) - currentChi_(63789.1) = 5.42382e-06] < 1e-05

Info:
TimeCost(SolveProblem) = 1.17305e+07 ms
TimeCost(BuildHessian) = 18156.1 ms

Saving optimization results...

    Result

    # g2o_viewer: just for visualization 
g2o_viewer ./result_lie_0.g2o

    before_after_optimization

    optimization_comparison

Uninstall

We can delete the LEGO header files (*.h/*.hpp) and libs (*.so) from where we installed it. Default:

# headers 
sudo rm -rf /usr/local/include/lego/ 
# libs 
sudo rm -rf /usr/local/lib/liblego_*

References