More Applications

While a detailed discussion of all the things you can do with GTSAM will take us too far, below is a small survey of what you can expect to do, and which we did using GTSAM.

Conjugate Gradient Optimization

|image: 17\_Users\_dellaert\_git\_github\_doc\_images\_Beijing.png| Figure 15: A map of Beijing, with a spanning tree shown in black, and the remaining loop-closing constraints shown in red. A spanning tree can be used as a preconditioner by GTSAM.

GTSAM also includes efficient preconditioned conjugate gradients (PCG) methods for solving large-scale SLAM problems. While direct methods, popular in the literature, exhibit quadratic convergence and can be quite efficient for sparse problems, they typically require a lot of storage and efficient elimination orderings to be found. In contrast, iterative optimization methods only require access to the gradient and have a small memory footprint, but can suffer from poor convergence. Our method, subgraph preconditioning, explained in detail in Dellaert et al. (2010); Jian et al. (2011), combines the advantages of direct and iterative methods, by identifying a sub-problem that can be easily solved using direct methods, and solving for the remaining part using PCG. The easy sub-problems correspond to a spanning tree, a planar subgraph, or any other substructure that can be efficiently solved. An example of such a subgraph is shown in Figure 15.

Visual Odometry

A gentle introduction to vision-based sensing is Visual Odometry (abbreviated VO, see e.g. Nistér et al. (2004)), which provides pose constraints between successive robot poses by tracking or associating visual features in successive images taken by a camera mounted rigidly on the robot. GTSAM includes both C++ and MATLAB example code, as well as VO-specific factors to help you on the way.

Visual SLAM

Visual SLAM (see e.g., Davison (2003)) is a SLAM variant where 3D points are observed by a camera as the camera moves through space, either mounted on a robot or moved around by hand. GTSAM, and particularly iSAM (see below), can easily be adapted to be used as the back-end optimizer in such a scenario.

Fixed-lag Smoothing and Filtering

GTSAM can easily perform recursive estimation, where only a subset of the poses are kept in the factor graph, while the remaining poses are marginalized out. In all examples above we explicitly optimize for all variables using all available measurements, which is called Smoothing because the trajectory is “smoothed” out, and this is where GTSAM got its name (GT Smoothing and Mapping). When instead only the last few poses are kept in the graph, one speaks of Fixed-lag Smoothing. Finally, when only the single most recent poses is kept, one speaks of Filtering, and indeed the original formulation of SLAM was filter-based (Smith et al., 1988).

Discrete Variables and HMMs

Finally, factor graphs are not limited to continuous variables: GTSAM can also be used to model and solve discrete optimization problems. For example, a Hidden Markov Model (HMM) has the same graphical model structure as the Robot Localization problem from Section 2, except that in an HMM the variables are discrete. GTSAM can optimize and perform inference for discrete models.