ISAM2: Incremental Smoothing and Mapping Using the Bayes Tree Michael Kaess, Hordur Johannsson, Richard Roberts, Viorela Ila, John Leonard, and Frank Dellaert.

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Presentation transcript:

iSAM2: Incremental Smoothing and Mapping Using the Bayes Tree Michael Kaess, Hordur Johannsson, Richard Roberts, Viorela Ila, John Leonard, and Frank Dellaert

iSAM (Kaess et al., TRO ‘08) Solving a growing system:  Exact/batch (quickly gets expensive)  Approximations  Incremental Smoothing and Mapping (iSAM)

iSAM (Kaess et al., TRO ‘08) Key Idea:  Append to existing matrix factorization.  “Repair” using Givens rotations. Periodic batch steps for  Relinearization.  Variable reordering (to keep sparsity)

Matrix vs. Graph Measurement Jacobian Factor Graph Information Matrix Markov Random Field Square Root Inf. Matrix

Factor Graph(Kschischang et al., 2001) A bipartite graph  Factor nodes  Variable nodes  Edges are always between factor nodes and variables nodes.

 The goal is to find the variable assignment that maximizes the function before:

Inference and Elimination  Inference  Converting the factor graph to a Bayes net using the elimination algorithm  Elimination is done by using bipartite elimination game

After eliminating all variables, the Bayes net density is defined by the product of the conditionals produced at each step:

Bayes Tree Definition  A directed graph  Similar to Bayes net as it encodes a factored probability density.  Includes one conditional density per node with separator S k  Frontal variables F k as the remaining variables

Creating Bayes Tree

Incremental Inference

Incremental Variable Ordering

The iSAM2 Algorithm

Fluid Relinearization

Partial State Updates