A first-order solution to simultaneous localization and mapping with graphical models

In this work we investigate the problem of Simultaneous Localization And Mapping (SLAM) for the case in which the information acquired by the robot is modeled as a network of constraints in a graphical model. Analyzing the resulting formulation we propose a closed-form approach to tackle the problem, which is proved to retrieve a first-order approximation of the actual nonlinear solution, under mild assumptions on the structure of the involved covariance matrices. The outcome of the analysis reveals several desirable properties of the proposed approach: no initial guess for optimization is needed and the technique is able to correctly estimate robot posterior also in presence of arbitrarily long loops. The approach is further validated by means of extensive simulations and real tests, and the consistency of the estimation process is also evaluated. We remark that this work is not intended to extend the already crowded literature on SLAM but is aimed at providing a consistent analytical insight, useful for efficiently attacking several open research issues, like active SLAM and exploration, for which the computational cost of simulating SLAM posterior still constitutes a troublesome bottleneck.

Authors

• Luca Carlone
• Rosario Aragues
• José A. Castellanos 0001
• Basilio Bona

Keywords

• Simultaneous localization and mapping
• Position measurement
• Trajectory
• Cost function
• Estimation
• Equations
• Graphical Model
• Covariance Matrix
• First Approximation
• Approximate Solution
• Real Test
• Mild Assumptions
• Reference Frame
• Relative Measure
• Linear Approximation
• Linear Problem
• Node Positions
• Pose Estimation
• Suboptimal Solution
• Cardinality Of The Set
• Incidence Matrix
• Extended Kalman Filter
• Local Frame
• Global Frame
• Orientation Of The Robot
• Absolute Orientation
• Loop Closure
• Relative Pose
• Orientation Estimation
• Unknown Position
• Open Loop
• Correction Factor
• Posterior Mode