The Bayes Tree: An Algorithmic Foundation for Probabilistic Robot Mapping

Kaess, Michael; Ila, Viorela; Roberts, Richard; Dellaert, Frank

doi:10.1007/978-3-642-17452-0_10

Cited by 80 publications

(90 citation statements)

References 22 publications

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“…The complete Gauss-Newton method consists of iteratively applying equations (7), (11), (12), (10), and (8), in that order, until some stopping criterion is satisfied.…”

Section: A the Gauss-newton Methodsmentioning

confidence: 99%

“…In that case, the use of the Bayes Tree [8] and fluid relinearization enables the system to be efficiently relinearized at every timestep by applying direct updates only to those (few) rows of the factorR that are modified when relinearization occurs. One obtains the corresponding RISE2 algorithm by replacing lines 4 to 13 (inclusive) of Algorithm 4 with a different incremental update procedure forḡ: writingR on the right-hand side of equation (29) as a stack of (sparse) row vectors, and then using knowledge of how the rows ofR and the elements ofd have been modified in the current timestep, enables the computation of an efficient incremental update toḡ.…”

Section: Rise: Incrementalizing Powell's Dog-legmentioning

confidence: 99%

See 1 more Smart Citation

An incremental trust-region method for Robust online sparse least-squares estimation

Rosen

Kaess

Leonard

2012

2012 IEEE International Conference on Robotics and Automation

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Abstract-Many online inference problems in computer vision and robotics are characterized by probability distributions whose factor graph representations are sparse and whose factors are all Gaussian functions of error residuals. Under these conditions, maximum likelihood estimation corresponds to solving a sequence of sparse least-squares minimization problems in which additional summands are added to the objective function over time. In this paper we present Robust Incremental least-Squares Estimation (RISE), an incrementalized version of the Powell's Dog-Leg trust-region method suitable for use in online sparse least-squares minimization. As a trust-region method, Powell's Dog-Leg enjoys excellent global convergence properties, and is known to be considerably faster than both Gauss-Newton and Levenberg-Marquardt when applied to sparse least-squares problems. Consequently, RISE maintains the speed of current state-of-the-art incremental sparse least-squares methods while providing superior robustness to objective function nonlinearities.

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“…The complete Gauss-Newton method consists of iteratively applying equations (7), (11), (12), (10), and (8), in that order, until some stopping criterion is satisfied.…”

Section: A the Gauss-newton Methodsmentioning

confidence: 99%

Section: Rise: Incrementalizing Powell's Dog-legmentioning

confidence: 99%

An incremental trust-region method for Robust online sparse least-squares estimation

Rosen

Kaess

Leonard

2012

2012 IEEE International Conference on Robotics and Automation

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“…Given more powerful measurement models, as in Chapter 3, the user can be more optimistic when introducing measurement information. We stress that changing to non-Gaussian posteriors does not preclude use of the Bayes (Junction) tree [113], but instead actually casts the Bayes tree as a general framework for reducing computational complexity, regardless of the form and shape of likelihood functions used to assemble the factor graph.…”

Section: Multi-modality: Displacing Assumptionsmentioning

confidence: 99%

Multi-modal and inertial sensor solutions for navigation-type factor graphs

Fourie¹

2017

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This thesis presents a sum-product inference algorithm for platform navigation called Multi-modal iSAM (incremental smoothing and mapping). Common Gaussianonly likelihoods are restrictive and require a complex front-end processes to deal with non-Gaussian measurements. Instead, our approach allows the front-end to defer ambiguities with non-Gaussian measurement models. We retain the acyclic Bayes tree (and incremental update strategy) from the predecessor iSAM2 maxproduct algorithm [Kaess et al., IJRR 2012]. The approach propagates continuous beliefs on the Bayes (Junction) tree, which is an efficient symbolic refactorization of the nonparametric factor graph, and asymptotically approximates the underlying Chapman-Kolmogorov equations. Our method tracks dominant modes in the marginal posteriors of all variables with minimal approximation error, while suppressing almost all low likelihood modes (in a non-permanent manner). Keeping with existing inertial navigation, we present a novel, continuous-time, retroactively calibrating inertial odometry residual function, using preintegration to seamlessly incorporate pure inertial sensor measurements into a factor graph. We centralize around a factor graph (with starved graph databases) to separate elements of the navigation into an ecosystem of processes. Practical examples are included, such as how to infer multi-modal marginal posterior belief estimates for ambiguous loop closures; raw beam-formed acoustic measurements; or conventional parametric likelihoods, and others.

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“…The Bayes tree data structure [37] can be considered as an intermediate representation between the Cholesky factor and a junction tree. While not obvious in the matrix formulation, the Bayes tree allows a fully incremental algorithm, with incremental variable reordering and fluid relinearization.…”

Section: Pose Graph Optimization Using Smoothing and Mappingmentioning

confidence: 99%

Simultaneous Localization and Mapping in Marine Environments

Fallon

Johannsson

Kaess

et al. 2012

Marine Robot Autonomy

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Accurate navigation is a fundamental requirement for robotic systemsmarine and terrestrial. For an intelligent autonomous system to interact effectively and safely with its environment, it needs to accurately perceive its surroundings. While traditional dead-reckoning filtering can achieve extremely low drift rates, the localization accuracy decays monotonically with distance traveled. Other approaches (such as external beacons) can help; nonetheless, the typical prerogative is to remain at a safe distance and to avoid engaging with the environment. In this chapter we discuss alternative approaches which utilize onboard sensors so that the robot can estimate the location of sensed objects and use these observations to improve its own navigation as well as its perception of the environment. This approach allows for meaningful interaction and autonomy. Three motivating autonomous underwater vehicle (AUV) applications are outlined herein. The first fuses external range sensing with relative sonar measurements. The second application localizes

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The Bayes Tree: An Algorithmic Foundation for Probabilistic Robot Mapping

Cited by 80 publications

References 22 publications

An incremental trust-region method for Robust online sparse least-squares estimation

An incremental trust-region method for Robust online sparse least-squares estimation

Multi-modal and inertial sensor solutions for navigation-type factor graphs

Simultaneous Localization and Mapping in Marine Environments

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