iSAM2 : incremental smoothing and mapping using the Bayes tree

Author Posting. © The Author(s), 2011. This is the author's version of the work. It is posted here by permission of Sage for personal use, not for redistribution. The definitive version was published in International Journal of Robotics Research 31 (2012): 216-235, doi:10.1177/0278364911430419.We present a novel data structure, the Bayes tree, that provides an algorithmic foundation enabling a better understanding of existing graphical model inference algorithms and their connection to sparse matrix factorization methods. Similar to a clique tree, a Bayes tree encodes a factored probability density, but unlike the clique tree it is directed and maps more naturally to the square root information matrix of the simultaneous localization and mapping (SLAM) problem. In this paper, we highlight three insights provided by our new data structure. First, the Bayes tree provides a better understanding of the matrix factorization in terms of probability densities. Second, we show how the fairly abstract updates to a matrix factorization translate to a simple editing of the Bayes tree and its conditional densities. Third, we apply the Bayes tree to obtain a completely novel algorithm for sparse nonlinear incremental optimization, named iSAM2, which achieves improvements in efficiency through incremental variable re-ordering and fluid relinearization, eliminating the need for periodic batch steps. We analyze various properties of iSAM2 in detail, and show on a range of real and simulated datasets that our algorithm compares favorably with other recent mapping algorithms in both quality and efficiency.M. Kaess, H. Johannsson and J. Leonard were partially supported by ONR grants N00014-06-1-0043 and N00014-10-1-0936. F. Dellaert and R. Roberts were partially supported by NSF, award number 0713162, “RI: Inference in Large-Scale Graphical Models”. V. Ila has been partially supported by the Spanish MICINN under the Programa Nacional de Movilidad de Recursos Humanos de Investigación

Efficient Factor Graph Fusion for Multi-robot Mapping

This work presents a novel method to efficiently factorize the combination of multiple factor graphs having common variables of estimation. The fast-paced innovation in the algebraic graph theory has enabled new tools of state estimation like factor graphs. Recent factor graph formulation for Simultaneous Localization and Mapping (SLAM) like Incremental Smoothing and Mapping using the Bayes tree (ISAM2) has been very successful and garnered much attention. Variable ordering, a well-known technique in linear algebra is employed for solving the factor graph. Our primary contribution in this work is to reuse the variable ordering of the graphs being combined to find the ordering of the fused graph. In the case of mapping, multiple robots provide a great advantage over single robot by providing a faster map coverage and better estimation quality. This coupled with an inevitable increase in the number of robots around us produce a demand for faster algorithms. For example, a city full of self-driving cars could pool their observation measurements rapidly to plan a traffic free navigation. By reusing the variable ordering of the parent graphs we were able to produce an order-of-magnitude difference in the time required for solving the fused graph. We also provide a formal verification to show that the proposed strategy does not violate any of the relevant standards. A common problem in multi-robot SLAM is relative pose graph initialization to produce a globally consistent map. The other contribution addresses this by minimizing a specially formulated error function as a part of solving the factor graph. The performance is illustrated on a publicly available SuiteSparse dataset and the multi-robot AP Hill dataset

Least squares optimization: From theory to practice

Nowadays, Nonlinear Least-Squares embodies the foundation of many Robotics and Computer Vision systems. The research community deeply investigated this topic in the last few years, and this resulted in the development of several open-source solvers to approach constantly increasing classes of problems. In this work, we propose a unified methodology to design and develop efficient Least-Squares Optimization algorithms, focusing on the structures and patterns of each specific domain. Furthermore, we present a novel open-source optimization system that addresses problems transparently with a different structure and designed to be easy to extend. The system is written in modern C++ and runs efficiently on embedded systemsWe validated our approach by conducting comparative experiments on several problems using standard datasets. The results show that our system achieves state-of-the-art performances in all tested scenarios

Incremental cycle bases for cycle-based pose graph optimization

Pose graph optimization is a special case of the simultaneous localization and mapping problem where the only variables to be estimated are pose variables and the only measurements are inter-pose constraints. The vast majority of PGO techniques are vertex based (variables are robot poses), but recent work has parameterized the pose graph optimization problem in a relative fashion (variables are the transformations between poses) that utilizes a minimum cycle basis to maximize the sparsity of the problem. We explore the construction of a cycle basis in an incremental manner while maximizing the sparsity. We validate an algorithm that constructs a sparse cycle basis incrementally and compare its performance with a minimum cycle basis. Additionally, we present an algorithm to approximate the minimum cycle basis of two graphs that are sparsely connected as is common in multi-agent scenarios. Lastly, the relative parameterization of pose graph optimization has been limited to using rigid body transforms on SE(2) or SE(3) as the constraints between poses. We introduce a methodology to allow for the use of lower-degree-of-freedom measurements in the relative pose graph optimization problem. We provide extensive validation of our algorithms on standard benchmarks, simulated datasets, and custom hardware

Information metrics for localization and mapping

Decades of research have made possible the existence of several autonomous systems that successfully and efficiently navigate within a variety of environments under certain conditions. One core technology that has allowed this is simultaneous localization and mapping (SLAM), the process of building a representation of the environment while localizing the robot in it. State-of-the-art solutions to the SLAM problem still rely, however, on heuristic decisions and options set by the user. In this thesis we search for principled solutions to various aspects of the localization and mapping problem with the help of information metrics. One such aspect is the issue of scalability. In SLAM, the problem size grows indefinitely as the experiment goes by, increasing computational resource demands. To maintain the problem tractable, we develop methods to build an approximation to the original network of constraints of the SLAM problem by reducing its size while maintaining its sparsity. In this thesis we propose three methods to build the topology of such approximated network, and two methods to perform the approximation itself. In addition, SLAM is a passive application. It means, it does not drive the robot. The problem of driving the robot with the aim of both accurately localizing the robot and mapping the environment is called active SLAM. In this problem two normally opposite forces drive the robot, one to new places discovering unknown regions and another to revisit previous configurations to improve localization. As opposed to heuristics, in this thesis we pose the problem as the joint minimization of both map and trajectory estimation uncertainties, and present four different active SLAM approaches based on entropy-reduction formulation. All methods presented in this thesis have been rigorously validated in both synthetic and real datasets.Dècades de recerca han fet possible l’existència de nombrosos sistemes autònoms que naveguen eficaçment i eficient per varietat d’entorns sota certes condicions. Una de les principals tecnologies que ho han fet possible és la localització i mapeig simultanis (SLAM), el procés de crear una representació de l’entorn mentre es localitza el robot en aquesta. De tota manera, els algoritmes d’SLAM de l’estat de l’art encara basen moltes decisions en heurístiques i opcions a escollir per l’usuari final. Aquesta tesi persegueix solucions fonamentades per a varietat d’aspectes del problema de localització i mappeig amb l’ajuda de mesures d’informació. Un d’aquests aspectes és l’escalabilitat. En SLAM, el problema creix indefinidament a mesura que l’experiment avança fent créixer la demanda de recursos computacionals. Per mantenir el problema tractable, desenvolupem mètodes per construir una aproximació de la xarxa de restriccions original del problema d’SLAM, reduint així el seu tamany a l’hora que es manté la seva naturalesa dispersa. En aquesta tesi, proposem tres métodes per confeccionar la topologia de l’approximació i dos mètodes per calcular l’aproximació pròpiament. A més, l’SLAM és una aplicació passiva. És a dir que no dirigeix el robot. El problema de guiar el robot amb els objectius de localitzar el robot i mapejar l’entorn amb precisió es diu SLAM actiu. En aquest problema, dues forces normalment oposades guien el robot, una cap a llocs nous descobrint regions desconegudes i l’altra a revisitar prèvies configuracions per millorar la localització. En contraposició amb mètodes heurístics, en aquesta tesi plantegem el problema com una minimització de l’incertesa tant en el mapa com en l’estimació de la trajectòria feta i presentem quatre mètodes d’SLAM actiu basats en la reducció de l’entropia. Tots els mètodes presentats en aquesta tesi han estat rigurosament validats tant en sèries de dades sintètiques com en reals

Information metrics for localization and mapping

Decades of research have made possible the existence of several autonomous systems that successfully and efficiently navigate within a variety of environments under certain conditions. One core technology that has allowed this is simultaneous localization and mapping (SLAM), the process of building a representation of the environment while localizing the robot in it. State-of-the-art solutions to the SLAM problem still rely, however, on heuristic decisions and options set by the user. In this thesis we search for principled solutions to various aspects of the localization and mapping problem with the help of information metrics. One such aspect is the issue of scalability. In SLAM, the problem size grows indefinitely as the experiment goes by, increasing computational resource demands. To maintain the problem tractable, we develop methods to build an approximation to the original network of constraints of the SLAM problem by reducing its size while maintaining its sparsity. In this thesis we propose three methods to build the topology of such approximated network, and two methods to perform the approximation itself. In addition, SLAM is a passive application. It means, it does not drive the robot. The problem of driving the robot with the aim of both accurately localizing the robot and mapping the environment is called active SLAM. In this problem two normally opposite forces drive the robot, one to new places discovering unknown regions and another to revisit previous configurations to improve localization. As opposed to heuristics, in this thesis we pose the problem as the joint minimization of both map and trajectory estimation uncertainties, and present four different active SLAM approaches based on entropy-reduction formulation. All methods presented in this thesis have been rigorously validated in both synthetic and real datasets.Dècades de recerca han fet possible l’existència de nombrosos sistemes autònoms que naveguen eficaçment i eficient per varietat d’entorns sota certes condicions. Una de les principals tecnologies que ho han fet possible és la localització i mapeig simultanis (SLAM), el procés de crear una representació de l’entorn mentre es localitza el robot en aquesta. De tota manera, els algoritmes d’SLAM de l’estat de l’art encara basen moltes decisions en heurístiques i opcions a escollir per l’usuari final. Aquesta tesi persegueix solucions fonamentades per a varietat d’aspectes del problema de localització i mappeig amb l’ajuda de mesures d’informació. Un d’aquests aspectes és l’escalabilitat. En SLAM, el problema creix indefinidament a mesura que l’experiment avança fent créixer la demanda de recursos computacionals. Per mantenir el problema tractable, desenvolupem mètodes per construir una aproximació de la xarxa de restriccions original del problema d’SLAM, reduint així el seu tamany a l’hora que es manté la seva naturalesa dispersa. En aquesta tesi, proposem tres métodes per confeccionar la topologia de l’approximació i dos mètodes per calcular l’aproximació pròpiament. A més, l’SLAM és una aplicació passiva. És a dir que no dirigeix el robot. El problema de guiar el robot amb els objectius de localitzar el robot i mapejar l’entorn amb precisió es diu SLAM actiu. En aquest problema, dues forces normalment oposades guien el robot, una cap a llocs nous descobrint regions desconegudes i l’altra a revisitar prèvies configuracions per millorar la localització. En contraposició amb mètodes heurístics, en aquesta tesi plantegem el problema com una minimització de l’incertesa tant en el mapa com en l’estimació de la trajectòria feta i presentem quatre mètodes d’SLAM actiu basats en la reducció de l’entropia. Tots els mètodes presentats en aquesta tesi han estat rigurosament validats tant en sèries de dades sintètiques com en reals

Information metrics for localization and mapping

Aplicat embargament des de la defensa de la tesi fins al 12/2019Decades of research have made possible the existence of several autonomous systems that successfully and efficiently navigate within a variety of environments under certain conditions. One core technology that has allowed this is simultaneous localization and mapping (SLAM), the process of building a representation of the environment while localizing the robot in it. State-of-the-art solutions to the SLAM problem still rely, however, on heuristic decisions and options set by the user. In this thesis we search for principled solutions to various aspects of the localization and mapping problem with the help of information metrics. One such aspect is the issue of scalability. In SLAM, the problem size grows indefinitely as the experiment goes by, increasing computational resource demands. To maintain the problem tractable, we develop methods to build an approximation to the original network of constraints of the SLAM problem by reducing its size while maintaining its sparsity. In this thesis we propose three methods to build the topology of such approximated network, and two methods to perform the approximation itself. In addition, SLAM is a passive application. It means, it does not drive the robot. The problem of driving the robot with the aim of both accurately localizing the robot and mapping the environment is called active SLAM. In this problem two normally opposite forces drive the robot, one to new places discovering unknown regions and another to revisit previous configurations to improve localization. As opposed to heuristics, in this thesis we pose the problem as the joint minimization of both map and trajectory estimation uncertainties, and present four different active SLAM approaches based on entropy-reduction formulation. All methods presented in this thesis have been rigorously validated in both synthetic and real datasets.Dècades de recerca han fet possible l’existència de nombrosos sistemes autònoms que naveguen eficaçment i eficient per varietat d’entorns sota certes condicions. Una de les principals tecnologies que ho han fet possible és la localització i mapeig simultanis (SLAM), el procés de crear una representació de l’entorn mentre es localitza el robot en aquesta. De tota manera, els algoritmes d’SLAM de l’estat de l’art encara basen moltes decisions en heurístiques i opcions a escollir per l’usuari final. Aquesta tesi persegueix solucions fonamentades per a varietat d’aspectes del problema de localització i mappeig amb l’ajuda de mesures d’informació. Un d’aquests aspectes és l’escalabilitat. En SLAM, el problema creix indefinidament a mesura que l’experiment avança fent créixer la demanda de recursos computacionals. Per mantenir el problema tractable, desenvolupem mètodes per construir una aproximació de la xarxa de restriccions original del problema d’SLAM, reduint així el seu tamany a l’hora que es manté la seva naturalesa dispersa. En aquesta tesi, proposem tres métodes per confeccionar la topologia de l’approximació i dos mètodes per calcular l’aproximació pròpiament. A més, l’SLAM és una aplicació passiva. És a dir que no dirigeix el robot. El problema de guiar el robot amb els objectius de localitzar el robot i mapejar l’entorn amb precisió es diu SLAM actiu. En aquest problema, dues forces normalment oposades guien el robot, una cap a llocs nous descobrint regions desconegudes i l’altra a revisitar prèvies configuracions per millorar la localització. En contraposició amb mètodes heurístics, en aquesta tesi plantegem el problema com una minimització de l’incertesa tant en el mapa com en l’estimació de la trajectòria feta i presentem quatre mètodes d’SLAM actiu basats en la reducció de l’entropia. Tots els mètodes presentats en aquesta tesi han estat rigurosament validats tant en sèries de dades sintètiques com en reals.Postprint (published version

Full State History Cooperative Localisation with Complete Information Sharing

This thesis presents a decentralised localisation method for multiple robots. We enable reduced bandwidth requirements whilst using local solutions that fuse information from other robots. This method does not specify a communication topology or require complex tracking of information. The methods for including shared data match standard elements of nonlinear optimisation algorithms. There are four contributions in this thesis. The first is a method to split the multiple vehicle problem into sections that can be iteratively transmitted in packets with bandwidth bounds. This is done through delayed elimination of external states, which are states involved in intervehicle observations. Observations are placed in subgraphs that accumulate between external states. Internal states, which are all states not involved in intervehicle observations, can then be eliminated from each subgraph and the joint probability of the start and end states is shared between vehicles and combined to yield the solution to the entire graph. The second contribution is usage of variable reordering within these packets to enable handling of delayed observations that target an existing state such as with visual loop closures. We identify the calculations required to give the conditional probability of the delayed historical state on the existing external states before and after. This reduces the recalculation to updating the factorisation of a single subgraph and is independent of the time since the observation was made. The third contribution is a method and conditions for insertion of states into existing packets that does not invalidate previously transmitted data. We derive the conditions that enable this method and our fourth contribution is two motion models that conform to the conditions. Together this permits handling of the general out of sequence case

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

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.United States. Office of Naval Research (Grant N00014-06-1-0043)United States. Office of Naval Research (Grant N00014-10-1-0936)United States. Air Force Research Laboratory (Contract FA8650-11-C-7137