Research Proposal

1 Motivation

Localization and Mapping is the most important and fundamental problem in developing CyberPhisical sytems like Robotics. The idea of simultaneously finding the pose of the device (Localiza-tion) and extracting the features of the unknown environment (Mapping), gave a breakthrough in1995 and became an eyeopener in 2005, when Stanley autonomous car won DARPA grand chal-lenge, which actually included Simultaneous Localization and Mapping (SLAM) system. Thesolution to SLAM problem has been seen as a holy grail for the mobile robotics community as itwould provide the means to make a robot truly autonomous. SLAM algorithms are employed in un-manned aerial vehicles, autonomous underwater vehicles, planetary rovers, Industrial systems andeven inside the human body. Solving SLAM problem efficiently demands robust solutions to DataAssociation, Feature extraction and Convergence related problems. Addressing these problemsto dynamically changing environments make the SLAM prolem more challenging and interesting.Moreover best possible Data Fusion techniques are to be developed, as multi-robot deployment hasbecome a recent fashion to share computations and hence reducing time complexity. InterestinglyOptimization based approaches can provide more accurate solutions to SLAM problem and hencemaking possible to develop interesting applications such as, Perpetual life assistants for older ordisabled people, Autonomous Vacuum Cleaner, The distributed autonomous gardening system,Self-driving Cars and many more.

2 Introduction

Robotic navigation, particularly when an external location reference such as a global positioningsystem (GPS) is not available (eg: Indoor locations), requires the robot to be able to build a mapof the unknown environment in real-time and simultaneously work out its own location within themap. Robust solutions to the Simultaneous Localization and Mapping (SLAM) problem, therefore,underpins successful robot deployment in many application. The essential problem in SLAM is toestimate robot location and the map of the environment, typically represented by a set of geometricfeatures, as measurements are gathered from a sensor as the robot moves through the environment.The important point to note is, there is no single best solution to SLAM problem [1]. The methodchosen depends on number of factors.

2.1 Taxonomy of SLAM problem

Most important research papers identify the type of problems addressed by making the underlyingassumptions explicit in the following factors,(i) Static vs Dyanmic : Static SLAM algorithms assume that the environment does not changeover time. Dynamic methods allow for changes in the environment. The vast majority of theliterature on SLAM assumes static environments. Mapping unstructured largesclae dynamic envi-ronments reamins an open research problem.

(ii) Topological vs Metric : A topological map might be defined over a set of distinct places anda set of qualitative relations between these places. Metric SLAM methods provide metric informa-tion between the relation of such places.(iii) Known vs Unknown Correspondence : The correspondence problem is the problem ofrelating the identity of sensed things to other sensed things. The algorithms that do not makeassumptions (i.e correspondence is known) provide special mechanisms for estimating the corre-spondence of measured features to previously observed landmarks in the map. The problem ofestimating the correspondence is known as the data association problem [2].(iv) Single-Robot Versus Multirobot SLAM : Most SLAM problems are defined for a single-robot platform, although recently the problem of multirobot exploration [3] has gained in popularity.By fusing data collected by different robots we can gain more insights about the environment andmoreover the job of computations can be divided among them so that computation time is reduced.(v) Online vs Oine SLAM : The algorithms for the oine SLAM problem are often batch,that is, they process all data at the same time [4]. Online SLAM seeks to recover the presentrobot location, instead of the entire path. Algorithms that address the online problem are usuallyincremental and can process one data item at a time. In the literature such algorithms are typicallycalled filters.

3 Statement of SLAM problem and Related Issues

Consider a mobile robot moving through an environment taking relative observations of a numberof unknown landmarks using a sensor located on the robot. At a time instant k, the followingquantities are defined as shown in figure 1 :

Figure 1: simultaneous esti-mate of robot and landmarks

Figure 2: Map and robot tra-jectory from SAM

xk : the state vector describing the location and orientation of the vehicle. uk : the control vector, applied at time k 1 to drive the vehicle to a state xk at time k. mi : a vector describing the location of the ith landmark whose true location is assumed time

invariant.

zik : an observation taken from the vehicle of the location of the ith landmark at time k.

In addition the following sets are also defined :

X0:k = {x0,x1, . . . ,xk} = {X0:k1,xk} : the history of vehicle locations. U0:k = {u1,u2, . . . ,uk} = {U0:k1,uk} : the history of control inputs. m = {m1,m2, . . . ,mn} : the set of all landmarks. Z0:k = {z1, z2, . . . , zk} = {Z0:k1, zk} : the set of all landmark observations.Since the control inputs and landmarks observations are prone to noise, we formulate the problem inprobabilistic form that requires the probability distribution P (xk,m|Z0:k,U0:k,x0) to be computedfor all times k. This can be done in a standard two-step recursive (sequential) prediction (time-update) correction (measurement-update) form as shown below,

Prediction Update :

P (xk,m|Z0:k1,U0:k,x0) =

P (xk|xk1,uk)P (xk1,m|Z0:k1,U0:k1,x0) dxk1 (1)

Correction Update :

P (xk,m|Z0:k,U0:k,x0) = P (zk|xk,m) P (xk,m|Z0:k1,U0:k,x0)P (zk|Z0:k1,U0:k) (2)

Solutions to the above probabilistic SLAM problem involve finding an appropriate representationfor both the observation model and motion model that allows efficient and consistent computationof the prior and posterior distributions in (1) and (2). The three main paradigms from which ahuge number of recently published methods are derived are

First comes the traditional approach, i.e the Extended Kalman Filter (EKF) for representingthe robots best estimate [5].

Second one uses the fact that the SLAM can be viewed as a Sparse Graph of constraints, andit applies nonlinear optimization [1] for recovering the map and the robots locations.

Finally Particle Filter which applies nonparametric density estimation and efficient factoriza-tion methods to the SLAM problem [5].

3.1 Sensor and Process Models

The sensor observation z(k) at time k is a function of robot pose X(k) and state of environmentm is given by

z (k) = h (X(k),m) + w(k) (3)

where w(k) is the sensor observation noise at time k. Virtually all SLAM literature assumes processmodels with additive noise of the form

X (k + 1) = f (X(k), u(k)) + v(k) (4)

where u(k), v(k), X(k) are the control, process noise and robot pose at time k repectively. The-oretical problems posed when the noises are not zero-mean as well as practical solutions to thisproblem, perhaps through use of external information such as known landmarks remain interestingchallenges.

3.2 Consistency and Computational Issues

A solution to a dynamic estimation problem is said to be consistent if the estimate is unbiased andthe estimated covariance matrix matches the real mean square error. Both the EKF and particlefilter based solutions to SLAM can produce inconsistent estimates. In recent years there has beena growing interest on the SLAM consistency issue among the research community. Despite manyadvances by [6] limitations, together with its quadratic computational complexity associated withthe presence of a dense covariance matrix of order (3 + 2n) (3 + 2n) where n is the number oflandmarks, makes it impractical to use EKF to solve large-scale SLAM problems [6]. Althoughextended Information lter (EIF) based algorithms can overcome the computational issues to someextent [7] the issue of inconsistency remained unresolved.

3.3 Convergence

On condition that observation model is avilable and the feature states are noise free and static,feature location uncertainty will monotonically decrease during SLAM.A number of researchersconrm this fact for both the linear case [2] and the nonlinear case [8] in their work on EKF basedSLAM algorithms. Acheiving convergence for dynamic environments is still a challenging task.

4 Research Focus

I intend to focus on Optimization based approaches for solving SLAM problem, as these approachescan provide more accurate and consistent solutions. Example of such approach is Smoothing andMapping [9] which estimate the complete robot trajectory and the map as shown in figure 2. Ingeneral SLAM problem is non-linear and non-convex with large search space. Most of the existingoptimization based SLAM algorithms are based on Gauss-Newton or Levenberg-Marquardt opti-mizers that requires an initial guess to the robot poses and the map. Recent research demonstratedthat use of Stochastic Gradient Descent, Tree based Network Optimizer algorithm makes SLAMproblem to achieve good convergence results eventhough it starts from a poor initial guess [10], oncondition that noise covariance matrix is spherical. SLAM for dynamic, complex and large scaleenvironments using vision as the sole external sensor i.e cameras, is also my focus of research, ascameras have become popular sensors in the robotics community and take the advantage of beingcheap, lightweight, and energy efficient. This vision based or visual SLAM [11] [12] uses conceptsfrom Computer Vision and Machine Learning [13] and Optimization as well, so as to address theproblem of Data Association and develop Data Fusion techniques (for example we can extract depthinformation by fusing two images.)[14]. Finally I intend to work on improvements in computationalefficiency by fromulating the SLAM problem as Nonnegative Linear Least Squares and employingDimensionality Reduction[15] and try to answer questions such as how to obtain a map with givenaccuracy in minimum time, or how to maximize the coverage with a fixed time horizon and arequired map quality.

5 Applications

Autonomous Cars : Intel survey discovered that 44 percent of American respondents said theywould like to live in a driverless city. This shows the demand in the market to build resilient

Figure 3: Wireless Capsule En-doscopy

Figure 4: Vacuum cleanerFigure 5: Walker Assistant

autonomous cars. Many researchers proved SLAM is a good substitute where ever GPS isabsent and more erroneous. Advancements in Optimization based approaches solves SLAMproblem more accurately, which is very much desired in safe navigation for autonomous cars.

Home Automation : Methods from Robotics (SLAM) and Machine Learning can be used toincrease household efficiency and extend device functionality. Interesting devices such asAutomatic Vacuum cleaner [16] in figure 4, Perpetual life assistant for old or disbles as shownin figure 5, etc can be build.

Wireless Capsule Endoscopy : SLAM also try to enhance Intels vision towards Health andLife Sciences, by building systems such as Body-SLAM, that finds applications inside humanbody. For example WCE (see figure 3) offers painless investigation of the entire small intestineof human body. To detect precise position of the intestinal disease we need to localize thecapsule in the unknown map of the intestine. Body SLAM [17] enhances the positioningaccuracy of WCE, as it takes the advantage of Data Fusion of image sequences captured bythe WCEs embedded camera and the RF signal emitted by the capsule.

References

[1] Bruno Siciliano, Oussama Khatib. Springer Handbook of Robotics. Springer science and busi-ness media, 20-May-2008 - Computers - 1611 pages.

[2] Dissanayake, M.W.M.G., Newman, P. ; Clark, S. ; Durrant-Whyte, H.F. ; Csorba, M.. Asolution to the simultaneous localization and map building (SLAM) problem. Robotics andAutomation, IEEE Transactions on (Volume:17 , Issue: 3 )Jun 2001.

[3] Fox, D., Seattle, WA Ko, J. ; Konolige, K. ; Limketkai, B. ; Schulz, D. ; Stewart, B.. DistributedMultirobot Exploration and Mapping Proceedings of the IEEE (Volume:94 , Issue: 7 )July2006.

[4] M Montemerlo, S Thrun, D Koller, B Wegbreit. FastSLAM: A factored solution to the simul-taneous localization and mapping problem Proc. AAAI Nat. Conf. Artif. Intell., pp.593 -5982002 .

[5] Durrant-Whyte H, Bailey, Tim. Simultaneous localization and mapping: part I. Robotics andAutomation Magazine, IEEE (Volume:13 , Issue: 2 )June 2006.

[6] T. Bailey and H. Durrant-Whyte, Simultanouse localization and mapping (SLAM): Part II.IEEE Robotics and Automation Magazine, 13(3):108-117, 2006.

[7] S. Thrun, W. Burgard, and D. Fox, Probabilistic Robotics. The MIT Press, 2005.

[8] S. Huang, G. Dissanayake. Convergence and consistency analysis for Extended Kalman FilterBased SLAM. IEEE Transactions on Robotics, 23(5):1036-1049, 2007.

[9] F. Dellaert and M. Kaess. Square root SAM: Simultaneous localization and mapping via squareroot information smoothing. International Journal of Robotics Research, 25(12):1181-1203,2006.

[10] Olson, E. (Comput. Sci. and Artificial Intelligence Lab, MIT, Cambridge), MA Leonard J.; Teller Fast iterative alignment of pose graphs with poor initial estimates.Robotics and Au-tomation, 2006. ICRA 2006.

[11] Se S, Lowe D.G. ; Little, Vision-based global localization and mapping for mobilerobots.Robotics, IEEE Transactions on (Volume:21 , Issue: 3 )June 2005.

[12] Seo-Yeon Hwang, Jae-Bok Song Monocular Vision-Based SLAM in Indoor Environment UsingCorner, Lamp, and Door Features From Upward-Looking Camera.Industrial Electronics, IEEETransactions on 28 January 2011.

[13] Casarrubias-Vargas H, Petrilli-Barcelo A. ; Bayro-Corrochano E. EKF-SLAM and MachineLearning Techniques for Visual Robot Navigation.Pattern Recognition (ICPR), 2010 20th In-ternational Conference on 23-26 Aug. 2010.

[14] Hollinger G.A.,Yerramalli S., Distributed Data Fusion for Multirobot Search.Robotics, IEEETransactions on (Volume:31 , Issue: 1 )22 December 2014.

[15] Heng Wanga, Shoudong Huang, Dimensionality reduction for point feature SLAM problemswith spherical covariance matrices.Automatica Volume 51, January 2015, Pages 149157.

[16] WooYeon Jeong, Kyoung Mu Lee, CV-SLAM: a new ceiling vision-based SLAM tech-nique.Intelligent Robots and Systems, 2005. (IROS 2005). 2005 IEEE/RSJ International Con-ference on 2-6 Aug. 2005.

[17] Guanqun Bao, Body-SLAM, https://www.wpi.edu/Pubs/ETD/Available/etd-042814-091313/unrestricted/main.pdf.