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Active SLAM : a Framework My, on-going, PhD Research

This document outlines the ongoing PhD research of Henry David Carrillo Lindado on Active SLAM (Simultaneous Localization and Mapping) under the supervision of José A. Castellanos at the University of Zaragoza, Spain. The research focuses on integrating path planning into SLAM processes, exploring mapping with mobile robots, and addressing uncertainty through various criteria such as A-optimal, D-optimal, and E-optimal designs. It also includes experimental data from both simulated and real-world environments, aiming to enhance the autonomy and efficiency of mobile robotics.

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Active SLAM : a Framework My, on-going, PhD Research

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  1. Active SLAM : a Framework My, on-going, PhD Research Henry Carrillo Lindado Advised by: José A. Castellanos

  2. Bio – Academic Background • Name: Henry David Carrillo Lindado. • Hometown: Barranquilla – Colombia. • Academic: • PhD in Computer Science and System Engineering (2010 -2014) • University of Zaragoza - Spain • M.Sc. in Computer Science and System Engineering • M.Sc. in Electronics Engineering • B.Eng. in Electronics Engineering • Funding: FPI scholarship by the Ministry of Science and Innovation of Spain. 2010-2014. • Contact: • Here: 0.59 Cartesium • hcarri@unizar.es • http://webdiis.unizar.es/~hcarri/pmwiki/pmwiki.php 1

  3. Preliminaries – SLAM • H0:A model of the operative environment is an essential requirement for an autonomous mobile robot. • Three basic tasks: • Where am I? • What does the world look like? • Where do I go? • SLAM => Joint of two tasks. • SLAM => Does not define the path-trajectory of the robot. • Integrated approach => On the way to autonomy. 2 Exploration and Mapping with Mobile Robots. CyrillStachniss. 2006.

  4. Preliminaries – Active SLAM (I) • Active SLAM => To integrate path planning into a SLAM process. • To explorer more area. • Navigate safely. • Reduce uncertainty. • Algorithms • 1º Alg. [Feder, Leonard](99) • Active perception [Bajacksy](86) • Infinite Horizon andMPC [Leung, Dissanayake](06) 1

  5. Preliminaries – Active SLAM • Pseudo-code: • Set of trajectories • Assign a score to each trajectory • Uncertainty of map+robot • Trajectory constraints • Execute the trajectory with the optimum . 3

  6. Preliminaries – Active SLAM • Pseudo-code: • Set of trajectories • Assign a score to each trajectory • Uncertainty of map+robot • Trajectory constraints • Execute the trajectory with the optimum . 4

  7. Preliminaries – Active SLAM • Pseudo-code: • Set of trajectories • Assign a score to each trajectory • Uncertainty of map+robot • Trajectory constraints • Execute the trajectory with the optimum . 4

  8. Preliminaries – Active SLAM • Pseudo-code: • Set of trajectories • Assign a score to each trajectory • Uncertainty of map+robot • Trajectory constraints • Execute the trajectory with the optimum . 4

  9. Uncertainty Criteria for Active SLAM (I) • Uncertainty/Inform. Criteria => • In the TOED, a design (i.e.), isbetterthan a design, if: • The above does not allow to quantify the improvement, therefore is desirable to: • It permits to quantify the uncertainty in . • Theory of Optimal Experiment Design (A-opt, D-opt, E-opt…). • Information Theory ( Entropy, MI…). 4

  10. Uncertainty Criteria for Active SLAM (II) • Some possible uncertainty criteria for active SLAM are: • Previous works ([Simand Roy, 2005], [Mihaylovaand De Schutter, 2003]) report A-opt as the best criterion and that D-opt gives null values. • A-opt, widely used:[Kollar2008] [MartinezCantin2008] [Meger2008] [Dissanayake2006]. • Although D-opt is commonly used in the TOED because it is optimal. Trace (A-opt) Max(E-opt) Determinant (D-opt) 4

  11. Uncertainty Criteria for Active SLAM (III) • It is indeed possible to use D-opt in the Active SLAM context: • The structure of the problem needs to be taken into account (i.e. The covariance matrix varies with time). • It is not informative to compare the determinant of a matrix lx lwith a mx m. • det(l x l) is homogeneous of grade l. • The computation of the determinant of a highly correlated matrix(e.g. SLAM) is prone to round-off errors. • Processing in the logarithm space • D-opt for a l x l covariance matrix: • Stem from [Kiefer, 1974] : 4

  12. Firstexperiment • Firstexperiment: on the computation • Is it possible to compute D-opt from a robot doing SLAM? • Execute a SLAM algorithm (e.g. EKF-SLAM, iSAM). • Compute in each step: A-opt, E-opt , D-opt, Determinant, entropy and mutual Information. • Simulated Robot indoor environment : MRPT/C++ • Real Robot indoor environment : Pioneer 3 DX - Ad-hoc • Real Robot indoor environment : DLR dataset • Real Robot outdoor environment : Victoria Park dataset 6

  13. 1E - Simulated Robot indoor environment (I) Scenario: • Area of 25x25 m • 2D EKF-SLAM • Sensor: Odometry + Camera(360º - 3m range) • 180 landmarks- DA Known. • Gaussian errors: Odometry + Sensors 7

  14. 1E-Simulated Robot indoor environment (II) Qualitative results (a)-(f) A-opt, E-opt, D-opt, determinant, entropy and MI. 8

  15. 1E-Real Robot indoor environment @ DLR (I) Scenario: • Area60x40 m • Sensor: Odometry + Camera • 2D EKF-SLAM • 576 landmarks – DA known. 9

  16. 1E-Real Robot indoor environment @ DLR (I) Qualitative results (a)-(f) A-opt, E-opt, D-opt, determinant, entropy and MI. 10

  17. Firstexperiment – Quantitative analysis • Average correlation between the uncertainty criteria: • Variance: A-E (0,0002) / A-D (0,0540) / D-E (0,0481). • A-opt y E-opt=> High correlation. • E-opt is guided by a single eigenvalue. • A-opt y D-opt => Medium correlation. • H0: D-opt take into account more components than A-opt. 11

  18. Second Experiment • Second experiment: Active SLAM • What is the effect of the uncertainty criteria in active SLAM? • Active SLAM => Unitary horizon (greedy). • Uncertainty criteria => A-opt, D-opt and Entropy. • Effect =>MSE y . • Simulated Robot with unitary horizon: MRPT / C++ 12

  19. 2E-Simulated Robot indoor environment(I) Scenario: • Area of 20x20m and 30x30m • 2D EKF-SLAM • Sensor: Odometry + Camera (360º - 3m range) • Gaussian errors: Odometry + sensors. • Path planner: Discrete (A*) and continuous (Attract-Repel). 13

  20. 2E-Simulated Robot indoor environment(II) • Resulting paths for each uncertainty criterion: (a) D-opt, (b) A-opt y (c) Entropy. Each colour represents an executed path. 20 x 20 m map. • Qualitativeanalysis 14

  21. 2E-Simulated Robot indoor environment(III) • Resulting trajectories for 10000 stepsactiveSLAMsimulation. (a). Initial trajectory. (b) A-opt. (c). D-opt. • Qualitative analysis. 15

  22. 2E – Quantitative Analysis 30x30 m • Evolution of MSE ((a)-(c)) y chi2 ((d)-(f)) ratio. Average of 10 MC simulations. 16

  23. Take home message • D-opt is the optimum criterion to measure uncertainty according to the TOED (i.e. better than A-opt (Trace)). • It is possible to obtain useful information regarding the uncertainty of a SLAM process with D-opt. • D-opt shows better performance than A-opt in our simulated experiments of active SLAM. • To compute D-opt in the context of a SLAM process => use the formulation presented here. 17

  24. OntheComparisonof UncertaintyCriteriafor Active SLAM Thanks!!! hcarri@unizar.es http://webdiis.unizar.es/~hcarri 19

  25. Experimentos • Primer experimento : acerca del cálculo • Segundo experimento : SLAM activo • Robot simulado ambiente interior : MRPT / C++ • Robot real ambiente interior : Pioneer 3 DX - Ad-hoc • Robot real ambiente interior : DLR dataset • Robot real ambiente exterior : Victoria Park dataset • Robot simulado con horizonte unitario : MRPT / C++ 7

  26. 1E-Robot en ambiente exterior @ VP (I) Escenario: • Área de 350 x 350 m • iSAM • Sensor: Odometría + Laser • 150 landmarks– DA conocida. 13

  27. 1E-Robot en ambiente exterior @ VP (II) – Resultados cualitativos (a)-(f) A-opt, E-opt, D-opt, determinante, entropía y MI. 14

  28. 1E-Robot en ambiente interior ad-hoc (I) Escenario: • Área 6x4 m • 2D EKF-SLAM • Sensor: Odometría + Kinect • 5 landmarks– DA conocida 15

  29. 1E-Robot en ambiente interior ad-hoc (II) – Resultados cualitativos (a)-(f) A-opt, E-opt, D-opt, determinante, entropía y MI. 16

  30. 2E - Análisis cuantitativo 20x20 m • Evolución del MSE ((a)-(c)) y chi2 ((d)-(f)). Promedio de 10 MC. 18

  31. Determinante Operación algebraica que transforma una matriz en un escalar. • Propiedades (matriz n x n) • Geométrica: Volumen del paralelepípedo definido en el espacio n-dimensional. • Homogéneo de grado n. Si, 15

  32. Artículos • “Experimental Comparison of Optimum Criteria for Active SLAM”. Oral presentation in the “III Workshop de Robótica: Robótica Experimental (ROBOT’11)”. • “On the Comparison of Uncertainty Criteria for Active SLAM”. Submitted to ICRA’12. • “Planning Minimum Uncertainty Paths Over Pose/Feature Graphs Constructed Via SLAM” . Submitted to ICRA’12. 18

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