Abstract
Autonomous mobile-manipulation robots need to sense and interact with objects to accomplish high-level tasks such as preparing meals and searching for objects. To achieve such tasks, robots need semantic world models, defined as object-based representations of the world involving task-level attributes. In this work, we address the problem of estimating world models from semantic perception modules that provide noisy observations of attributes. Because attribute detections are sparse, ambiguous, and are aggregated across different viewpoints, it is unclear which attribute measurements are produced by the same object, so data association issues are prevalent. We present novel clustering-based approaches to this problem, which are more efficient and require less severe approximations compared to existing tracking-based approaches. These approaches are applied to data containing object type-and-pose detections from multiple viewpoints, and demonstrate comparable quality to the existing approach using a fraction of the computation time.
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Notes
- 1.
Indices have been dropped to reduce clutter; please refer to two paragraphs above for indices.
- 2.
The correct Bayesian approach is to integrate over the posterior distribution of each light’s location, which is intractable. This can be approximated by sampling the locations, then averaging the subsequent computations. In practice we found that using the posterior mean was sufficient.
- 3.
For simplicity, we assume that the error covariance is axis-aligned and use an independent normal-gamma prior for each dimension, but it is straightforward to extend to general covariances.
- 4.
The typical interpretation of normal-gamma hyperparameters is that the mean is estimated from \(\lambda \) observations with mean \(\nu \), and the precision from \(2 \alpha \) observations with mean \(\nu \) and variance \(\frac{\beta }{\alpha }\).
References
Anati, R., Scaramuzza, D., Derpanis, K., Daniilidis, K.: Robot localization using soft object detection. In: IEEE International Conference Robotics and Automation (2012)
Antoniak, C.: Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Ann. Stat. 2(6), 1152–1174 (1974)
Atanasov, N., Sankaran, B., Ny, J.L., Koletschka, T., Pappas, G., Daniilidis, K.: Hypothesis testing framework for active object detection. In: International Conference Robotics and Automation (2013)
Bar-Shalom, Y., Fortmann, T.: Tracking and Data Association. Academic Press, New York (1988)
Bernardo, J., Smith, A.: Bayesian Theory. John Wiley, New York (1994)
Cox, I., Hingorani, S.: An efficient implementation of Reid’s multiple hypothesis tracking algorithm and its evaluation for the purpose of visual tracking. IEEE Trans. Pattern Anal. Mach. Intell. 18(2), 138–150 (1996)
Cox, I., Leonard, J.: Modeling a dynamic environment using a Bayesian multiple hypothesis approach. AI J. 66(2), 311–344 (1994)
Cox, I.J.: A review of statistical data association techniques for motion correspondence. Int. J. Comput. Vis. 10(1), 53–66 (1993)
Dellaert, F., Seitz, S., Thorpe, C., Thrun, S.: EM, MCMC, and chain flipping for structure from motion with unknown correspondence. Mach. Learn. 50(1–2), 45–71 (2003)
Eidenberger, R., Scharinger, J.: Active perception and scene modeling by planning with probabilistic 6D object poses. In: IEEE/RSJ Intl. Conf. Intelligent Robots and Systems (2010)
Elfring, J., van den Dries, S., van de Molengraft, M., Steinbuch, M.: Semantic world modeling using probabilistic multiple hypothesis anchoring. Robot. Auton. Syst. 61(2), 95–105 (2013)
Glover, J., Popovic, S.: Bingham Procrustean alignment for object detection in clutter. In: IEEE/RSJ Intl. Conf. Intelligent Robots and Systems (2013)
Hager, G., Wegbreit, B.: Scene parsing using a prior world model. Int. J. Robot. Res. 30(12), 1477–1507 (2011)
Kurien, T.: Issues in the design of practical multitarget tracking algorithms. In: Y. Bar-Shalom (ed.) Multitarget-Multisensor Tracking: Advanced Applications, pp. 43–84. Artech House (1990)
Neal, R.: Markov chain sampling methods for Dirichlet process mixture models. J. Comput. Graph. Stat. 9(2), 249–265 (2000)
Oh, S., Russell, S., Sastry, S.: Markov chain Monte Carlo data association for multi-target tracking. IEEE Trans. Autom. Control 54(3), 481–497 (2009)
Ranganathan, A., Dellaert, F.: Semantic modeling of places using objects. In: Robotics: Science and Systems (2007)
Reid, D.: An algorithm for tracking multiple targets. IEEE Trans. Autom. Control 24(6), 843–854 (1979)
Sethuraman, J.: A constructive definition of Dirichlet priors. Stat. Sin. 4, 639–650 (1994)
Acknowledgments
This work was supported in part by the NSF under Grant No. 1117325. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. We also gratefully acknowledge support from ONR MURI grant N00014-09-1-1051, from AFOSR grant FA2386-10-1-4135, and from the Singapore Ministry of Education under a grant to the Singapore-MIT International Design Center.
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Appendix: Posterior and Predictive Distributions for a Single Light
Appendix: Posterior and Predictive Distributions for a Single Light
In this appendix, we verify the claim from Sect. 2 that finding the posterior and predictive distributions on color and location for a single light is straightforward, given that we know which observations were generated by that light. Let \(\left\{ (o, x) \right\} \) denote the set of light color-location detections that correspond to a light with unknown parameters (c, l). Color and location measurements are assumed to be independent given (c, l) and will be considered separately. We assume a known discrete prior distribution \(\pi \in \varDelta ^{(T-1)}\) on colors, reflecting their relative prevalence. Using the color noise model (Eq. 1), the posterior and predictive distributions on c are:
We can use this to find the light’s probability of detection:
Unlike the constant false positive rate \(p_{\text {FP}}\), the detection (and false negative) rate is dependent on the light’s color posterior.
For location measurements, we emphasize that both the mean \(\mu \) and precision \(\tau = \frac{1}{\sigma ^2}\) of the Gaussian noise model is unknown. Modeling the variance as unknown allows us to attain a better representation of the location estimate’s empirical uncertainty, and not naïvely assume that repeated measurements give a known fixed reduction in uncertainty each time. We use a standard conjugate prior, the distribution \(\text {NormalGamma} (\mu , \tau ; \lambda , \nu , \alpha , \beta )\).Footnote 4 It is well known (e.g., [5]) that after observing n observations with sample mean \(\hat{\mu }\) and sample variance \(\hat{s}^2\), the posterior is a normal-gamma distribution with parameters:
The upshot of using a conjugate prior for location measurements is that the marginal likelihood of location observations has a closed-form expression. The posterior predictive distribution for the next location observation \(x'\) is obtained by integrating out the latent parameters \(\mu , \tau \), and has the following expression:
where the hyperparameters with ‘\('\)’ superscripts are updated according to Eq. 17 using the empirical statistics of \(\left\{ x \right\} \) only (excluding \(x'\)), and the ones with ‘\(+\)’ superscripts are likewise updated but including \(x'\). The ratio in Eq. 18 assesses the fit of \(x'\) with the existing observations \(\left\{ x \right\} \) associated with the light.
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Wong, L.L.S., Kaelbling, L.P., Lozano-Pérez, T. (2016). Data Association for Semantic World Modeling from Partial Views. In: Inaba, M., Corke, P. (eds) Robotics Research. Springer Tracts in Advanced Robotics, vol 114. Springer, Cham. https://doi.org/10.1007/978-3-319-28872-7_25
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