Tag Archives: Computational Complexity

SLAM based on submap joining that achieves linear cost through a novel choice of the reference frame of each submap, and an interesting related works on map joining, i.e., considering submaps as observations

Liang Zhao, Shoudong Huang, Gamini Dissanayake, Linear SLAM: Linearising the SLAM problems using submap joining, Automatica, Volume 100, 2019, Pages 231-246, DOI: 10.1016/j.automatica.2018.10.037.

The main contribution of this paper is a new submap joining based approach for solving large-scale Simultaneous Localization and Mapping (SLAM) problems. Each local submap is independently built using the local information through solving a small-scale SLAM; the joining of submaps mainly involves solving linear least squares and performing nonlinear coordinate transformations. Through approximating the local submap information as the state estimate and its corresponding information matrix, judiciously selecting the submap coordinate frames, and approximating the joining of a large number of submaps by joining only two maps at a time, either sequentially or in a more efficient Divide and Conquer manner, the nonlinear optimization process involved in most of the existing submap joining approaches is avoided. Thus the proposed submap joining algorithm does not require initial guess or iterations since linear least squares problems have closed-form solutions. The proposed Linear SLAM technique is applicable to feature-based SLAM, pose graph SLAM and D-SLAM, in both two and three dimensions, and does not require any assumption on the character of the covariance matrices. Simulations and experiments are performed to evaluate the proposed Linear SLAM algorithm. Results using publicly available datasets in 2D and 3D show that Linear SLAM produces results that are very close to the best solutions that can be obtained using full nonlinear optimization algorithm started from an accurate initial guess. The C/C++ and MATLAB source codes of Linear SLAM are available on OpenSLAM.

Towards taking into account the complexity of finding the best option in decision-making systems

Peter Bossaerts, Carsten Murawski, Computational Complexity and Human Decision-Making, Trends in Cognitive Sciences, Volume 21, Issue 12, 2017, Pages 917-929, DOI: 10.1016/j.tics.2017.09.005.

The rationality principle postulates that decision-makers always choose the best action available to them. It underlies most modern theories of decision-making. The principle does not take into account the difficulty of finding the best option. Here, we propose that computational complexity theory (CCT) provides a framework for defining and quantifying the difficulty of decisions. We review evidence showing that human decision-making is affected by computational complexity. Building on this evidence, we argue that most models of decision-making, and metacognition, are intractable from a computational perspective. To be plausible, future theories of decision-making will need to take into account both the resources required for implementing the computations implied by the theory, and the resource constraints imposed on the decision-maker by biology.