The Complexity of Reasoning for Fragments of Default Logic

Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified the complexity of the extension existence problem for propositional default logic as \SigmaPtwo-complete, and the complexity of the credulous and skeptical reasoning problem as SigmaP2-complete, resp. PiP2-complete. Additionally, he investigated restrictions on the default rules, i.e., semi-normal default rules. Selman made in 1992 a similar approach with disjunction-free and unary default rules. In this paper we systematically restrict the set of allowed propositional connectives. We give a complete complexity classification for all sets of Boolean functions in the meaning of Post's lattice for all three common decision problems for propositional default logic. We show that the complexity is a hexachotomy (SigmaP2-, DeltaP2-, NP-, P-, NL-complete, trivial) for the extension existence problem, while for the credulous and skeptical reasoning problem we obtain similar classifications without trivial cases.Comment: Corrected versio

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

Petri Net Plans A framework for collaboration and coordination in multi-robot systems

Programming the behavior of multi-robot systems is a challenging task which has a key role in developing effective systems in many application domains. In this paper, we present Petri Net Plans (PNPs), a language based on Petri Nets (PNs), which allows for intuitive and effective robot and multi-robot behavior design. PNPs are very expressive and support a rich set of features that are critical to develop robotic applications, including sensing, interrupts and concurrency. As a central feature, PNPs allow for a formal analysis of plans based on standard PN tools. Moreover, PNPs are suitable for modeling multi-robot systems and the developed behaviors can be executed in a distributed setting, while preserving the properties of the modeled system. PNPs have been deployed in several robotic platforms in different application domains. In this paper, we report three case studies, which address complex single robot plans, coordination and collaboration

Real-time smart and standalone vision/IMU navigation sensor

In this paper, we present a smart, standalone, multi-platform stereo vision/IMU-based navigation system, providing ego-motion estimation. The real-time visual odometry algorithm is run on a nano ITX single-board computer (SBC) of 1.9 GHz CPU and 16-core GPU. High-resolution stereo images of 1.2 megapixel provide high-quality data. Tracking of up to 750 features is made possible at 5 fps thanks to a minimal, but efficient, features detection–stereo matching–feature tracking scheme runs on the GPU. Furthermore, the feature tracking algorithm benefits from assistance of a 100 Hz IMU whose accelerometer and gyroscope data provide inertial features prediction enhancing execution speed and tracking efficiency. In a space mission context, we demonstrate robustness and accuracy of the real-time generated 6-degrees-of-freedom trajectories from our visual odometry algorithm. Performance evaluations are comparable to ground truth measurements from an external motion capture system

The Hand-bot, a Robot Design for Simultaneous Climbing and Manipulation

We present a novel approach to mobile object manipulation for service in indoor environments. Current research in service robotics focus on single robots able to move, manipulate objects, and transport them to various locations. Our approach differs by taking a collective robotics perspective: different types of small robots perform different tasks and exploit complementarity by collaborating together. We propose a robot design to solve one of these tasks: climbing vertical structures and manipulating objects. Our robot embeds two manipulators that can grasp both objects or structures. To help climbing, it uses a rope to compensate for the gravity force. This allows it to free one of its manipulators to interact with an object while the other grasps a part of a structure for stabilization. Our robot can launch and retrieve the rope autonomously, allowing multiple ascents. We show the design and the implementation of our robot and demonstrate the successful autonomous retrieval of a book from a shelf