Andrea Censi. On achievable accuracy for pose tracking. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), 2009. [ bib | http | .pdf ]

This paper presents Cramer-Rao bound-like inequalities for pose tracking, which is defined as the problem of recovering the robot displacement given two successive readings of a relative sensor. Computing the exact Fisher Information Matrix (FIM) for pose tracking is hard, because the state comprises the map, which is infinite-dimensional and unknown. This paper shows that the FIM for pose tracking can be bounded by a function of the FIM for localization on a known map, thereby reducing the analysis to a finite-dimensional problem. The resulting bounds are independent of the map prior and representation. The results are valid for any relative sensor; the experimental verification is done for the particular case of pose tracking using range-finders (scan matching).

Andrea Censi and Stefano Carpin. HSM3D: Feature-Less Global 6DOF Scan-Matching in the Hough/Radon Domain. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), 2009. [ bib | http | .pdf ]

This paper presents HSM3D, an algorithm for global rigid 6DOF alignment of 3D point clouds. The algorithm works by projecting the two input sets into the Radon/Hough domain, whose properties allow to decompose the 6DOF search into a series of fast one-dimensional cross-correlations. No planes or other particular features must be present in the input data, and the algorithm is provably complete in the case of noise-free input. The algorithm has been experimentally validated on publicly available data sets.

Andrea Censi. On the performance of Kalman filtering with intermittent observations: a geometric approach with fractals. In Proceedings of the American Control Conference (ACC), 2009. [ bib | http | .pdf ]

This paper describes the stationary distribution of the a-posteriori covariance matrix of a Kalman filter when the availability of measurements is subject to random phenomena such as lossy network links. If a certain non-overlapping condition is satisfied, the cdf has a fractal nature, and there exists a closed-form expression for it. If the condition is not satisfied, deciding whether the cdf is singular or not, even in the scalar case, is at least as hard as some open problems in measure and number theory.

Andrea Censi and Richard M. Murray. Real-valued consensus over noisy quantized channels. In Proceedings of the American Control Conference (ACC), 2009. [ bib | http | .pdf ]

This paper concerns the average consensus problem with the constraint of quantized communication between nodes. A broad class of algorithms is analyzed, in which the transmission strategy, which decides what value to communicate to the neighbors, can include various kinds of rounding, probabilistic quantization, and bounded noise. The arbitrariness of the transmission strategy is compensated by a feedback mechanism which can be interpreted as a self-inhibitory action. The result is that the average of the nodes state is not conserved across iterations, and the nodes do not converge to a consensus; however, we show that both errors can be made as small as desired. Bounds on these quantities involve the spectral properties of the graph and can be proved by employing elementary techniques of LTI systems analysis.

Daniele Calisi, Andrea Censi, Luca Iocchi, and Daniele Nardi. OpenRDK: A Modular Framework for Robotic Software Development. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Nice, France, September 2008. [ bib | http | .pdf ]

In this paper we conduct an analysis of existing frameworks for robot software development and we present OpenRDK, a modular framework focused on rapid development of distributed robotic systems. It has been designed following users' advice and has been in use within our group for several years. By now OpenRDK has been successfully applied in diverse applications with heterogeneous robots and as we believe it is fruitfully usable by others we are releasing it as open source..

Andrea Censi, Daniele Calisi, Alessandro De Luca, and Giuseppe Oriolo. A Bayesian framework for optimal motion planning with uncertainty. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Pasadena, CA, May 2008. [ bib | DOI | http | .pdf ]

Modeling robot motion planning with uncertainty in a Bayesian framework leads to a computationally intractable stochastic control problem. We seek hypotheses that can justify a separate implementation of control, localization and planning. In the end, we reduce the stochastic control problem to path-planning in the extended space of poses x covariances; the transitions between states are modeled through the use of the Fisher information matrix. In this framework, we consider two problems: minimizing the execution time, and minimizing the final covariance, with an upper bound on the execution time. Two correct and complete algorithms are presented. The first is the direct extension of classical graph-search algorithms in the extended space. The second one is a back-projection algorithm: uncertainty constraints are propagated backward from the goal towards the start state.

Andrea Censi. An ICP variant using a point-to-line metric. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Pasadena, CA, May 2008. [ bib | DOI | http | .pdf ]

This paper describes PLICP, an ICP (Iterative Closest/Corresponding Point) variant that uses a point-to-line metric, and an exact closed-form for minimizing such metric. The resulting algorithm has some interesting properties: it converges quadratically, and in a finite number of steps. The method is validated against vanilla ICP, IDC (Iterative Dual Correspondences), and MbICP (Metric-Based ICP) by reproducing the experiments performed in Minguez et al. (2006). The experiments suggest that PLICP is more precise, and requires less iterations. However, it is less robust to very large initial displacement errors. The last part of the paper is devoted to purely algorithmic optimization of the correspondence search; this allows for significant speed-up of the computation. The source code is available for download.

Andrea Censi and Gian Diego Tipaldi. Lazy Localization using the Frozen-Time Smoother. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Pasadena, CA, May 2008. [ bib | DOI | http | .pdf ]

We present a new algorithm for solving the global localization problem called Frozen-Time Smoother (FTS). Time is `frozen', in the sense that the belief always refers to the same time instant, instead of following a moving target, like Monte Carlo Localization does. This algorithm works in the case in which global localization is formulated as a smoothing problem, and a precise estimate of the incremental motion of the robot is usually available. These assumptions correspond to the case when global localization is used to solve the loop closing problem in SLAM. We compare FTS to two Monte Carlo methods designed with the same assumptions. The experiments suggest that a naive implementation of the FTS is more efficient than an extremely optimized equivalent Monte Carlo solution. Moreover, the FTS has an intrinsic laziness: it does not need frequent updates (scans can be integrated once every many meters) and it can process data in arbitrary order. The source code and datasets are available for download.

Andrea Censi, Luca Marchionni, and Giuseppe Oriolo. Simultaneous maximum-likelihood calibration of robot and sensor parameters. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Pasadena, CA, May 2008. [ bib | DOI | http | .pdf ]

For a differential-drive mobile robot equipped with an on-board range sensor, there are six parameters to calibrate: three for the odometry (radii and distance between the wheels), and three for the pose of the sensor with respect to the robot frame. This paper describes a method for calibrating all six parameters at the same time, without the need for external sensors or devices. Moreover, it is not necessary to drive the robot along particular trajectories. The available data are the measures of the angular velocities of the wheels and the range sensor readings. The maximum-likelihood calibration solution is found in a closed form.

Andrea Censi. An accurate closed-form estimate of ICP's covariance. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages 3167-3172, Rome, Italy, April 2007. [ bib | DOI | http | .pdf ]

Existing methods for estimating the covariance of the ICP (Iterative Closest/Corresponding Point) algorithm are either inaccurate or are computationally too expensive to be used online. This paper proposes a new method, based on the analysis of the error function being minimized. It considers that the correspondences are not independent (the same measurement being used in more than one correspondence), and explicitly utilizes the covariance matrix of the measurements, which are not assumed to be independent either. The validity of the approach is verified through extensive simulations: it is more accurate than previous methods and its computational load is negligible. The ill-posedness of the surface matching problem is explicitly tackled for under-constrained situations by performing an observability analysis; in the analyzed cases the method still provides a good estimate of the error projected on the observable manifold.

Andrea Censi. On achievable accuracy for range-finder localization. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages 4170-4175, Rome, Italy, April 2007. [ bib | DOI | http | .pdf ]

The covariance of every unbiased estimator is bounded by the Cramer-Rao lower bound, which is the inverse of Fisher's information matrix. This paper shows that, for the case of localization with range-finders, Fisher's matrix is a function of the expected readings and of the orientation of the environment's surfaces at the sensed points. The matrix also offers a mathematically sound way to characterize under- constrained situations as those for which it is singular: in those cases the kernel describes the direction of maximum uncertainty. This paper also introduces a simple model of unstructured environments for which the Cramer-Rao bound is a function of two statistics of the shape of the environment: the average radius and a measure of the irregularity of the surfaces. Although this model is not valid for all environments, it allows for some interesting qualitative considerations. As an experimental validation, this paper reports simulations comparing the bound with the actual performance of the ICP (Iterative Closest/Corresponding Point) algorithm. Finally, it is discussed the difficulty in extending these results to find a lower bound for accuracy in scan matching and SLAM.

Andrea Censi. Scan matching in a probabilistic framework. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages 2291-2296, Orlando, Florida, 2006. [ bib | http | .pdf ]

Andrea Censi, Luca Iocchi, and Giorgio Grisetti. Scan matching in the Hough domain. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages 2739-2744, Barcelona, Spain, 2005. [ bib | http | .pdf ]