Andrea Censi

An ICP variant using a point-to-line metric

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 a significant speed-up of the computation. The source code is available for download.

An accurate closed-form estimate of ICP's covariance

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.

Scan Matching in the Hough Domain

Scan matching is used as a building block in many robotic applications, for localization and simultaneous localization and mapping (SLAM). Although many techniques have been proposed for scan matching in the past years, more efficient and effective scan matching procedures allow for improvements of such associated problems. In this paper we present a new scan matching method that, exploiting the properties of the Hough domain, allows for combining advantages of dense scan matching algorithms with feature-based ones.

OpenRDK: A modular framework for robotic software development

Intense efforts to define a common structure in robotic applications, both from a conceptual and from an implementation point of view, have been carried out in the last years and several frameworks have been realized for helping in developing robotic applications. However, due to the diversity of these applications, as well as of the research groups involved, a common framework is still far from being accepted. In this paper we focus on modularity and re-usability, as major features for robotic applications. We thus characterize existing frameworks for robot software development through the choices made on concurrent execution of modules and information sharing among them and we present OpenRDK, a modular framework focused on rapid development of distributed robotic systems. OpenRDK has been designed and developed with many years of experience following userspsila advice and has been successfully used for the development of many diverse applications with different kinds of robots. After such an extensive test, OpenRDK is now an open source project.

Kalman Filtering With Intermittent Observations: Convergence for Semi-Markov Chains and an Intrinsic Performance Measure

This technical note shows that the stationary distribution for the covariance of Kalman filtering with intermittent observations exists under mild conditions for a very general class of packet dropping models (semi-Markov chain). These results are proved using the geometric properties of Riccati recursions with respect to a particular Riemannian distance. Moreover, the Riemannian mean induced by that distance is always bounded, therefore it can be used for characterizing the performance of the system for regimes where the moments of the covariance do not exist. Other interesting properties of that mean include the symmetry between covariance and information matrices (averaging covariances or their inverse gives the same result), and its interpretation in information geometry as the “natural” mean for the manifold of Gaussian distributions.

Controlling free flight of a robotic fly using an onboard vision sensor inspired by insect ocelli

Scaling a flying robot down to the size of a fly or bee requires advances in manufacturing, sensing and control, and will provide insights into mechanisms used by their biological counterparts. Controlled flight at this scale has previously required external cameras to provide the feedback to regulate the continuous corrective manoeuvres necessary to keep the unstable robot from tumbling. One stabilization mechanism used by flying insects may be to sense the horizon or Sun using the ocelli, a set of three light sensors distinct from the compound eyes. Here, we present an ocelli-inspired visual sensor and use it to stabilize a fly-sized robot. We propose a feedback controller that applies torque in proportion to the angular velocity of the source of light estimated by the ocelli. We demonstrate theoretically and empirically that this is sufficient to stabilize the robots upright orientation. This constitutes the first known use of onboard sensors at this scale. Dipteran flies use halteres to provide gyroscopic velocity feedback, but it is unknown how other insects such as honeybees stabilize flight without these sensory organs. Our results, using a vehicle of similar size and dynamics to the honeybee, suggest how the ocelli could serve this role.

A Bayesian framework for optimal motion planning with uncertainty

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.

Simultaneous Calibration of Odometry and Sensor Parameters for Mobile Robots

Consider a differential-drive mobile robot equipped with an on-board exteroceptive sensor that can estimate its own motion, e.g., a range-finder. Calibration of this robot involves estimating six parameters: three for the odometry (radii and distance between the wheels) and three for the pose of the sensor with respect to the robot. After analyzing the observability of this problem, this paper describes a method for calibrating all parameters at the same time, without the need for external sensors or devices, using only the measurement of the wheel velocities and the data from the exteroceptive sensor. The method does not require the robot to move along particular trajectories. Simultaneous calibration is formulated as a maximum-likelihood problem and the solution is found in a closed form. Experimental results show that the accuracy of the proposed calibration method is very close to the attainable limit given by the Cramér–Rao bound.

On achievable accuracy for range-finder localization

The covariance of every unbiased estimator is bounded by the Cramer-Rao lower bound, which is the inverse of Fishers information matrix. This paper shows that, for the case of localization with range-finders, Fishers matrix is a function of the expected readings and of the orientation of the environments 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.

Simultaneous maximum-likelihood calibration of odometry and sensor parameters

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.