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

Calibration by correlation using metric embedding from non-metric similarities

This paper presents a new intrinsic calibration method that allows us to calibrate a generic single-view point camera just by waving it around. From the video sequence obtained while the camera undergoes random motion, we compute the pairwise time correlation of the luminance signal for a subset of the pixels. We show that, if the camera undergoes a random uniform motion, then the pairwise correlation of any pixels pair is a function of the distance between the pixel directions on the visual sphere. This leads to formalizing calibration as a problem of metric embedding from non-metric measurements: we want to find the disposition of pixels on the visual sphere from similarities that are an unknown function of the distances. This problem is a generalization of multidimensional scaling (MDS) that has so far resisted a comprehensive observability analysis (can we reconstruct a metrically accurate embedding?) and a solid generic solution (how to do so?). We show that the observability depends both on the local geometric properties (curvature) as well as on the global topological properties (connectedness) of the target manifold. We show that, in contrast to the Euclidean case, on the sphere we can recover the scale of the points distribution, therefore obtaining a metrically accurate solution from non-metric measurements. We describe an algorithm that is robust across manifolds and can recover a metrically accurate solution when the metric information is observable. We demonstrate the performance of the algorithm for several cameras (pin-hole, fish-eye, omnidirectional), and we obtain results comparable to calibration using classical methods. Additional synthetic benchmarks show that the algorithm performs as theoretically predicted for all corner cases of the observability analysis

A group-theoretic approach to formalizing bootstrapping problems

The bootstrapping problem consists in designing agents that learn a model of themselves and the world, and utilize it to achieve useful tasks. It is different from other learning problems as the agent starts with uninterpreted observations and commands, and with minimal prior information about the world. In this paper, we give a mathematical formalization of this aspect of the problem. We argue that the vague constraint of having "no prior information" can be recast as a precise algebraic condition on the agent: that its behavior is invariant to particular classes of nuisances on the world, which we show can be well represented by actions of groups (diffeomorphisms, permutations, linear transformations) on observations and commands. We then introduce the class of bilinear gradient dynamics sensors (BGDS) as a candidate for learning generic robotic sensorimotor cascades. We show how framing the problem as rejection of group nuisances allows a compact and modular analysis of typical preprocessing stages, such as learning the topology of the sensors. We demonstrate learning and using such models on real-world range-finder and camera data from publicly available datasets

Bootstrapping bilinear models of robotic sensorimotor cascades

We consider the bootstrapping problem, which consists in learning a model of the agent's sensors and actuators starting from zero prior information, and we take the problem of servoing as a cross-modal task to validate the learned models. We study the class of bilinear dynamics sensors, in which the derivative of the observations are a bilinear form of the control commands and the observations themselves. This class of models is simple yet general enough to represent the main phenomena of three representative robotics sensors (field sampler, camera, and range-finder), apparently very different from one another. It also allows a bootstrapping algorithm based on hebbian learning, and that leads to a simple and bioplausible control strategy. The convergence properties of learning and control are demonstrated with extensive simulations and by analytical arguments

Real-valued average consensus over noisy quantized channels

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 neighbours, 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

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

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