Bootstrapping bilinear models of Simple Vehicles

Learning and adaptivity will play a large role in robotics in the future. Two questions are open: (1) in principle, how much it is possible to learn; and (2) in practice, how much should an agent be able to learn. The bootstrapping scenario describes the extreme case in which agents need to learn “everything” from scratch, including a torque-to-pixels model for its robotic body. This paper considers the bootstrapping problem for a subset of the set of all robots. The Simple Vehicles are an idealization of mobile robots equipped with a set of “canonical” exteroceptive sensors: the camera, the range finder and the field sampler. The sensorimotor dynamics of these sensors are derived and shown to be surprising similar. These sensorimotor dynamics are well approximated by a class of nonlinear systems that assume an instantaneous bilinear relation among observations, commands, and changes in the observations. The bilinear approximation is sufficient to guarantee success in the task of generalized “servoing”: driving the observations to a given goal snapshot. Simulations and experiments substantiate the theoretical results. This is the first instance of a bootstrapping agent that can learn the model of the dynamics of a relatively large universe of systems and use the models to solve well-defined tasks, with no parameter tuning or hand-designed features.

Calibration by correlation using metric embedding from nonmetric 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 nonmetric 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 do we 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 nonmetric 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.