Learning how to be robust: Deep polynomial regression

Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased results when the input data is heavily contaminated by outliers. Moreover, the problem is even harder when outliers have strong structure. Departing from problem-tailored heuristics for robust estimation of parametric models, we explore deep convolutional neural networks. Our work aims to find a generic approach for training deep regression models without the explicit need of supervised annotation. We bypass the need for a tailored loss function on the regression parameters by attaching to our model a differentiable hard-wired decoder corresponding to the polynomial operation at hand. We demonstrate the value of our findings by comparing with standard robust regression methods. Furthermore, we demonstrate how to use such models for a real computer vision problem, i.e., video stabilization. The qualitative and quantitative experiments show that neural networks are able to learn robustness for general polynomial regression, with results that well overpass scores of traditional robust estimation methods.Comment: 18 pages, conferenc

Long term nonlinear propagation of uncertainties in perturbed geocentric dynamics using automatic domain splitting

Current approaches to uncertainty propagation in astrodynamics mainly refer tolinearized models or Monte Carlo simulations. Naive linear methods fail in nonlinear dynamics, whereas Monte Carlo simulations tend to be computationallyintensive. Differential algebra has already proven to be an efficient compromiseby replacing thousands of pointwise integrations of Monte Carlo runs with thefast evaluation of the arbitrary order Taylor expansion of the flow of the dynamics. However, the current implementation of the DA-based high-order uncertainty propagator fails in highly nonlinear dynamics or long term propagation. We solve this issue by introducing automatic domain splitting. During propagation, the polynomial of the current state is split in two polynomials when its accuracy reaches a given threshold. The resulting polynomials accurately track uncertainties, even in highly nonlinear dynamics and long term propagations. Furthermore, valuable additional information about the dynamical system is available from the pattern in which those automatic splits occur. From this pattern it is immediately visible where the system behaves chaotically and where its evolution is smooth. Furthermore, it is possible to deduce the behavior of the system for each region, yielding further insight into the dynamics. In this work, the method is applied to the analysis of an end-of-life disposal trajectory of the INTEGRAL spacecraft

Learning by observation through system identification

In our previous works, we present a new method to program mobile robots —“code identification by demonstration”— based on algorithmically transferring human behaviours to robot control code using transparent mathematical functions. Our approach has three stages: i) first extracting the trajectory of the desired behaviour by observing the human, ii) making the robot follow the human trajectory blindly to log the robot’s own perception perceived along that trajectory, and finally iii) linking the robot’s perception to the desired behaviour to obtain a generalised, sensor-based model. So far we used an external, camera based motion tracking system to log the trajectory of the human demonstrator during his initial demonstration of the desired motion. Because such tracking systems are complicated to set up and expensive, we propose an alternative method to obtain trajectory information, using the robot’s own sensor perception. In this method, we train a mathematical polynomial using the NARMAX system identification methodology which maps the position of the “red jacket” worn by the demonstrator in the image captured by the robot’s camera, to the relative position of the demonstrator in the real world according to the robot. We demonstrate the viability of this approach by teaching a Scitos G5 mobile robot to achieve door traversal behaviour