Sensor-based sorting is a machine vision application that has found industrial application in various fields. An accept-or-reject task is executed by separating a material stream into two fractions. Current systems use line-scanning sensors, which is convenient as the material is perceived during transportation. However, line-scanning sensors yield a single observation of each object and no information about their movement. Due to a delay between localization and separation, assumptions regarding the location and point in time for separation need to be made based on the prior localization. Hence, it is necessary to ensure that all objects are transported at uniform velocities. This is often a complex and costly solution. In this paper, we propose a new method for reliably separating particles at non-uniform velocities. The problem is transferred from a mechanical to an algorithmic level. Our novel advanced image processing approach includes equipping the sorter with an area-scan camera in combination with a real-time multiobject tracking system, which enables predictions of the location of individual objects for separation. For the experimental validation of our approach, we present a modular sorting system, which allows comparing sorting results using a line-scan and area-scan camera. Results show that our approach performs reliable separation and hence increases sorting efficiency.

Directional Statistics and Filtering Using libDirectional

We present a novel dual quaternion filter for recursive estimation of rigid body motions. Based on the sequential Monte Carlo scheme, particles are deployed on the manifold of unit dual quaternions. This allows non-parametric modeling of arbitrary distributions underlying on the SE(3) group. The proposal distribution for importance sampling is estimated particle-wise by a novel dual quaternion unscented Kalman filter (DQ-UKF). It is adapted to the manifold geometric structure and drives the prior particles towards high-likelihood regions on the manifold. The resultant unscented dual quaternion particle filter (U-DQPF) incorporates the most recently observed evidence, raising the particle efficiency considerably for nonlinear pose estimation tasks. Compared with ordinary particle filters and other parametric model-based dual quaternion filtering schemes, the proposed U-DQPF shows superior performance in nonlinear SE(3) estimation.

In state estimation theory, two directions are mainly followed in order to model disturbances and errors. Either uncertainties are modeled as stochastic quantities or they are characterized by their membership to a set. Both approaches have distinct advantages and disadvantages making each one inherently better suited to model different sources of estimation uncertainty. This paper is dedicated to the task of combining stochastic and set-membership estimation methods. A Kalman gain is derived that minimizes the mean squared error in the presence of both stochastic and additional unknown but bounded uncertainties, which are represented by Gaussian random variables and ellipsoidal sets, respectively. As a result, a generalization of the well-known Kalman filtering scheme is attained that reduces to the standard Kalman filter in the absence of set-membership uncertainty and that otherwise becomes the intersection of sets in case of vanishing stochastic uncertainty. The proposed concept also allows to prioritize either the minimization of the stochastic uncertainty or the minimization of the set-membership uncertainty.