Recursive calculation of the probability density function characterizing the state estimate of a nonlinear stochastic dynamic system in general cannot be performed exactly, since the type of the density changes with every processing step and the complexity increases. Hence, an approximation of the true density is required. Instead of using a single complicated approximating density, this paper is concerned with bounding the true density from below and from above by means of two simple densities. This provides a kind of guaranteed estimator with respect to the underlying true density, which requires a mechanism for ordering densities. Here, a partial ordering with respect to the cumulative distributions is employed. Based on this partial ordering, a modified Bayesian filter step is proposed, which recursively propagates lower and upper density bounds. A specific implementation for piecewise linear densities with finite support is used for demonstrating the performance of the new approach in simulations

In this paper we attempt to lay the foundation for a novel filtering technique for the fusion of two random vectors with imprecisely known stochastic dependency. This problem mainly occurs in decentralized estimation, e.g., of a distributed phenomenon, where the stochastic dependencies between the individual states are not stored. Thus, we derive parameterized joint densities with both Gaussian marginals and Gaussian mixture marginals. These parameterized joint densities contain all information about the stochastic dependencies between their marginal densities in terms of a parameter vector xi, which can be regarded as a generalized correlation parameter. Unlike the classical correlation coefficient, this parameter is a sufficient measure for the stochastic dependency even characterized by more complex density functions such as Gaussian mixtures. Once this structure and the bounds of these parameters are known, bounding densities containing all possible density functions could be found

Calibration is the procedure of quantifying mechanical deficiencies of machines and compensating them by appropriate adjustment. This paper introduces a model-based measurement framework for improving calibration procedures of machine tools. The goal is to precisely estimate the mechanical deficiencies based on a minimal number of measurements. For that purpose, the mechanical deficiencies of linear and rotary joints are modeled using splines. Uncertainties of the deficiency model are formulated stochastically, which allows incorporation of imprecise measurement data and prediction of optimal measurement parameters. We derive a method for optimally estimating a set of splines, i.e., joint errors, based on a set of measurements and for predicting the optimal joint configuration for new measurements.

Robotic fetch-and-carry tasks are commonly facilitated to demonstrate a number of research directions such as navigation, mobile manipulation, systems integration, etc. As a part of an integrated system in terms of a service robot framework, this paper describes a set of methods for real-world object manipulation tasks. We concentrate here on two particular parts of a manipulation sequence: i) robust visual servoing, and ii) grasping strategies. In terms of visual servoing we discuss the handling of singularities during a manipulation sequence. For grasping, we present a biologically motivated strategy using tactile feedback.