In this work, a framework is proposed to build topological models in mobile robotics, using an omnidirectional vision sensor as the only source of information. The model is structured hierarchically into three layers, from one high-level layer which permits a coarse estimation of the robot position to one low-level layer to refine this estimation efficiently. The algorithm is based on the use of clustering approaches to obtain compact topological models in the high-level layers, combined with global appearance techniques to represent robustly the omnidirectional scenes. Compared to the classical approaches based on the extraction and description of local features, global-appearance descriptors lead to models that can be interpreted and handled more intuitively. However, while local-feature techniques have been extensively studied in the literature, global-appearance ones require to be evaluated in detail to test their efficacy in map-building tasks. The proposed algorithms are tested with a set of publicly available panoramic images captured in realistic environments. The results show that global-appearance descriptors along with some specific clustering algorithms constitute a robust alternative to create a hierarchical representation of the environment.

This paper analyzes the multiplicity of the solutions to forward kinematics of two classes of analytic robots: 2RPR-PR robots with a passive leg and 3-RPR robots with nonsimilar flat platform and base. Since their characteristic polynomials cannot have more than two valid roots, one may think that triple solutions, and hence nonsingular transitions between different assembly modes, are impossible for them. However, the authors show that the forward kinematic problems of these robots always admit quadruple solutions and obtain analytically the loci of points of the joint space where these solutions occur. Then, it is shown that performing trajectories in the joint space that enclose these points can produce nonsingular transitions, demonstrating that it is possible to design simple analytic parallel robots with two and three degrees-of-freedom (DOF) and the ability to execute these transitions.

A recently published treatment of nonredundant manipulator kinematics and dynamics on differentiable manifolds is extended to kinematically redundant manipulators. Analysis at the configuration level shows that forward kinematics and dynamics of redundant manipulators are identical to that for nonredundant manipulators. The manifold-based inverse kinematics formulation that is presented for redundant manipulators, in contrast, yields parameterizations of set-valued inverse kinematic mappings at the configuration level, where sharper results are obtained than those presented in the literature using velocity formulations. Explicit expressions are derived for set-valued inverse kinematic mappings for both serial and nonserial (called compound) kinematically redundant manipulators, as functions of vectors of arbitrary parameters. Parameterizations are presented for both manipulator regular configuration manifolds and self-motion manifolds, the latter comprised of sets of inputs that map into the same output. It is shown that kinematically redundant configuration manifolds and self-motion differentiable manifolds are distinctly different and play complementary roles in redundant manipulator kinematics. Computational methods are presented for evaluation of set-valued inverse kinematic mappings, without problem-dependent ad hoc analytical manipulations. Redundant serial and compound manipulator examples are presented to illustrate computation of set-valued inverse kinematic mappings and the use of self-motion manifold mappings in obstacle avoidance applications. Differentiation of configuration level inverse mappings yields inverse velocity and acceleration mappings as functions of time-dependent arbitrary parameters that play a central role in manipulator dynamics and control.