There are only three 6-SPS parallel manipulators with triangular base and platform, i.e., the octahedral, the flagged, and the partially flagged, which are studied in this paper. The forward kinematics of the octahedral manipulator is algebraically intricate, while those of the other two can be solved by three trilaterations. As an additional nice feature, the flagged manipulator is the only parallel platform for which a cell decomposition of its singularity locus has been derived. Here, we prove that the partially flagged manipulator also admits a well-behaved decomposition, technically called a stratification, some of whose strata are not topological cells, however. Remarkably, the adjacency diagram of the 5-D and 6-D strata (which shows what 5-D strata are contained in the closure of a 6-D one) is the same as for the flagged manipulator. The availability of such a decomposition permits devising a redundant 7-SPS manipulator, combining two partially flagged ones, which admits a control strategy that completely avoids singularities. Simulation results support these claims.

Robot egomotion can be estimated from an acquired video stream up to the scale of the scene. To remove this uncertainty (and obtain true egomotion), a distance within the scene needs to be known. If no a priori knowledge on the scene is assumed, the usual solution is to derive "in some way" the initial distance from the camera to a target object. This paper proposes a new, very simple way to obtain such a distance, when a zooming camera is available and there is a planar target in the scene. Similarly to "two-grid calibration" algorithms, no estimation of the camera parameters is required, and no assumption on the optical axis stability between the different focal lengths is needed. Quite the reverse, the non stability of the optical axis between the different focal lengths is the key ingredient that enables to derive our depth estimate, by applying a result in projective geometry. Experiments carried out on a mobile robot platform show the promise of the approach.

The conditions for a parallel manipulator to be flagged can be simply expressed in terms of linear dependencies between the coordinates of its leg attachments, both on the base and on the platform. These dependencies permit to describe the manipulator singularities in terms of incidences between two flags (hence, the name ldquoflaggedrdquo). Although these linear dependencies might look, at first glance, too restrictive, in this paper, the family of flagged manipulators is shown to contain large subfamilies of six-legged and three-legged manipulators. The main interest of flagged parallel manipulators is that their singularity loci admit a well-behaved decomposition with a unique topology irrespective of the metrics of each particular design. In this paper, this topology is formally derived and all the cells, in the configuration space of the platform, of dimension 6 (nonsingular) and dimension 5 (singular), together with their adjacencies, are worked out in detail.

Flagged in-parallel manipulators are attractive because their singularity loci admit a well-behaved decomposition, with a unique topology irrespective of the metrics of each particular design. In this paper, this topology is formally derived and all the cells, in the configuration space of the platform, of dimension 6 (non-singular) and dimension 5 (singular), together with their adjacencies, are worked out in detail. This characterization of the singularity loci is useful to come up with designs which admit control strategies free of singularities. In particular, it is shown that by adding an extra leg to any flagged manipulator, the resulting 7-leg structure admits a control strategy (by appropriately choosing which leg remains passive) that completely avoids singularities

Some in-parallel robots, such as the 3-2-1 and the 3/2 manipulators, have attracted attention because their forward kinematics can be solved by three consecutive trilaterations. In this paper, we identify a class of these robots, which we call flagged manipulators, whose singularity loci admit a well-behaved decomposition, i.e., a stratification, derived from that of the flag manifold. Two remarkable properties must be highlighted. First, the decomposition has the same topology for all members in the class, irrespective of the metric details of each particular robot instance. Thus, we provide explicitly all the singular strata and their connectivity, which apply to all flagged manipulators without any tailoring. Second, the strata can be easily characterized geometrically, because it is possible to assign local coordinates to each stratum (in the configuration space of the manipulator) that correspond to uncoupled rotations and/or translations in the workspace.