The sensor localization problem can be formalized using distance and orientation constraints, typically in 3D. Local methods can be used to refine an initial location estimation, but in many cases such estimation is not available and a method able to determine all the feasible solutions from scratch is necessary. Unfortunately, existing methods able to find all the solutions in distance space can not take into account orientations, or they can only deal with one- or two-dimensional problems and their extension to 3D is troublesome. This paper presents a method that addresses these issues. The proposed approach iteratively projects the problem to decrease its dimension, then reduces the ranges of the variable distances, and back-projects the result to the original dimension, to obtain a tighter approximation of the feasible sensor locations. This paper extends previous works introducing accurate range reduction procedures which effectively integrate the orientation constraints. The mutual localization of a fleet of robots carrying sensors and the position analysis of a sensor moved by a parallel manipulator are used to validate the approach.
Distance Bound Smoothing (DBS) is a basic operation originally developed in Computational Chemistry to determine point configurations that are within certain pairwise ranges of distances. This operation consist in the iterative application of filtering processes that reduce the given ranges using triangular and tetrangular inequalities. Standard DBS has a limited range of applications because it does not take into account constraints on the orientations of simplices (triangles or tetrahedra, depending on the dimension of the problem). This paper discusses an extension of DBS that permits incorporating these constraints. This paves the way for the application of DBS techniques to a broad range of problems in Robotics.
The HumanoidLab is a more than 5 year old activity aimed to use educational robots to approach students to our Research Centre. Different commercial educative humanoid platforms have been used to introduce students to different aspects of robotics using projects and offering guidance and assistance. About 40 students have performed small mechanics, electronics or programming projects that are used to improve the robots by adding features. Robotics competitions are used as a motivation tool. A two weeks course was started that has received 80 undergraduate students, and more than 100 secondary school students in a short version. The experience has been very positive for students and for the institution: some of these students have performed their scholar projects and research in robotics and continue enrolled in the robotics field, and some of them are currently in research groups at IRI.
This paper first explores the generalization of Euler angles to the case in which the rotation axes are not necessarily members of an orthonormal triad, and presents a concise solution to their computation that relies on the calculation of standard Euler angles. Then, this generalization is taken one step further by introducing translations, that is, by defining generalized Euler angles about screw axes using a variation of the principle of transference that avoids the use of dual numbers. As an example, the obtained formulation is applied to solve the inverse kinematics of a 3C manipulator.