A fast branch-and-prune algorithm for the position analysis of spherical mechanisms

The final publication is available at link.springer.comDifferent branch-and-prune schemes can be found in the literature for numerically solving the position analysis of spherical mechanisms. For the prune operation, they all rely on the propagation of motion intervals. They differ in the way the problem is algebraically formulated. This paper exploits the fact that spherical kinematic loop equations can be formulated as sets of 3 multi-affine polynomials. Multi-affinity has an important impact on how the propagation of motion intervals can be performed because a multi-affine polynomial is uniquely determined by its values at the vertices of a closed hyperbox defined in its domain.Peer ReviewedPostprint (author's final draft

A space decomposition method for path planning of loop linkages

This paper introduces box approximations as a new tool for path planning of closed-loop linkages. Box approximations are finite collections of rectangloids that tightly envelop the robot's free space at a desired resolution. They play a similar role to that of approximate cell decompositions for open-chain robots - they capture the free-space connectivity in a multi-resolutive fashion and yield rectangloid channels enclosing collision-free paths - but have the additional property of enforcing the satisfaction of loop closure constraints frequently arising in articulated linkages. We present an efficient technique to compute such approximations and show how resolution-complete path planners can be devised using them. To the authors' knowledge, this is the first space-decomposition approach to closed-loop linkage path planning proposed in the literature.Peer Reviewe

A space decomposition method for path planning of loop linkages

This paper introduces box approximations as a new tool for path planning of closed-loop linkages. Box approximations are finite collections of rectangloids that tightly envelop the robot's free space at a desired resolution. They play a similar role to that of approximate cell decompositions for open-chain robots - they capture the free-space connectivity in a multi-resolutive fashion and yield rectangloid channels enclosing collision-free paths - but have the additional property of enforcing the satisfaction of loop closure constraints frequently arising in articulated linkages. We present an efficient technique to compute such approximations and show how resolution-complete path planners can be devised using them. To the authors' knowledge, this is the first space-decomposition approach to closed-loop linkage path planning proposed in the literature.This work has been partially supported by the Spanish Ministryof Education and Science through the contract DPI2004-07358, by the“Comunitat de Treball dels Pirineus” under contract 2006ITT-10004, andby Ram ́on y Cajal and I3 programme funds.Peer ReviewedPostprint (author's final draft

Modified flower pollination algorithm for global optimization

In this paper, a modified flower pollination algorithm (MFPA) is proposed to improve the performance of the classical algorithm and to tackle the nonlinear equation systems widely used in engineering and science fields. In addition, the differential evolution (DE) is integrated with MFPA to strengthen its exploration operator in a new variant called HFPA. Those two algorithms were assessed using 23 well-known mathematical unimodal and multimodal test functions and 27 well-known nonlinear equation systems, and the obtained outcomes were extensively compared with those of eight well-known metaheuristic algorithms under various statistical analyses and the convergence curve. The experimental findings show that both MFPA and HFPA are competitive together and, compared to the others, they could be superior and competitive for most test cases