Interval Analysis and Robotics

Abstract

Interval analysis is a relatively new mathematical tools that allows one to deal with problems that may have to be solved numerically with a computer. Examples of such problems are system solving and global optimization but numerous other problems may be addressed as well. This approach has the following general advantages:• it allows to find solutions of a problem only within some finite domain• numerical computer round-off errors are taken into account so that the solutions are guaranteed A further inherent property that is of interest for robotics problems is that this approach allows one to deal with the uncertainties that are unavoidable in robotics. Although the basic principles of interval analysis are easy to understand and to implement, this approach will be efficient only if additional methods are used and if the problem at hand is formulated appropriately. In this paper we will emphasize various robotics problems that have been solved with interval analysis, many of which are currently beyond the reach of other mathematical approaches.

Singularity Maps of Space Robots and their Application to Gradient-based Trajectory Planning

“…Interval Arithmetic (IA). The application of IA is not new to singularity analysis; see for example the work of Merlet [24] and Kotlarski et al [18] for workspace analysis, in particular for parallel robots. Benoit et al [4], proposes to analyze the configuration space and workspace singularities using IA.…”

“…Whenever a box cannot be proven to be singularity-free, it is bisected along its largest range, in a similar fashion to other numerical approaches, e.g. Bohigas et al [6], Benoit et al [4] and Merlet [24]. The bisection proceeds recursively up to a given maximum precision ∈ IR + .…”

Adaptive filtering strategy for numerical constraint satisfaction problems

“…Their reliability and increasing performance make them applicable to various expert system domains, such as robotics design and kinematics (Merlet, 2011), dynamic systems in robust control and autonomous robot localization (Kieffer, Jaulin, Walter, & Meizel, 2000), and proofs of conjectures (Sandretto, Trombettoni, & Daney, 2013;Tucker, 2002). Three main features distinguish this approach from others: their reliability, i.e., their robustness w.r.t.…”

Estudo do impacto da variabilidade geométrica no comportamento cinemático e dinâmico de manipuladores robóticos paralelos com redundância cinemática

“…Tannous et al (2014) fizeram uma análise da sensibilidade do 3RRR às variações de parâmetros geométricos usando um método de linearização de intervalos. Para o estudo dessa influência, foi usada a análise de intervalos, um método numérico muito poderoso que permite a resolução de uma vasta gama de problemas, de resolução de sistemas até a otimização global (Merlet, 2011).…”

“…A finalidade dessa técnica é determinar limites garantidos de mínimo e máximo de uma dada função com incógnitas consideradas intervalos (Merlet, 2011).…”