Algorithm 681: INTBIS, a portable interval Newton/bisection package
ACM Transactions on Mathematical Software (TOMS)
Sufficient Conditions for Regularity and Singularity of Interval Matrices
SIAM Journal on Matrix Analysis and Applications
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Fast continuous collision detection for articulated models
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Incremental construction of the robot's environmental map using interval analysis
COCOS'03 Proceedings of the Second international conference on Global Optimization and Constraint Satisfaction
Design of a large-scale cable-driven robot with translational motion
Robotics and Computer-Integrated Manufacturing
Formally verified conditions for regularity of interval matrices
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
Symmetry breaking in numeric constraint problems
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Tuning the multithreaded interval method for solving underdetermined systems of nonlinear equations
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part II
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Interval analysis is a relatively new mathematical tool 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: (a) it allows to find solutions of a problem only within some finite domain which make sense as soon as the unknowns in the problem are physical parameters; (b) numerical computer round-off errors are taken into account so that the solutions are guaranteed; (c) it allows one to take into account the uncertainties that are inherent to a physical system. Properties (a) and (c) are of special interest in robotics problems, in which many of the variables are parameters that are measured (i.e., known only up to some bounded errors) while the modeling of the robot is based on parameters that are submitted to uncertainties (e.g., because of manufacturing tolerances). Taking into account these uncertainties is essential for many robotics applications such as medical or space robotics for which safety is a crucial issue. A further inherent property of interval analysis 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 the right heuristics 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.