  Many problems in robust control and motion planning can be reduced to either
find a sound approximation of the solution space determined by a set of
nonlinear inequalities, or to the ``guaranteed tuning problem'' as defined by
Jaulin and Walter, which amounts to finding a value for some tuning parameter
such that a set of inequalities be verified for all the possible values of some
perturbation vector. A classical approach to solve these problems, which
satisfies the strong soundness requirement, involves some quantifier
elimination procedure such as Collins' Cylindrical Algebraic Decomposition
symbolic method. Sound numerical methods using interval arithmetic and local
consistency enforcement to prune the search space are presented in this paper
as much faster alternatives for both soundly solving systems of nonlinear
inequalities, and addressing the guaranteed tuning problem whenever the
perturbation vector has dimension one. The use of these methods in camera
control is investigated, and experiments with the prototype of a declarative
modeller to express camera motion using a cinematic language are reported and
commented.
