Approximations of space-filling curves for numerical applications in robotics

In this article, the problem of approximating and visualizing the solution set of system of nonlinear inequalities is considered. In particular the proposed methods are based on two different approximations of Peano-Hilbert space-filling curves which are able to reduce the dimension of the problem for functions satisfying the Lipschitz condition. Numerical experiments showing a promising performance of the algorithms are presented.