Spatial representation for navigation in animats

This article considers the problem of spatial representation for animat navigation systems. It is proposed that the global navigation task, or "wayfinding, " is best supported by multiple interacting subsystems, each of which builds its own partial representation of relevant world knowledge. Evidence from the study of animal navigation is reviewed to demonstrate that similar principles underlie the wayfinding behavior of animals, including humans. A simulated wayfinding system is described that embodies and illustrates several of the themes identified with animat navigation. This system constructs a network of partial models of the quantitative spatial relations between groups of salient landmarks. Navigation tasks are solved by propagating egocentric view information through this network, using a simple but effective heuristic to arbitrate between multiple solutions

Solving nonlinear polynomial systems in the barycentric Bernstein basis

We present a method for solving arbitrary systems of N nonlinear polynomials in n variables over an n-dimensional simplicial domain based on polynomial representation in the barycentric Bernstein basis and subdivision. The roots are approximated to arbitrary precision by iteratively constructing a series of smaller bounding simplices. We use geometric subdivision to isolate multiple roots within a simplex. An algorithm implementing this method in rounded interval arithmetic is described and analyzed. We find that when the total order of polynomials is close to the maximum order of each variable, an iteration of this solver algorithm is asymptotically more efficient than the corresponding step in a similar algorithm which relies on polynomial representation in the tensor product Bernstein basis. We also discuss various implementation issues and identify topics for further study.National Science Foundation (U.S.) (grant DMI-062933)Alexander von Humboldt Foundation (fellowship