Comparison of constrained geometric approximation strategies for planar information states

This paper describes and analyzes a new technique for reasoning about uncertainty called constrained geometric approximation (CGA). We build upon recent work that has developed methods to explicitly represent a robot´s knowledge as an element, called an information state, in an appropriately defined information space. The intuition of our new approach is to constrain the I-state to remain in a structured subset of the I-space, and to enforce that constraint using appropriate over-approximation methods. The result is a collection of algorithms that enable mobile robots with extreme limitations in both sensing and computation to maintain simple but provably mean-ingful representations of the incomplete information available to them. We present a simulated implementation of this technique for a sensor-based navigation task, along with experimental results for this task showing that CGA, compared to a high-fidelity representation of the un-approximated I-state, achieves a similar success rate at a small fraction of the computational cost.