On eye-sensor based path planning for robots with non-trivial geometry/kinematics

We formally pose and explore some novel issues that arise for eye-sensor based motion planning for robots with non-trivial geometry/kinematics. The key issue is that while the sensor senses in physical space, the planning takes place in configuration space, and the two spaces are distinctly different for robots with nontrivial geometry/kinematics. This lends to some very interesting, fundamental yet novel issues. In particular, we introduce several novel notions: notion of s-reachability, notion of s-completeness that characterizes completeness for sensor-based planning algorithms, notion of explorability of configuration space, and notion of observability of physical space. We give sufficient conditions for a (discrete) eye-sensor based planner to be s-complete.