Transforming system formulations in robotics for efficient perception and planning

For efficient perception and planning, it is necessary for an autonomous robot to find a formulation with good computational properties. An especially important computational property is decomposability. The perspective of this work is to view a system's state space as though it were physical space, and the system's behavior as though it were physical motion. Following the analogy with physics, a formulation is an abstract coordinate system whose axes specify a decomposition, and formulations are transformed by changing coordinates. The mathematical basis for this analogy is given. Continuous and discrete formulations for a robot vehicle are transformed to yield decompositions, which shed light on the relationship between the continuous and discrete formulations.