Fig. 2: Two-stage process to building artificial spacetimes.
From: Artificial spacetimes for reactive control of resource-limited robots
Coordinate transformations enable metrics for behaviors to be composed with metrics for boundary avoidance. First, we map a physical space with a complex boundary to a simple virtual space by a conformal transformation. A control metrics is then implemented in virtual space to dictate the robot’s behavior. For example, here robots all travel to a target location. Mapping back to physical space, we produce a composite metric that both encodes the behavior and boundary information in a single scalar field.
