Invariant-Based World Models for Robust Robotic Systems Demonstrated on an Autonomous Football Table

Abstract

This work explains the use of invariants in robotic perception and control skills. An “invariant” is a mathematical constraint that remains unchanged under a particular transformation in a system. This property makes robotic functionalities more robust against “disturbances” that cause these transformation. These invariants are stored in a world model (WM), which has a central role in the information architecture of the robot to share information between components. A “robotic” football table serves as an example to illustrate the effectiveness of invariants. Despite looking different, all standard football tables satisfy the same set of invariants; the common layout of the field, line markings and puppets, which are not identical but satisfy the same set of constraints, such as parallelism, partial ordering, and relative colour and intensity differences between objects. During initialization, the invariants are actively identified and saved to the world model. During game play this world model is used by the perception and action skills and is updated when necessary. This work shows how the use of invariants creates robustness against variation in placement of the perception system and against variation in table dimensions and colours. When the camera is misaligned or moved mid-play, the world model is updated to ensure a smooth continuation of the game. The approach is tested on three standard football tables, with different dimensions and colours, showing that the approach is robust on standard tables that adhere to the invariants.