Counterexample-Guided Repair for Symbolic-Geometric Action Abstractions

Integrated task and motion planning (TMP) offers a promising class of approaches for solving robot planning problems with intricate symbolic and geometric constraints. However, TMP planners rely on difficult-to-construct abstract models of robot actions. In this article, we propose a method for automatically constructing and continuously improving an abstraction of robot actions via observations of the robot performing the actions. This method, called
automatic abstraction repair
, allows action abstractions to be initially incorrect or incomplete and converge toward a correct model over time. Here, we demonstrate abstraction repair using constrained polynomial zonotopes (CPZs), an expressive nonconvex set representation for modeling predicates over joint symbolic and geometric state. The repair process performs a hybrid optimizing search over symbolic edit operations to predicate formulae and continuous predicate parameters to improve the grounding of the abstraction to the behavior of a physical robot. In this work, we describe the predicate model, introduce the
symbolic-geometric abstraction repair
problem, and present an anytime algorithm for automatic abstraction repair. We demonstrate that abstraction repair can improve realistic action abstractions for common mobile manipulation actions from a handful of observations and discuss the tradeoffs of the CPZ model for predicate representation.