Using constrained intuitionistic linear logic for hybrid robotic planning problems

Abstract — Synthesis of robot behaviors towards nontrivial goals often requires reasoning about both discrete and contin-uous aspects of the underlying domain. Existing approaches in building automated tools for such synthesis problems attempt to augment methods from either discrete planning or continuous control with hybrid elements, but largely fail to ensure a uniform treatment of both aspects of the domain. In this paper, we present a new formalism, Constrained Intuitionistic Linear Logic (CILL), merging continuous constraint solvers with linear logic to yield a single language in which hybrid properties of robotic behaviors can be expressed and reasoned with. Following a gentle introduction to linear logic, we describe the two new connectives of CILL, introduced to interface the constraint domain with the logical fragment of the language. We then illustrate the application of CILL for robotic planning problems within the Balanced Blocks World, a “physically realistic ” extension of the Blocks World domain. Even though some of the formal proofs for the semantic foundations of the language as well as an efficient implementation of a theorem prover are yet to be completed, CILL promises to be a powerful formalism in reasoning within hybrid domains. I