Using Constrained Intuitionistic Linear Logic for Hybrid Robotic Planning Problems

Abstract

Abstract-Synthesis of robot behaviors towards nontrivial goals often requires reasoning about both discrete and continuous 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.

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“…In addition to the semantic formulation of the connection between these logical connectives and the planning domain, both the structure and the construction of LinGraph would need to be extended to correctly handle proof construction in the presence of new connectives. Other possible extensions include the incorporation of continuous constraint expressions into linear logic as was proposed in [54], allowing native modeling of hybrid systems.…”

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Policy Compliance in Collaborative Systems

“…We have not explored the possible connections and equivalences between the problems of this work and problems in classical planning. In a similar vein, the authors of [37] modify linear logic to incoporate constraints that correspond to the more continuous aspects of traditional planning problems that one encounters in the real world.…”