What to Do When You Can't Do It All: Temporal Logic Planning with Soft Temporal Logic Constraints

Abstract

In this paper, we consider a temporal logic planning problem in which the objective is to find an infinite trajectory that satisfies an optimal selection from a set of soft specifications expressed in linear temporal logic (LTL) while nevertheless satisfying a hard specification expressed in LTL. Our previous work considered a similar problem in which linear dynamic logic for finite traces (LDL f ), rather than LTL, was used to express the soft constraints. In that work, LDL f was used to impose constraints on finite prefixes of the infinite trajectory. By using LTL, one is able not only to impose constraints on the finite prefixes of the trajectory, but also to set 'soft' goals across the entirety of the infinite trajectory. Our algorithm first constructs a product automaton, on which the planning problem is reduced to computing a lasso with minimum cost. Among all such lassos, it is desirable to compute a shortest one. Though we prove that computing such a shortest lasso is computationally hard, we also introduce an efficient greedy approach to synthesize short lassos nonetheless. We present two case studies describing an implementation of this approach, and report results of our experiment comparing our greedy algorithm with an optimal baseline.

Reinforcement Learning Based Temporal Logic Control with Soft Constraints Using Limit-deterministic Generalized Buchi Automata

“…Then, γ can be obtained by solving (11). Finally, the range of β can be determined by solving (8) and (12). In order to minimize the violation cost, a great value of β is preferred.…”

“…For instance, some areas of interest to be visited can be probabilistically prohibitive to the agent in practice (e.g., potentially surrounded by water due to heavy rain that the ground robot cannot traverse), resulting in part of the userspecified tasks cannot be achieved and AMECs do not exist in the product MDP. Although minimal revision of motion plans in a potentially conflicting environment has been investigated in the works of [12], [27]- [30], only deterministic transition systems are considered, and it is not yet clear how to address the above-mentioned issues in stochastic systems.…”