This Time the Robot Settles for a Cost: A Quantitative Approach to Temporal Logic Planning with Partial Satisfaction

Abstract

The specification of complex motion goals through temporal logics is increasingly favored in robotics to narrow the gap between task and motion planning. A major limiting factor of such logics, however, is their Boolean satisfaction condition. To relax this limitation, we introduce a method for quantifying the satisfaction of co-safe linear temporal logic specifications, and propose a planner that uses this method to synthesize robot trajectories with the optimal satisfaction value. The method assigns costs to violations of specifications from user-defined proposition costs. These violation costs define a distance to satisfaction and can be computed algorithmically using a weighted automaton. The planner utilizes this automaton and an abstraction of the robotic system to construct a product graph that captures all possible robot trajectories and their distances to satisfaction. Then, a plan with the minimum distance to satisfaction is generated by employing this graph as the high-level planner in a synergistic planning framework. The efficacy of the method is illustrated on a robot with unsatisfiable specifications in an office environment.

Iterative Temporal Planning in Uncertain Environments With Partial Satisfaction Guarantees

“…Then, the user-defined priority list is used to synthesize the least-violating strategy. Similarly, the work in [45] employs user-defined costs to define a distance to satisfaction of co-safe LTL specifications. The costs in that work, however, are over propositions, and the authors introduce a method of constructing a weighted automoton and generating a robot plan with the least distance to satisfaction.…”

Synthesis from Satisficing and Temporal Goals

“…A salient feature of our algorithm is that the complexity to solve the final product game is primarily governed by the temporal goal and not the satisficing goal. What we mean is that if the temporal goal is given by a fragment of LTL, such as co-safe LTL (Lahijanian et al 2015), then the final product game would be reachability game. This is because co-safe LTL formulas are represented by co-safety automata and thus their combination with comparators would also be a co-safety automata.…”

“…This feature has implications on the practicality of our algorithm. In practice, it has been observed that wide-ranging temporal goals in robotics domains can be expressed in simpler fragments and variants of LTL, such as co-safe LTL (Lahijanian et al 2015) and LTLf (He et al 2017). These fragments can be expressed as conjunctions of safety and reachability goals.…”

Generating Explanations for Temporal Logic Planner Decisions

“…Early work on planning with linear temporal logic (LTL) specifications in MDPs includes that of Ding et al (2011), who employ dynamic programming to construct a policy which almost surely satisfies an LTL specification. Subsequent work has considered how to plan with LTL specifications that are only partially satisfiable (Lacerda, Parker, and Hawes 2015;Lahijanian et al 2015), and how to work with multiple specifications which may not all be satisfiable (Tumova et al 2013;Kasenberg and Scheutz 2018) or represented as beliefs over formulas (Shah, Li, and Shah 2019). The present work builds on these latter approaches, describing how an agent planning with multiple specifications in LTL may answer questions about its behavior, including "why" questions.…”