Numeric Planning with Disjunctive Global Constraints via SMT

Abstract

This paper describes a novel encoding for sequential numeric planning into the problem of determining the satisfiability of a logical theory T. We introduce a novel technique, orthogonal to existing work aiming at producing more succinct encodings that enables the theory solver to roll up an unbounded yet finite number of instances of an action into a single plan step, greatly reducing the horizon at which T models valid plans. The technique is then extended to deal with problems featuring disjunctive global constraints, in which the state space becomes a non-convex n dimensional polytope. In order to empirically evaluate the encoding, we build a planner, SPRINGROLL, around a state–of–the–art off– the–shelf SMT solver. Experiments on a diverse set of domains are finally reported, and results show the generality and efficiency of the approach.

Cyber-Physical Planning: Deliberation for Hybrid Systems with a Continuous Numeric State

“…Again fined-grained control could in theory be obtained by multiplying the number of actions, but one would quickly hit the scalability limits of current planners. The work of Scala et al (2016b) is a notable exception in its capability to handle the long actions sequence that are necessary for trajectory planning, but imposes important limitation on the feasible trajectories and has no support for time which prevents its use for constraining the state evolution beside simple invariants.…”

Compiling Optimal Numeric Planning to Mixed Integer Linear Programming

“…Admissible heuristics for these problems are the sub-goaling heuristic ĥrmax (Scala, Haslum, and Thiébaux 2016), cost-optimal partitioning based on landmarks h lma+ (Scala et al 2017), and delete relaxation and network flow heuristics . While non-admissible heuristics (Hoffmann 2003;Coles et al 2008;Scala et al 2016a;Illanes and McIlraith 2017) and SMT compilations (Scala et al 2016b) for linear effects have been proposed, none have considered the optimal setting.…”

“…While heuristic search is the most widely used approach for classical planning, there are several techniques based on compilation to other approaches such as Boolean Satisfiability (SAT) (Rintanen 2012), Constraint Satisfaction (Vidal 2011), and Integer Programming (IP) (Vossen et al 1999;Kautz and Walser 1999;van den Briel, Vossen, and Kambhampati 2005). Compilation techniques have been proven particularly useful for extensions of classical planning, such as SAT Modulo Theory (SMT) approaches to numeric and hybrid planning (Scala et al 2016b;Cashmore et al 2016).…”

LM-Cut Heuristics for Optimal Linear Numeric Planning

“…Planning with Simple Numeric Conditions Scala et al (2016b) introduced the notion of a simple effect and a simple numeric condition (SC). If an effect changes a variable only by a constant, i.e., of the form v += c, it is a simple effect.…”