We investigate the problem of cost-optimal planning in ASP. Current ASP planners can be trivially extended to a cost-optimal one by adding weak constraints, but only for a given makespan (number of steps). It is desirable to have a planner that guarantees global optimality. In this paper, we present two approaches to addressing this problem. First, we show how to engineer a cost-optimal planner composed of two ASP programs running in parallel. Using lessons learned from this, we then develop an entirely new approach to cost-optimal planning, stepless planning, which is completely free of makespan. Experiments to compare the two approaches with the only known cost-optimal planner in SAT reveal good potentials for stepless planning in ASP. The paper is under consideration for acceptance in TPLP.
Stepless planning is a brand new approach to logic-based planning and brings with it a lot of unknowns and potentials for future directions. One issue is that the lack of any notion of simultaneity makes certain standard optimizations difficult, such as incorporating mutex constraints and supporting conditional-effects (an extension to STRIPS planning). The latter extension has been realized in SAT-based planning @cite_1 , but incorporating it to stepless planning appears to be non-trivial. Our stepless planner is a nontrivial application that requires supportedness cycles to extend across different program sections, it would be nice if supported iterative solving with this.
@cite_1
2403583150 1600919542 2135939055 160902222
Path planning is often a high-dimensional computationally-expensive planning problem as it requires reasoning about the kinodynamic constraints of the robot and collisions of the robot with the environment. However, large regions of the environment are typically benign enough that a much faster low-dimensional planning combined with a local path following controller suffice. Planning with Adaptive Dimensionality that was recently developed makes use of this observation and iteratively constructs and searches a state-space consisting of mainly low-dimensional states. It only introduces regions of high-dimensional states into the state-space where they are necessary to ensure completeness and bounds on sub-optimality. However, due to its iterative nature, the approach relies on running a series of weighted A* searches. In this paper, we introduce and apply to Planning with Adaptive Dimensionality a simple but very effective incremental version of weighted A* that reuses its previously generated search tree if available. On the theoretical side, the new algorithm preserves guarantees on completeness and bounds on sub-optimality. On the experimental side, it speeds up 3D (x,y,heading) path planning with a full-body collision checking by up to a factor of 5. Our results also show that it tends to be much faster than applying alternative incremental graph search techniques such as D* to Planning with Adaptive Dimensionality. Planning is a notoriously hard combinatorial search problem. In many interesting domains, current planning algorithms fail to scale up gracefully. By combining a general, stochastic search algorithm and appropriate problem encodings based on propositional logic, we are able to solve hard planning problems many times faster than the best current planning systems. Although stochastic methods have been shown to be very effective on a wide range of scheduling problems, this is the first demonstration of its power on truly challenging classical planning instances. This work also provides a new perspective on representational issues in planning. Multi-robot path planning is dificult due to the combinatorial explosion of the search space with every new robot added. Complete search of the combined state-space soon becomes intractable. In this paper we present a novel form of abstraction that allows us to plan much more eficiently. The key to this abstraction is the partitioning of the map into subgraphs of known structure with entry and exit restrictions which we can represent compactly. Planning then becomes a search in the much smaller space of subgraph configurations. Once an abstract plan is found, it can be quickly resolved into a correct (but possibly sub-optimal) concrete plan without the need for further search. We prove that this technique is sound and complete and demonstrate its practical effiectiveness on a real map. A contending solution, prioritised planning, is also evaluated and shown to have similar performance albeit at the cost of completeness. The two approaches are not necessarily conflicting; we demonstrate how they can be combined into a single algorithm which out-performs either approach alone. Recent new planning paradigms, such as Graphplan and Satplan, have been shown to outperform more traditional domain-independent planners. An interesting aspect of these planners is that they do not incorporate domain specific control knowledge, but instead rely on efficient graph-based or propositional representations and advanced search techniques. An alternative approach has been proposed in the TLPlan system. TLPlan is an example of a powerful planner incorporating declarative control specified in temporal logic formulas. We show how these control rules can be parsed into Satplan. Our empirical results show up to an order of magnitude speed up. We also provide a detailed comparison with TLPlan, and show how the search strategies in TLPlan lead to efficient plans in terms of the number of actions but with little or no parallelism. The Satplan and Graphplan formalisms on the other hand do find highly parallel plans, but are less effective in sequential domains. Our results enhance our understanding of the various tradeoffs in planning technology, and extend earlier work on control knowledge in the Satplan framework by (1997) and Kautz and Selman (1998).