Abstract-We present a new approach to integrated task and motion planning (ITMP) for robots performing mobile manipulation. In our approach, the user writes a high-level specification that captures partial knowledge about a mobile manipulation setting. In particular, this specification includes a plan outline that syntactically defines a space of plausible integrated plans, a set of logical requirements that the generated plan must satisfy, and a description of the physical space that the robot manipulates. A synthesis algorithm is now used to search for an integrated plan that falls within the space defined by the plan outline, and also satisfies all requirements.Our synthesis algorithm complements continuous motion planning algorithms with calls to a Satisfiability Modulo Theories (SMT) solver. From the scene description, a motion planning algorithm is used to construct a placement graph, an abstraction of a manipulation graph whose paths represent feasible, low-level motion plans. An SMT-solver is now used to symbolically explore the space of all integrated plans that correspond to paths in the placement graph, and also satisfy the constraints demanded by the plan outline and the requirements.Our approach is implemented in a system called RO-BOSYNTH. We have evaluated ROBOSYNTH on a generalization of an ITMP problem investigated in prior work. The experiments demonstrate that our method is capable of generating integrated plans for a number of interesting variations on the problem. I. INTRODUCTION Integrated task and motion planning (ITMP) [1]-[4]is a challenging class of planning problems that involve complex combinations of high-level task planning and low-level motion planning. In this paper, we present a new approachembodied in a system called ROBOSYNTH-to ITMP.In the version of ITMP considered here, the task planning level is discrete and requires combinatorial exploration of the space of possible integrated plans, while the motion planning level is responsible for finding paths in continuous spaces. The task level planner has to search a space that is exponential in the number of actions required to achieve a goal, while the continuous planning problem is PSPACE-complete in the degrees of freedom of the robot [5]. Unsurprisingly, the seamless integration of these two levels is difficult. A strictly hierarchical approach where the task planner operates on an abstraction and passes the solution to a continuous motion planner does not always work: it either sacrifices completeness or requires extensive backtracking, which can be highly timeconsuming. While we do not solve the above problem in its

Guided program synthesis is an existing methodology for systematic development of algorithms. Speci c algorithms are viewed as instances of very general algorithm schemas.For example, the Global Search schema generalizes traditional branch-and-bound search, and includes both depth-rst and breadth-rst strategies. Algorithm development involves systematic specialization of the algorithm schema based on problem-speci c constraints to create e cient algorithms that are correct by construction, obviating the need for a separate veri cation step. Guided program synthesis has been applied to a wide range of algorithms, but there is still no systematic process for the synthesis of large search programs such as AI planners.v Our rst contribution is the specialization of Global Search to a class we call E cient Breadth-First Search (EBFS), by incorporating dominance relations to constrain the size of the frontier of the search to be polynomially bounded. Dominance relations allow two search spaces to be compared to determine whether one dominates the other, thus allowing the dominated space to be eliminated from the search. We further show that EBFS is an e ective characterization of greedy algorithms, when the breadth bound is set to one. Surprisingly, the resulting characterization is more general than the well-known characterization of greedy algorithms, namely the Greedy Algorithm parametrized over algebraic structures called greedoids.Our second contribution is a methodology for systematically deriving dominance relations, not just for individual problems but for families of related problems. The techniques are illustrated on numerous well-known problems. Combining this with the program schema for EBFS results in e cient greedy algorithms.Our third contribution is application of the theory and methodology to the practical problem of synthesizing fast planners. Nearly all the state-of-the-art planners in the planning literature are heuristic domain-independent planners. They generally do not scale well and their space requirements also become quite prohibitive. Planners such as TLPlan that incorporate domain-speci c information in the form of control rules are orders of magnitude faster. However, devising the control rules is labor-intensive task and requires domain expertise and insight. The correctness of the rules is also not guaranteed. We introduce a method by which domain-speci c dominance relations can be systematically derived, which can then be turned into control rules, and demonstrate the method on a planning problem (Logistics).vi Many of the derivations are straightforward enough to be automatable.Our third main contribution is showing how to apply the theory and techniqueswe have introduced to a practical problem, namely synthesizing fast AI planners [GNT04].Many of the state-of-the-art planners in the planning literature are domain-independent heuristic planners. They generally do not scale very well and their space requirements also become quite prohibitive. The key to scalable planners is to incorpora...

It is well-known that a naive algorithm can often be turned into an efficient program by applying appropriate semanticspreserving transformations. This technique has been used to derive programs to solve a variety of maximum-sum programs. One problem with this approach is that each problem variation requires a new set of transformations to be derived. An alternative approach to synthesis combines problem specifications with flexible algorithm theories to derive efficient algorithms. We show how this approach can be implemented in Haskell and applied to solve constraint satisfaction problems. We illustrate this technique by deriving programs for three varieties of maximum-weightsum problem. The derivations of the different programs are similar, and the resulting programs are asymptotically faster in practice than the programs created by transformation.

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