SMT-based synthesis of integrated task and motion plans from plan outlines

Abstract

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

Implan: Scalable Incremental Motion Planning for Multi-Robot Systems

“…SMT solvers have been used in motion planning with rectangular obstacles [8] and in synthesizing integrated task and motion plans from plan outlines [14]. We introduce the use of an SMT solver in solving the multi-robot motion planning problem in a scalable way, and show how different capabilities of SMT solvers, for example, finding a satisfiable solution and finding an unsatisfiable core can be effectively applied to solve motion planning problems.…”

Controller synthesis with inductive proofs for piecewise linear systems: An SMT-based algorithm

“…Although many control systems can only be modeled by means of nonlinear arithmetic over the real numbers involving transcendental functions that make the corresponding SMT problems undecidable, the solvers are evolving rapidly and several incorporate approximate decision procedures for nonlinear arithmetic [15]. These technological developments motivated us (and others [20], [21]) to explore SMT-based controller synthesis.…”

Incremental Task and Motion Planning: A Constraint-Based Approach

“…Incremental SMT solvers maintain a stack of constraints or assertions and can efficiently perform repeated satisfiability checks as constraints are pushed onto and popped from the constraint stack [1,15]. Our use of incremental SMT solving to update constraints is a new feature compared to previous use of SMT solvers in TMP [62,80].…”

“…SMT extends boolean satisfiability with rules (theories) for domains such as linear arithmetic. Compared to traditional SAT solvers, SMT solvers provide a more expressive and high-level interface with useful features for expressing constraints in robotics domains [62,80]. Crucially, some SMT solvers [1,15] enable incremental solving -adding and deleting constraints at run-time to produce alternate solutions.…”

“…[57] formulates the motion side of TMP as a constraint satisfaction problem over a discretized, preprocessed subset of the configuration space. [62,80] use an SMT solver to generate task and motion plans from a static roadmap, employing plan outlines to guide the planning process in a manner similar to Hierarchical Task Networks [26]. FFRob [29] develops an FF-like [39] task-layer heuristic based on a lazily-expanded roadmap.…”