We study robot construction problems where multiple autonomous robots rearrange stacks of prefabricated blocks to build stable structures. These problems are challenging due to ramifications of actions, true concurrency, and requirements of supportedness of blocks by other blocks and stability of the structure at all times. We propose a formal hybrid planning framework to solve a wide range of robot construction problems, based on Answer Set Programming. This framework not only decides for a stable final configuration of the structure, but also computes the order of manipulation tasks for multiple autonomous robots to build the structure from an initial configuration, while simultaneously ensuring the stability, supportedness and other desired properties of the partial construction at each step of the plan. We prove the soundness and completeness of our formal method with respect to these properties. We introduce a set of challenging robot construction benchmark instances, including bridge building and stack overhanging scenarios, discuss the usefulness of our framework over these instances, and demonstrate the applicability of our method using a bimanual Baxter robot.
Note that for sophisticated constructions that involve temporary scaffolding, counterweights, and subassemblies, it is required to express ramifications of actions as well as true concurrency. However, expressing ramifications directly by simple Strips operators is not possible [Theorem 3] thiebauxHN05 due to lack of logical inference. Also, expressing true concurrency is not possible unless the description is extended with exponential number of new operators, where each operator characterizes a concurrent action. Due to these theoretical results, other studies @cite_27 @cite_13 @cite_44 that rely on simple Strips operators, do not present general methods for such sophisticated constructions either. It is important to note that these methods do not cover sophisticated structures, like bridges or overhangs, since objects are not necessarily placed on support areas of other objects. Such sophisticated structures require definition of transitive closure to ensure supportedness or connectedness. Transitive closure is not definable in first-order logic [Theorem 5] Fagin75 ; it is not directly supported by Strips either @cite_25 .
@cite_44 @cite_27 @cite_13 @cite_25
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Abstract This paper presents the application of geometric reasoning to the automatic construction of an assembly partial order from an attributed liaison graph representation of an assembly. The construction is based on the principle of assembly by disassembly and on the extraction of preferred subassemblies. On the basis of accessibility and manipulability criteria, the system first decomposes the given assembly into clusters of mutually inseparable parts. An abstract liaison graph is then generated wherein each cluster of mutually inseparable parts is represented as a supernode. A set of subassemblies is then generated by decomposing the abstract liaison graph into subgraphs, verifying the disassemblability of individual subgraphs, and applying the criteria for selecting preferred subassemblies to the disassemblable subgraphs. The recursive application of this process to the selected subassemblies results in a Hierarchical Partial-Order Graph (HPOG). A HPOG not only provides the precedence relations among assembly operations but also presents the temporal and spatial parallelism for implementing distributed and cooperative assembly. The system is organized under the “cooperative problem solving (CPS)” paradigm. In this paper we consider the motion planning problem of humanoid with articulated-spine for object manipulation in double support phase. Complexity of motion planning increases due to higher degrees-of-freedom (DOF), redundancy arising due to articulated spine, inherent underactuation and stability constraint. Additionally, loop-closure constraints arise during double-support phase, and self-collision constraints exist independent of the task to be performed. These problems make motion planning of humanoids a challenging task. In this work, we address the above issues by proposing a sampling based approach for planning the motion of the humanoid. Our approach to the problem is based on RRT* which can generate asymptotically optimal paths. The proposed approach deals with the stability constraints by rejective sampling approach which divides random configurations generated into valid and invalid configurations. Additionally, the loop-closure constraints are tackled by separating the humanoid into two open-kinematic sub-chains, and then generating random configurations in one sub-chain whereas the remaining sub-chain uses inverse kinematics for closure. Efficacy of the proposed approach is demonstrated for whole-body motion planning of a 25-DOF humanoid in generating asymptotically optimal end-effector paths. Abstract One way to think about a STRIPS operator is as a mapping from databases to databases, in the following sense: suppose we want to know what the world would be like if an action, represented by the STRIPS operator α, were done in some world, represented by the STRIPS database D 0. To find out, simply perform the operator α on D 0 (by applying α's elementary add and delete revision operators to D 0). We describe this process as progressing the database D 0 in response to the action α. In this paper, we consider the general problem of progressing an initial database in response to a given sequence of actions. We appeal to the situation calculus and an axiomatization of actions which addresses the frame problem (Reiter (1991)). This setting is considerably more general than STRIPS. Our results concerning progression are mixed. The (surprising) bad news is that, in general, to characterize a progressed database we must appeal to second-order logic. The good news is that there are many useful special cases for which we can compute the progressed database in first-order logic; not only that, we can do so efficiently. Finally, we relate these results about progression to STRIPS-like systems by providing a semantics for such systems in terms of a purely declarative situation calculus axiomatization for actions and their effects. On our view, STRIPS operators provide a mechanism for computing the progression of an initial situation calculus database under the effects of an action. We illustrate this idea by describing two different STRIPS mechanisms, and proving their correctness with respect to their situation calculus specifications. We present a novel boundary integral formulation of the Helmholtz transmission problem for bounded composite scatterers (that is, piecewise constant material parameters in "subdomains") that directly lends itself to operator preconditioning via Calderon projectors. The method relies on local traces on subdomains and weak enforcement of transmission conditions. The variational formulation is set in Cartesian products of standard Dirichlet and special Neumann trace spaces for which restriction and extension by zero are well defined. In particular, the Neumann trace spaces over each subdomain boundary are built as piecewise @math -distributions over each associated interface. Through the use of interior Calderon projectors, the problem is cast in variational Galerkin form with an operator matrix whose diagonal is composed of block boundary integral operators associated with the subdomains. We show existence and uniqueness of solutions based on an extension of Lions' projection lemma for non-closed subspaces. We also investigate asymptotic quasi-optimality of conforming boundary element Galerkin discretization. Numerical experiments in 2-D confirm the efficacy of the method and a performance matching that of another widely used boundary element discretization. They also demonstrate its amenability to different types of preconditioning.