Khen Elimelech

Khen Elimelech, James Motes, Marco Morales et al.

Multi-Robot Task Planning (MR-TP) is the search for a discrete-action plan a team of robots should take to complete a task. The complexity of such problems scales exponentially with the number of robots and task complexity, making them challenging for online solution. To accelerate MR-TP over a system's lifetime, this work looks at combining two recent advances: (i) Decomposable State Space Hypergraph (DaSH), a novel hypergraph-based framework to efficiently model and solve MR-TP problems; and \mbox{(ii) learning-by-abstraction,} a technique that enables automatic extraction of generalizable planning strategies from individual planning experiences for later reuse. Specifically, we wish to extend this strategy-learning technique, originally designed for single-robot planning, to benefit multi-robot planning using hypergraph-based MR-TP.

Khen Elimelech, Vadim Indelman

In this work, we examine the problem of online decision making under uncertainty, which we formulate as planning in the belief space. Maintaining beliefs (i.e., distributions) over high-dimensional states (e.g., entire trajectories) was not only shown to significantly improve accuracy, but also allows planning with information-theoretic objectives, as required for the tasks of active SLAM and information gathering. Nonetheless, planning under this "smoothing" paradigm holds a high computational complexity, which makes it challenging for online solution. Thus, we suggest the following idea: before planning, perform a standalone state variable reordering procedure on the initial belief, and "push forwards" all the predicted loop closing variables. Since the initial variable order determines which subset of them would be affected by incoming updates, such reordering allows us to minimize the total number of affected variables, and reduce the computational complexity of candidate evaluation during planning. We call this approach PIVOT: Predictive Incremental Variable Ordering Tactic. Applying this tactic can also improve the state inference efficiency; if we maintain the PIVOT order after the planning session, then we should similarly reduce the cost of loop closures, when they actually occur. To demonstrate its effectiveness, we applied PIVOT in a realistic active SLAM simulation, where we managed to significantly reduce the computation time of both the planning and inference sessions. The approach is applicable to general distributions, and induces no loss in accuracy.

Khen Elimelech, Vadim Indelman

In this work, we introduce a new and efficient solution approach for the problem of decision making under uncertainty, which can be formulated as decision making in a belief space, over a possibly high-dimensional state space. Typically, to solve a decision problem, one should identify the optimal action from a set of candidates, according to some objective. We claim that one can often generate and solve an analogous yet simplified decision problem, which can be solved more efficiently. A wise simplification method can lead to the same action selection, or one for which the maximal loss in optimality can be guaranteed. Furthermore, such simplification is separated from the state inference and does not compromise its accuracy, as the selected action would finally be applied on the original state. First, we present the concept for general decision problems and provide a theoretical framework for a coherent formulation of the approach. We then practically apply these ideas to decision problems in the belief space, which can be simplified by considering a sparse approximation of their initial belief. The scalable belief sparsification algorithm we provide is able to yield solutions which are guaranteed to be consistent with the original problem. We demonstrate the benefits of the approach in the solution of a realistic active-SLAM problem and manage to significantly reduce computation time, with no loss in the quality of solution. This work is both fundamental and practical, and holds numerous possible extensions.