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Using sampling to estimate the connectivity of high-dimensional configuration spaces has been the theoretical underpinning for effective sampling-based motion planners. Typical strategies either build a roadmap, or a tree as the underlying search structure that connects sampled configurations, with a focus on guaranteeing completeness and optimality as the number of samples tends to infinity. Roadmap-based planners allow preprocessing the space, and can solve multiple kinematic motion planning problems, but need a steering function to connect pairwise-states. Such steering functions are difficult to define for kinodynamic systems, and limit the applicability of roadmaps to motion planning problems with dynamical systems. Recent advances in the analysis of single query tree-based planners has shown that forward search trees based on random propagations are asymptotically optimal. The current work leverages these recent results and proposes a multi-query framework for kinodynamic planning. Bundles of kinodynamic edges can be sampled to cover the state space before the query arrives. Then, given a motion planning query, the connectivity of the state space reachable from the start can be recovered from a forward search tree reasoning about a local neighborhood of the edge bundle from each tree node. The work demonstrates theoretically that considering any constant radial neighborhood during this process is sufficient to guarantee asymptotic optimality. Experimental validation in five and twelve dimensional simulated systems also highlights the ability of the proposed edge bundles to express high-quality kinodynamic solutions. Our approach consistently finds higher quality solutions compared to SST, and RRT, often with faster initial solution times. The strategy of sampling kinodynamic edges is demonstrated to be a promising new paradigm. 

Rearranging objects on a planar surface arises in a variety of robotic applications, such as product packaging. Using two arms can improve efficiency but introduces new computa- tional challenges. This paper studies the problem structure of object rearrangement using two arms in synchronous, monotone tabletop setups and develops an optimal mixed integer model. It then describes an efficient and scalable algorithm, which first minimizes the cost of object transfers and then of moves between objects. This is motivated by the fact that, asymptotically, object transfers dominate the cost of solutions. Moreover, a lazy strategy minimizes the number of motion planning calls and results in significant speedups. Theoretical arguments support the benefits of using two arms and indicate that synchronous execution, in which the two arms perform together either transfers or moves, introduces only a small overhead. Experiments support these claims and show that the scalable method can quickly compute solutions close to the optimal for the considered setup. 

Rearranging objects on a planar surface arises in a variety of robotic applications, such as product packaging. Using two arms can im- prove efficiency but introduces new computational challenges. This paper studies the structure of dual-arm rearrangement for synchronous, mono- tone tabletop setups and develops an optimal mixed integer model. It then describes an efficient and scalable algorithm, which first minimizes the cost of object transfers and then of moves between objects. This is motivated by the fact that, asymptotically, object transfers dominate the cost of solutions. Moreover, a lazy strategy minimizes the number of motion planning calls and results in significant speedups. Theoreti- cal arguments support the benefits of using two arms and indicate that synchronous execution, in which the two arms perform together either transfers or moves, introduces only a small overhead. Experiments sup- port these points and show that the scalable method can quickly compute solutions close to the optimal for the considered setup.