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Integrated task and motion planning problems describe a multi-modal statespace, which is often abstracted as a set of smooth manifolds that areconnected via sets of transitions states. One approach to solving such problemsis to sample reachable states in each of the manifolds, while simultaneouslysampling transition states. Prior work has shown that in order to achieveasymptotically optimal (AO) solutions for such piecewise-smooth task planningproblems, it is sufficient to double the connection radius required for AOsampling-based motion planning. This was shown under the assumption that thetransition sets themselves are smooth. The current work builds upon this resultand demonstrates that it is sufficient to use the same connection radius as forstandard AO motion planning. Furthermore, the current work studies the casethat the transition sets are non-smooth boundary points of the valid statespace, which is frequently the case in practice, such as when a gripper graspsan object. This paper generalizes the notion of clearance that is typicallyassumed in motion and task planning to include such individual, potentiallynon-smooth transition states. It is shown that asymptotic optimality isretained under this generalized regime.

Pushing the Boundaries of Asymptotic Optimality in Integrated Task and Motion Planning