Completeness of Randomized Kinodynamic Planners with State-based Steering

Probabilistic completeness is an important property in motion planning. Although it has been established with clear assumptions for geometric planners, the panorama of completeness results for kinodynamic planners is still incomplete, as most existing proofs rely on strong assumptions that are difficult, if not impossible, to verify on practical systems. In this paper, we focus on an important class of kinodynamic planners, namely those that interpolate trajectories in the state space. We provide a proof of probabilistic completeness for these planners under assumptions that can be readily verified from the system's equations of motion and the user-defined interpolation function. Our proof relies crucially on a property of interpolated trajectories, termed second-order continuity (SOC), which we show is tightly related to the ability of a planner to benefit from denser sampling. We analyze the impact of this property in simulations on a low-torque pendulum. Our results show that a simple RRT using a second-order continuous interpolation swiftly finds solution, while it is impossible for the same planner using standard Bezier curves (which are not SOC) to find any solution.Comment: 21 pages, 5 figure

FFRob: An Efficient Heuristic for Task and Motion Planning

Manipulation problemsinvolvingmany objects present substantial challenges for motion planning algorithms due to the high dimensionality and multi-modality of the search space. Symbolic task planners can efficiently construct plans involving many entities but cannot incorporate the constraints from geometry and kinematics. In this paper, we show how to extend the heuristic ideas from one of the most successful symbolic planners in recent years, the FastForward (FF) planner, to motion planning, and to compute it efficiently. We use a multi-query roadmap structure that can be conditionalized to model different placements of movable objects. The resulting tightly integrated planner is simple and performs efficiently in a collection of tasks involving manipulation of many objects.National Science Foundation (U.S.) (Grant No. 019868)United States. Office of Naval Research. Multidisciplinary University Research Initiative (grant N00014-09-1-1051)United States. Air Force. Office of Scientific Research (grant AOARD-104135)Singapore. Ministry of Educatio

Streamlines for Motion Planning in Underwater Currents

Motion planning for underwater vehicles must consider the effect of ocean currents. We present an efficient method to compute reachability and cost between sample points in sampling-based motion planning that supports long-range planning over hundreds of kilometres in complicated flows. The idea is to search a reduced space of control inputs that consists of stream functions whose level sets, or streamlines, optimally connect two given points. Such stream functions are generated by superimposing a control input onto the underlying current flow. A streamline represents the resulting path that a vehicle would follow as it is carried along by the current given that control input. We provide rigorous analysis that shows how our method avoids exhaustive search of the control space, and demonstrate simulated examples in complicated flows including a traversal along the east coast of Australia, using actual current predictions, between Sydney and Brisbane.Comment: 7 pages, 4 figures, accepted to IEEE ICRA 2019. Copyright 2019 IEE