Many robotics applications benefit from being able to compute multiple geodesic paths in a given configuration space. Existing paradigm is to use topological path planning, which can compute optimal paths in distinct topological classes. However, these methods usually require nontrivial geometric constructions, which are prohibitively expensive in 3-D, and are unable to distinguish between distinct topologically equivalent geodesics that are created due to high-cost/curvature regions or prismatic obstacles in 3-D. In this article, we propose an approach to compute$k$geodesic paths using the concept of a novel neighborhood-augmented graph, on which graph search algorithms can compute multiple optimal paths that are topo-geometrically distinct. Our approach does not require complex geometric constructions, and the resulting paths are not restricted to distinct topological classes, making the algorithm suitable for problems where finding and distinguishing between geodesic paths are of interest. We demonstrate the application of our algorithm to planning shortest traversible paths for a tethered robot in 3-D with cable-length constraint.

Attempts to achieve robotic Within-Hand-Manipulation (WIHM) generally utilize either high-DOF robotic hands with elaborate sensing apparatus or multi-arm robotic systems. In prior work we presented a simple robot hand with variable friction robot fingers, which allow a low-complexity approach to within-hand object translation and rotation, though this manipulation was limited to planar actions. In this work we extend the capabilities of this system to 3D manipulation with a novel region-based WIHM planning algorithm and utilizing extrinsic contacts. The ability to modulate finger friction enhances extrinsic dexterity for three-dimensional WIHM, and allows us to operate in the quasi-static level. The region-based planner automatically generates 3D manipulation sequences with a modified A* formulation that navigates the contact regions between the fingers and the object surface to reach desired regions. Central to this method is a set of object-motion primitives (i.e. within-hand sliding, rotation and pivoting), which can easily be achieved via changing contact friction. A wide range of goal regions can be achieved via this approach, which is demonstrated via real robot experiments following a standardized in-hand manipulation benchmarking protocol.