Real-time obstacle avoidance for manipulators and mobile robots
International Journal of Robotics Research
The complexity of robot motion planning
The complexity of robot motion planning
Manifolds, tensor analysis, and applications: 2nd edition
Manifolds, tensor analysis, and applications: 2nd edition
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Theoretical Computer Science - Special issue on design and analysis of geometrical algorithms for robot motion planning and vision
Handbook of discrete and computational geometry
Motion planning for a rigid body using random networks on the medial axis of the free space
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Numerical Recipes in C++: the art of scientific computing
Numerical Recipes in C++: the art of scientific computing
Robot Motion Planning
A Voronoi-Based Hybrid Motion Planner for Rigid Bodies
A Voronoi-Based Hybrid Motion Planner for Rigid Bodies
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Simple wriggling is hard unless you are a fat hippo
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
A family of skeletons for motion planning and geometric reasoning applications
Artificial Intelligence for Engineering Design, Analysis and Manufacturing - Representing and Reasoning About Three-Dimensional Space
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We present a new roadmap for a rod-shaped robot operating in a three-dimensional workspace, whose configuration space is diffeomorphic to R3 X S2. This roadmap is called the rod hierarchical generalized Voronoi graph (rod-HGVG) and can be used to find a path between any two points in an unknown configuration space using only the sensor data. More importantly, the rod-HGVG serves as a basis for an algorithm to explore an unknown configuration space without explicitly constructing it. Once the rod-HGVG is constructed, the planner can use it to plan a path between any two configurations. One of the challenges in defining the roadmap revolves around a homotopy theory result, which asserts that there cannot be a one-dimensional deformation retract of a non-contractible space with dimension greater than two. Instead, we define an exact cellular decomposition on the free configuration space and a deformation retract in each cell (each cell is contractible). Next, we "connect" the deformation retracts of each of the cells using a roadmap of the workspace. We call this roadmap a piecewise retract because it comprises many deformation retracts. Exploiting the fact that the rod-HGVG is defined in terms of workspace distance measurements, we prescribe an incremental procedure to construct the rod-HGVG that uses the distance information that can be obtained from conventional range sensors.