Feasibility of motion planning on acyclic and strongly connected directed graphs
Discrete Applied Mathematics
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Path planning has been widely studied by computer scientists. However, it is a very simplified version of the motion planning problems occurring in robotics. This paper examines extensions yielding two important issues: controllability and recognizability. The controllability issue arises when the number of controls is smaller than the number of independent parameters defining the robot's configuration: Can the motions span the configuration space? The recognizability issue occurs when there are errors in control and sensing: Can the robot recognize goal achievement? Both issues have interesting impact on the computational complexity of motion planning. This paper will also discuss a new path planning scheme based on random sampling of configuration space, to deal with many-degree-of-freedom robots. The blend of controllability, recognizability, and complexity issues discussed in this paper is unique to robotics and its study is key to the development of autonomous robots.