Evaluation and Transformation of Unrealizable Tasks for Robot Systems in Representation Space

This paper proposes a framework for a robot system to actively evaluate its realizability for a specific task based on its representation space. The representation space (R-space) of a robot system could be constructed to describe the distributions of system attributes (called representation), whose transitions reflect the process of task realization. All factors blocking transitions of the system representation, hence the task realization, including physical configurations of the robot system and environmental constraints, are defined as unreachable areas in the R-space, specifying the limitation of the system's capability to execute the prescribed task. The reachable area in the R-space, showing the representations that the robot system could be of, is figured out to formalize the criteria for task realizability. The potential optimal scheme to accomplish a realizable task can further be recognized from the shortest path that the robot representation transits along. Otherwise, causes for unrealizable tasks are investigated to suggest clues for transforming the tasks to be realizable ones. Meanwhile, conditions and the total cost to fix unrealizable tasks are compared to make out the best strategy under the given cost index, if there is more than one scheme. The proposed framework is applied to the typical task of path planning for a robot manipulator and parking task of a mobile robot to show its effectiveness as well as its performance.