This study presents an approach, the unit circle (UC), to bridge numerical data from each variable of robotic systems and its corresponding qualitative state so that current qualitative methods (e.g. fuzzy models) can apply to general robotic systems. A manipulator is described as a collection of constraints holding among time-varying, interval-valued parameters. The UC representation is presented, and the continuous motion of the end-effector is evaluated by the change of directions of qualitative angle and qualitative length. Analytical formulas of qualitative velocity and qualitative acceleration are derived. The characteristic mapping is introduced for fault detection and diagnosis in terms of the UC. In the end simulation results demonstrate the feasibility of the UC approach for fault diagnosis. The UC representation of robots concerns a global assessment of the systems behaviour, and it might be used for the purpose of monitoring, diagnosis, and explanation of physical systems. This is the first step to fault diagnosis and remediation for robots (e.g. Beagle 2) using qualitative methods.

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