Analysis and Control of Underactuated Systems based on RelativeDegree Structure

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In this project, we have investigated characteristic motions of underactuated mechanical systems on the basis of the theory introduced in our previous work, and discussed a controller design to realize the characteristic motions. We have categorized the control problems of underactuated systems into three problems: (1) generating quick motion caused by divergent, (2) generating limit cycles, and (3) effective control of an underactuated system that has singularity of controllability at the origin. We have showed that the motions of (1) and (2) have been achieved by the controller designed based on the analysis using our previous work. In terms of (3), we have presented the conditions for designing a well-defined controller even at the singular point.