Unified Approach to Modeling and Control of Rigid Multibody Systems

Aunified approach is developed to model complex multibody mechanical systems and design controls for them. The characterization of such complex systems often requires the use of more coordinates than the minimum number to describe their configurations and/or the use of modeling constraints to capture their proper physical descriptions. When required to satisfy prescribed control requirements, it becomes necessary that the generalized control forces they are subjected to exactly satisfy these modeling constraints so that their physical descriptions are correctly preserved. The control requirements imposed can always be interpreted as a set of additional control constraints, and they may or may not be consistent with the modeling constraints that describe the physical system. This paper considers both the cases when the control constraints are consistent with the modeling constraints and when they are inconsistent. Such inconsistencies can arise when dealing with underactuated systems. A user-prescribed control cost is minimized at each instant of time in both cases. No linearizations/approximations of the nonlinear mechanical systems are made throughout. Insights into the control methodology are afforded through its geometric interpretation. Numerical examples with full-state control and underactuated control are considered, demonstrating the simplicity of the approach, its ease of implementation, and its effectiveness.