Inverse dynamics control of a crane-like underactuated multibody system with penalty formulation

Zana, Roland Reginald and Zelei, Ambrus (2023) Inverse dynamics control of a crane-like underactuated multibody system with penalty formulation. In: The 6th International Conference on Dynamics, Vibration and Control, 21-24, October, 2022, Shanghai.

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Abstract

Inverse dynamics method is an effective approach if the mathematical model of the controlled system is available. Underactuated mechanical systems are special in the sense that the number of independent inputs is less than the degrees of freedom. The Augmented Lagrangian formalism is a well-known and useful approach in forward dynamics simulation and in the control of multibody systems if the mathematical description of the system does not include redundant geometric constraints. In case of redundant constraints, the Penalty formulation serves as a plausible solution. We are not aware of any application of the Penalty formulation for control purposes of underactuated crane-like multibody systems. The Penalty formulation not only allows the inclusion of redundant constraints in the controlled physical system description, but allows redundancy in the task formulation too, i.e. in the servo constraints. Furthermore, the Penalty formulation reduces the computational demand compared to the Augmented Lagrangian formalism in most of the cases. The feasibility and the performance of the Penalty formulation is demonstrated on a crane-like underactuated robot.

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