Constrained System

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A systematic approach for designing analytical dynamics and servo
control of constrained mechanical systems is proposed. Fundamental
equation of constrained mechanical systems is first obtained
according to Udwadia-Kalaba approach which is applicable to
holonomic and nonholonomic constrained systems no matter whether
they satisfy the D'Alember's principle. The performance
specifications are modeled as servo constraints.
Constraint-following servo control is used to realize the servo
constraints. For this inverse dynamics control problem, the
determination of control inputs is based on the Moore-Penrose
generalized inverse to complete the specified motion. Second-order
constraints are used in the dynamics and servo control. Constraint
violation suppression methods can be adopted to eliminate constraint
drift in the numerical simulation. Furthermore, this proposed
approach is  applicable to not only fully actuated but also
underactuated and redundantly actuated mechanical systems. Two-mass spring system and coordinated robot system are presented as examples for illustration.

Citation: Xiaoli Liu, Shengchao Zhen, Kang Huang, Han Zhao, Ye-Hwa Chen, Ke Shao. A systematic approach for designing analytical
dynamics and servo control of constrained mechanical systems. IEEE/CAA Journal of Automatica Sinica, 2015,  2(4): 382-393

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