The motion control problem for a class of mechanical systems is addressed. The system configuration can be represented in terms of a set of generalized coordinates in R^n and l rotation matrices in the special orthogonal (SO)(3) group. A key point is the choice of a globally valid parameterization of SO(3) in lieu of the usual three parameter representations. To this end, the unit quaternionis adopted.A novel control lawis proposed that is based on a velocity observer to avoid velocity measurements. Exponential tracking of the commanded motion trajectory is proven via the Lyapunovdirectmethod. The proposed controller–observer scheme is first applied in a simulation case study to the attitude control of a rigid spacecraft. Then, the problemof position and orientation control of the end effector of a robot manipulator is considered. For the latter case, experimental results are provided to show the potential of the approach in tackling practical problems.
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