Abstract
In this paper, we incorporate velocity observer design into the virtual decomposition control (VDC) strategy of an n-DoF open chain robotic manipulator. Descending from the VDC strategy, the proposed design is based on decomposing the n-DoF manipulator into subsystems, i.e., rigid links and joints, for which the decentralized controller-observer implementation can be done locally. Similar to VDC, the combined controller-observer design is passivity-based, and we show that it achieves semiglobal exponential convergence of the tracking error. The convergence analysis is carried out using Lyapunov functions based on the observer and controller error dynamics. The proposed design is demonstrated in a simulation study of a 2-DoF open chain robotic manipulator in the vertical plane.
Highlights
The virtual decomposition control (VDC) approach [1], [2] is a nonlinear model-based control method that is developed for controlling complex systems, and it has been demonstrated to be very effective especially in robotic control [3]–[7]
In comparison to the existing literature [8]–[17] where the designs are based on the dynamics of the whole manipulator, in the proposed decentralized design the control and observer gains are proportional to the individual link/joint dynamics
Virtual decomposition control (VDC) is a control design method where the original system is decomposed into subsystems by placing conceptual virtual cutting points (VCP) [1, Def. 2.13]
Summary
The virtual decomposition control (VDC) approach [1], [2] is a nonlinear model-based control method that is developed for controlling complex systems, and it has been demonstrated to be very effective especially in robotic control [3]–[7]. Velocity data can naturally be obtained by numerical differentiation of the position sensor data but there is no theoretical justification for this method [8], [9] Due to these challenges, control of n-DoF robotic manipulators without velocity data has been extensively studied, e.g., in [8], [10]–[15], see the survey [9], where the actuator dynamics have been neglected. In comparison to the existing literature [8]–[17] where the designs are based on the dynamics of the whole manipulator, in the proposed decentralized design the control and observer gains are proportional to the individual link/joint dynamics. (5c) for some Mc,A > 0 and for all α1, α2 > 0 and Aω1, Aω2 ∈ R3
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