Abstract
ABSTRACTIn this paper, an adaptive impedance control combined with disturbance observer (DOB) is developed for a general class of uncertain robot manipulators in discrete time. The impedance control is applied to realize the interaction force control of robot manipulators in unknown, time-varying environments. The optimal reference trajectory is produced by impedance control, and the impedance parameters are achieved using Q-learning technique, which is implemented based on trajectory tracking errors. The position control with DOB of robot manipulators is implemented to track the virtual desired trajectory, and the DOB is designed to compensate for unknown compounded disturbance function by bounding both tracking error inputs and compounded disturbance inputs in a permitted control region, of which the compounded disturbance function is taken into account of all uncertain terms and external disturbances. The appropriate DOB parameters are selected applying linear matrix inequalities (LMIs) method. Both the impedance control and the bounded DOB control can well guarantee semiglobal uniform boundness of the closed-loop robot systems based on Lyapunov analysis and Schur complement theory. Simulation results are performed to test and verify effectiveness of the investigated combining adaptive impedance control with DOB.
Highlights
Applications of robot manipulators have been extended to many fields, such as domestic service, medical care, industrial production and so on, and robot manipulators are anticipated to work by interacting with fragile object, other machines and even humans (Peshkin et al, 2001; Lambercy et al, 2007)
In Jung and Hsia (2010), Hosseinzadeh, Aghabalaie, Talebi, and Shafie (2010) and Li, Sam Ge, and Yang (2012), desirable impedance parameters are chosen as constant values, while in many tasks, interaction environment is timevarying, uncertain and unstructured, the conventional impedance control methods are incapable of incorporating environment properties
Impedance iterative learning method, adaptive impedance control and disturbance observer (DOB) method have been developed and applied, but very few control methods have been proposed both for environments with unknown time-varying parameters and robot manipulator with nonliear uncertainties
Summary
Applications of robot manipulators have been extended to many fields, such as domestic service, medical care, industrial production and so on, and robot manipulators are anticipated to work by interacting with fragile object, other machines and even humans (Peshkin et al, 2001; Lambercy et al, 2007). Impedance iterative learning method, adaptive impedance control and DOB method have been developed and applied, but very few control methods have been proposed both for environments with unknown time-varying parameters and robot manipulator with nonliear uncertainties. This is the motivation to develop novel trajectory tracking control using optimal impedance control with DOB in the rest of this paper. The optimal virtual desired reference trajectory is derived subject to unknown environment dynamics in Cartesian space by applying the impedance control with Q-learning, and the online adaptation of impedance parameters are achieved. 0n 0a×b Im x fe xd xr q qr τ τe Description the Euclidean norm of vectors and induced norm of matrices the transpose of a vector or a matrix the inverse of a n-order reversible matrix n-dimensional zero vector a×b-dimension zero matrix m-dimensional identity matrix n-dimensional position vector n-dimensional impedance force vector n-dimensional desired trajectory in Cartesian space n-dimensional virtual desired reference trajectory n-dimensional joint position n-dimensional virtual desired reference joint position n-dimensional vector of control input torque n-dimensional external force torque
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