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A force sensorless impedance controller is proposed in this paper for robot manipulators without using force estimators. From the observation of the impedance control law, the force feedback term can be canceled if the inertia matrix in the target impedance is the same as the robot inertia matrix. However, the inertia matrix in the target impedance is almost always a constant matrix, while the robot inertia matrix is a function of the robot configuration, and hence, they may not be identical in general. A modification of the coefficient matrix for the contact force term in the target impedance is suggested in this paper to enable cancelation of the force feedback term in the impedance control law so that a force sensorless impedance controller without using force estimators can be obtained. The tracking performance in the free space phase and the motion trajectory in the compliant motion phase of the new design are almost the same as those in the traditional impedance control. Modification of the inertia matrix in the target impedance will result in small variations of the contact force which is acceptable in practical applications. For robot manipulators containing uncertainties, an adaptive version of the new controller is also developed in this paper to give satisfactory performance without the need for force sensors. Rigorous mathematical justification in closed-loop stability is given in detail, and computer simulations are performed to verify the efficacy of the proposed design.
Slotine and Li's modification is a well-known, simple, and elegant approach for robot adaptive control to avoid the feedback of joint accelerations. This paper presents a simple strategy to implement a regressor-free adaptive impedance controller without using Slotine and Li's modification. In the new strategy, the joint acceleration vector and the dynamics of robot are assumed to be unavailable. Their effects are covered by using the function approximation technique so that there is no need for the joint acceleration feedback. The closed-loop stability and boundedness of internal signals are justified by the Lyapunov-like technique. Experimental results for a two-dimensional (2D) robot are presented to show the effectiveness of the proposed strategy.
Similar to the traditional adaptive strategies for robot manipulators, the regressor-free adaptive controller design also requires applying Slotine and Li's modification to avoid the feedback of joint accelerations. In this paper, a simple method is proposed to construct a regressor-free adaptive controller for robot manipulators without Slotine and Li's modification. In the new design, the joint acceleration vector is lumped into an unknown time-varying function and the function approximation technique is utilized to cover its effect; therefore, its implementation is free from joint acceleration feedback. The closed-loop stability and boundedness of internal signals are justified by the Lyapunov-like technique. Both simulation and experimental results for a two-link robot are presented to show the effectiveness of the proposed design.
To the best of our knowledge, this is the first paper focus on the adaptive impedance control of robot manipulators with consideration of joint flexibility and actuator dynamics. Controller design for this problem is difficult because each joint of the robot has to be described by a fifth-order cascade differential equation. In this paper, a backstepping-like procedure incorporating the model reference adaptive control strategy is employed to construct the impedance controller. The function approximation technique is applied to estimate time-varying uncertainties in the system dynamics. The proposed control law is free from the calculation of the tedious regressor matrix, which is a significant simplification in implementation. Closed-loop stability and boundedness of internal signals are proved by the Lyapunov-like analysis with consideration of the function approximation error. Computer simulation results are presented to demonstrate the usefulness of the proposed scheme.
In this paper, an adaptive control scheme is proposed for an n-link rigid robot manipulator without using the regressor. The robot is firstly modeled as a set of second-order nonlinear differential equations with the assumption that all of the matrices in that model are unavailable. Since these matrices are time-varying and their variation bounds are not given, traditional adaptive or robust designs do not apply. The function approximation technique (FAT) is used here to represent uncertainties in some finite linear combinations of orthonormal basis. The dynamics of the output tracking can thus be proved to be a stable first order filter driven by function approximation errors. Using the Lyapunov stability theory, a set of update laws is derived to give closed loop stability with proper tracking performance. Experiments are also performed on a 2-D robot to test the efficacy of the proposed scheme.
This paper presents an adaptive impedance control scheme for an $n$-link constrained rigid robot manipulator without using the regressor. In addition, inversion of the estimated inertia matrix is also avoided and the new design is free from end-point acceleration measurements. The dynamics of the robot manipulator is assumed that all of the matrices in robot model are unavailable. Since these matrices are time-varying and their variation bounds are not given, traditional adaptive or robust designs do not apply. The function approximation technique is used here to represent uncertainties in some finite linear combinations of the orthogonal basis. The dynamics of the output tracking can thus be proved to be a stable first order filter driven by function approximation errors. Using the Lyapunov stability theory, a set of update laws is derived to give closed loop stability with proper tracking performance. A 2 DOF planar robot with environment constraint is used in the computer simulations to test the efficacy of the proposed scheme.
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