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This paper presents a general methodology for the analysis and synthesis of a positive semi-definite system described by mass, damping and stiffness matrices that is often encountered in impedance control in robotics research. This general methodology utilizes the fundamental kinematic concept of rigid-body and non-rigid-body motions of which all m...
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This study presents an adaptive variable impedance control methodology for force tracking on multi-axis robotic activity in uncertain environmental stiffness along with redundancy exploitation. The classical impedance control schemes are not effective for force tracking in uncertain environments; therefore, a revised impedance control scheme is pro...
Citations
... As shown in mechanical vibration of unconstrained discrete systems, the motion of a redundant robot under impedance control consists of oscillatory and nonoscillatory motion [7,14,15]. 3 Based on the theoretical and experimental study conducted in this article, the nonoscillatory motion (or the rigid-body mode) is the root cause of the discrepancy between the initial and the final configurations. ...
... The ZP motions [15,17] of a redundant manipulator generate a steady-state deviation from the initial intended joint configuration, which makes the robot settle down at a new equilibrium joint configuration after a perturbation (also see Fig. 2). ...
... The joint steady-state values of a redundant robot performing impedance control can be analytically obtained, for which we must solve the dynamics that involves the computation of the inertia mass (M), damping (C), and stiffness (K) matrices, as well as the configuration-dependent Jacobian and the initial displacement. The closed-form solution requires a methodology to solve for the free and forced vibration responses of the system under impedance control [15]. ...
This paper presents an experimental study with theory to identify quantitatively the zero-potential-energy (ZP) motion in Cartesian impedance control of redundant manipulators, based on a new analytical methodology. This ZP mode of motion, analogous to the rigid-body mode in classic mechanical systems, is a result of the redundancy of the robot. When subject to an external perturbation under impedance control, a redundant robot will assume a new equilibrium configuration determined by the ZP motion, governed by the least-energy principle. Consequently, this creates a steady-state deviation from its initial configuration after a perturbation and reaches a new equilibrium. We determine such ZP motion(s) by utilizing a closed-form solution based on vibration theory. Experiments were conducted on a 7-DoF redundant Panda robot to determine the new equilibrium after a perturbation. The experimental results are compared with the theoretical prediction of the ZP motions to validate the theoretical results of the zero-potential-energy motions due to stiffness in impedance control. Furthermore, we demonstrated that the ZP motion due to redundancy can be eliminated by removing the redundancy through experimental validation by employing the null-space control, as expected.
... The analytical solution provides the response of q(t) or x(t) [23]; therefore, one can systematically choose the elements of the matrices C and K in order to modulate dynamic response. This is possible because the response is obtained in the modal space in which the multiple DoFs system in (2) or (3) are made decoupled and independent, such that each single DoF in the modal space can be analyzed separately to study the damping ratios and natural frequencies of the dynamic response. ...
... We consider redundant robots, which are equivalent to unconstrained systems, as described in the theory of vibration analysis [23], [24]. An unconstrained system has freedom to move without being constrained in an inertial frame. ...
... where E p is the net potential energy of the system due to the stiffness matrix K. Based on the kinematic and dynamic theory [25], the motion of systems can be separated into the RB and nonrigid-body (NRB) motions, which are referred to as the ZP and non-ZP-energy (NZP) motions under the context of impedance control in this article. 3 The characteristic of an unconstrained, positive semidefinite system, corresponding to the general case of a redundant manipulator, is a singular stiffness matrix K. Following (6), the ZP mode u 0 belongs to the null space of K [23], [26], denoted by N (K), i.e., ...
This article presents an analytical method to modulate the dynamic response of a robotic manipulator interacting with its environment when performing impedance-related robotic tasks, through the choice of stiffness and damping parameters. By joint space analysis of vibration and experiments, we prove that in order to preserve a desired dynamic behavior of the robot in the Cartesian space, neither a stiffness nor damping matrix can be arbitrarily chosen; this choice has to meet the desired dynamic criteria for any given configuration. After mapping the parameters (matrices) into the joint space, we analyze the vibratory dynamics of the robot and identify the proper way of suppressing of the vibration modes by specific elements in the Cartesian damping matrix without need of trial and error. Our method is especially useful for redundant robots. We show and compare experimental results from two different 7 degrees of freedom robotic manipulators.
