Abstract
Inverse dynamics control is considered for flexible-joint parallel manipulators in order to obtain a good trajectory tracking performance in the case of modeling error and disturbances. It is known that, in the absence of modeling error and disturbance, inverse dynamics control leads to linear fourth-order error dynamics, which is asymptotically stable if the feedback gains are chosen to make the real part of the eigenvalues of the system negative. However, when there are modeling errors and disturbances, a linear time-varying error dynamics is obtained whose stability is not assured only by keeping the real parts of the frozen-time eigenvalues of the system negative. In this paper, the stability of such systems is investigated and it is proved that the linear time-varying system can be rendered stable by selecting the feedback gains such that the variation of the system becomes sufficiently slow. To illustrate the performance of the control method, deployment motion of a 3-RPR planar parallel manipulator subject to impact is simulated. For the impact model, the impulse-momentum and the coefficient of restitution equations for the system are derived.
Highlights
Owing to their closed-loop structure, parallel manipulators have been widely popular for many years, especially for applications that demand precise positioning and high load-carrying capacity
The main objective of this study is to address the stability of inverse dynamics control of flexible-joint parallel manipulators in the presence of modeling error and disturbances for which a fourth-order, linear timevarying, nonhomogeneous error dynamics is obtained
In this paper, trajectory tracking control of parallel manipulators involving flexible-joint drives is analyzed in the presence of modeling error and disturbances
Summary
Owing to their closed-loop structure, parallel manipulators have been widely popular for many years, especially for applications that demand precise positioning and high load-carrying capacity. In order to carry high loads with high motion accuracy, flexibilities in the manipulator structure should be considered in the control system design. For the motion control of parallel manipulators involving joint flexibility in their drives, the following studies can be mentioned. The main objective of this study is to address the stability of inverse dynamics control of flexible-joint parallel manipulators in the presence of modeling error and disturbances for which a fourth-order, linear timevarying, nonhomogeneous error dynamics is obtained. There are many studies in the literature on modeling and simulation of serial robotic manipulator collisions, with or without link or joint flexibility [7,8,9,10], impact dynamics of parallel manipulators has not been addressed before. The velocity jump, the impulse of the impact force, and the impulses of the loop closure constraint forces are obtained and the states of the system are updated to generate the effects of the impact on the manipulator motion
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