Abstract
A series of fractional robust trajectory tracking controls are proposed for the Delta parallel robot with uncertainty. For the high speed and heavy load, the Delta parallel robot could not ignore the influences of the high nonlinearity (by the dynamics of the multiple closed-loops mechanism and the nonlinear joints friction) and the various kinds of uncertainties (i.e., the unknown dynamic parameters and external disturbances caused by the residual vibration). By formulating the motion equation of the Delta parallel robot, the nonlinearity is settled by a norm model based control design. The uncertainty considered in the paper is time-varying but unknown. An online estimation with an exponential type leakage term and dead-zone is construct to investigate the realtime information of the uncertainty. In virtue of the estimated information, two fractional robust trajectory tracking controls with the joints friction compensation are designed. Under the proposed controls, the system performance of the Delta parallel robot can be deterministically guaranteed (which includes uniform boundedness and uniform ultimate boundedness).
Highlights
Parallel robot is a kind of multiple closed-loop mechanism and widely used in the industrial areas by virtue of the high rigidity, high accuracy and outstanding weight/load ratio [1], [2]
In the early works [11]–[13], the kinematic control method is proposed for the Delta parallel robot, which has been widely used in the present industry
With the increase of speed and load, there arise some challenges: the dynamics of the Delta parallel robot, consisting the high nonlinearity and coupling, could inevitably influence the system performance; the presence of uncertainties such as, the residual vibration caused by the effect of the lightweight parallelogram, the uncertain system parameters with the random external load and the imperfectly known inputs, can not be ignored in the control design
Summary
Parallel robot is a kind of multiple closed-loop mechanism and widely used in the industrial areas by virtue of the high rigidity, high accuracy and outstanding weight/load ratio [1], [2]. Two novel robust controls with online estimation for the Delta parallel robot are proposed Both controls contain a model based friction compensation and a precise trajectory tracking scheme. C. THE MOTION EQUATION OF THE UNCERTAIN DELTA PARALLEL ROBOT WITH JOINTS FRICTION For a Delta parallel robot, the driven motors are assembled in the active joints, which give occasion to the coupling effects of the active joints friction and the control input torques [23]. THE MOTION EQUATION OF THE UNCERTAIN DELTA PARALLEL ROBOT WITH JOINTS FRICTION For a Delta parallel robot, the driven motors are assembled in the active joints, which give occasion to the coupling effects of the active joints friction and the control input torques [23] Those coupling effects may influence the control accuracy and are considered as a difficulty in the friction compensation. We model the normal force in the paper as an uncertainty with a certain bound
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