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).

An optimal control design for the uncertain Delta robot is proposed in the paper. The uncertain factors of the Delta robot include the unknown dynamic parameters, the residual vibration disturbances and the nonlinear joints friction, which are (possibly fast) time-varying and bounded. A fuzzy set theoretic approach is creatively used to describe the system uncertainty. With the fuzzily depicted uncertainty, an adaptive robust control, based on the fuzzy dynamic model, is established. It designs an adaptation mechanism, consisting of the leakage term and the dead-zone, to estimate the uncertainty information. An optimal design is constructed for the Delta robot and solved by minimizing a fuzzy set-based performance index. Unlike the traditional fuzzy control methods (if-then rules-based), the proposed control scheme is deterministic and fuzzily optimized. It is proven that the global solution in the closed form for this optimal design always exists and is unique. This research provides the Delta parallel robot a novel optimal control to guarantee the system performance regardless of the uncertainty. The effectiveness of the proposed control is illustrated by a series of simulation experiments. The results reveal that the further applications in other robots are feasible.