Optimization of Robust Control for the Uncertain Delta-Type Parallel Manipulator with Active Constraints: A Fuzzy-Set Theory-Based Approach

We investigate an optimization problem of robust control for the Delta-type parallel manipulator. The task is to render the uncertain Delta-type parallel manipulator to follow the pre-specified active constraints. Uncertainties in this paper are deemed to be (possibly fast) time-varying and bounded, and the information of boundaries is creatively depicted via a fuzzy set. By this fuzzy depiction, a robust control scheme, which is deterministic and not the traditional if-then rules-based, is designed. On top of that, we construct an optimization problem that targets the choice of the performance-dependent control parameter. Then, the existence and uniqueness of the global solution to this problem, which could be solved by minimizing a fuzzy performance index, is proven. In addition to meeting active constraints, the Delta-type parallel manipulator under the proposed control scheme assures two attractive performances: the deterministic performance and the fuzzy performance. The results of simulations illustrate the validity and practicability of the control scheme.