An LMI-based optimal design of parallel manipulators

This paper deals with the problem of optimal design of parallel manipulators which have large workspaces, and are singularityless, of high stiffness and manipulability and the most economic. By observing that those requirements can be cast into Linear Matrix Inequalities (LMIs), we formulate the design problem as a convex optimization problem subject to LMIs with either a linear function or a max-det function as its objective function. The variables x associated with LMIs are nonlinear functions of some key kinematic parameters a. Since generally the dimension of x is greater than the number of key kinematic parameters (i.e., x are not linearly independent), we consider the constrained semi-definite programming problems and the constrained max-det problems by taking account of an additional set of nonlinear constraints. Simulation results verify the effectiveness of the proposed algorithms.