A general approach for optimal kinematic design of parallel manipulators

This paper deals with the problem of optimal geometry design of parallel manipulators. In order to reduce the main drawbacks of parallel manipulators, relatively small workspace and more singularities, two requirements, workspace and condition number, are considered. The design problem is thus formulated to find a parallel mechanism such that its Cartesian workspace contains a prescribed workspaces with good condition numbers in it. By observing that those requirements can be locally cast into Linear Matrix Inequalities (LMIs), we formulate the design problem locally as a convex optimization problem subject to LMIs with a max-det function as its objective function. Hence, at each node of discretized space of design parameters, there is an LMI-based convex optimization problem. A two-level algorithm can be applied to solve for a set of optimal design parameters: (1) Discretize the space of design parameters into a set of discrete nodes; (2) At each node the Newton algorithm is applied to solve the max-det optimization problem. By comparing all the locally optimal costs, we can obtain a corresponding set of globally optimal design parameters correspondingly. Simulation results verify the effectiveness of the proposed approach.