Dimensional Synthesis of Parallel Robots Using Bilevel Optimization for Design Optimization and Resolution of Functional Redundancy

Parallel-kinematic machines or parallel robots have only been established in a few applications where their advantage over serial kinematics due to their high payload capacity, stiffness, or dynamics with their limited workspace-to-installation-space ratio pays out. However, some applications still have not yet been sufficiently or satisfactorily automated in which parallel robots could be advantageous. As their performance is much more dependent on their complex dimensioning, an automated design tool—not existing yet—is required to optimize the parameterization of parallel robots for applications. Combined structural and dimensional synthesis considers all principally possible kinematic structures and performs a separate dimensioning for each to obtain the best task-specific structure. However, this makes the method computationally demanding. The proposed computationally efficient approach for dimensional synthesis extends multi-objective particle swarm optimization with hierarchical constraints. A cascaded (bilevel) optimization includes the design optimization of components and the redundancy resolution for tasks with rotational symmetry, like milling. Two case studies for different end-effector degrees of freedom demonstrate the broad applicability of the combined structural and dimensional synthesis for symmetric parallel robots with rigid links and serial-kinematic leg chains. The framework produces many possible task-optimal structures despite numerous constraints and can be applied to other problems as an open-source Matlab toolbox.