The concurrent design optimization of robots refers to the problem of optimizing parameters that affects different kinds of features at the same time. For instance, this work presents a study case for the concurrent design optimization of the structure and control of a parallelogram mechanism. The main contribution of this work is the definition of an integrated optimization model that considers two conflicting objectives, defined as the energy and error during a trajectory tracking. In addition, the optimization model considers an error constraint, with the purpose of automatically discarding designs that can not closely follow the trajectory, and the simulation considers a saturation constraint that avoids to deliver torques above a threshold. The multi-objective optimization problem is solved using the Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D), the resulting solutions, named Pareto set, are delivered to a final decision maker, to select the adequate design among those with the best compromise between minimum tracking error and energy consumption. A design is a set of lengths and control gains, hence, notice that the control gains are optimized for the corresponding geometry.
