## 1 Introduction  
Mechatronics and Robotics are well-established engineering disciplines that were conceived as the integration of electronics and computing science with mechanical design. Currently, these disciplines are required to develop systems capable of dealing with complex tasks while improving system performance. Moreover, given current technological advances and the growth of system-level concepts, engineering design can consider new procedures to fulfill integration among all its components [1]. The integration of combined mechanical design and control optimization received attention from engineers and researchers to investigate and develop novel strategies. A concurrent design approach that worked on the improvement of the mechanical design toward reducing the complexity of a controller was proposed in [2], where the objective function was chosen to reduce the shaking force/moment. An extended version of this procedure is presented in [3], where the Design for Control (DFC) approach is introduced. DFC describes the importance of the simultaneous design of a controller and the mechanical subsystems. Robust design with robust control in [4] investigates the coupling between the mechanical system and control strategies for an electric DC motor using an optimization approach. A nested optimization scheme is described in [5] to solve the integrated design problem of mechanical and control of the motor driving system. Two of the critical issues that guide the research in considering multiple aspects are reduction of energy consumption [6] and precision when developing a task [7]. In this context, a significant number of different approaches have addressed mainly these two problems by optimizing hardware, software, or a combination of these two. Hardware solutions involve a mechanical design to develop lightweight systems [8] and balanced multi-body systems with the aim of facilitating a control design algorithm. Software solutions deal with operation scheduling [9], operation control based on energy consumption [10] and accuracy [11]. Hardware and Software integration can be described as an initial step toward a use of dynamic models and suitable controls to include dynamics of a system as for example in [12]. Moreover, an example of optimal concurrent formulation of mechanical characteristics and control strategies is presented in [13] by formulating a design problem as an optimization problem and solving it with both gradient-based and heuristic approaches. However, the concurrent consideration of multi-criteria aspects in the design of a synergistic combination of hardware and software can still be improved. The research and inclusion of multiple criteria are also topics of interest in mechatronic design. For example, the Mechatronic Design Quotient (MDQ) is a multi-criteria index that presents a systematic methodology for mechatronic design [14]. This methodology considers seven main criteria: meeting the task requirements, component matching, efficiency, intelligence, reliability, controller friendliness, and cost. However, it performs the optimization process in two distinct stages to overcome numerical issues and require expert intervention when switching from these two stages. Concurrent optimization of the mechanical characteristics, control strategies, and selection of actuators is carried in [15] for industrial robots considering multiple criteria. Criteria considering workspace volume, manipulator dexterity, static efficiency, and stiffness are chosen to design the geometrical parameters of the mechanism for a robotic leg in [16]. As described above with different applications [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16], there are several examples in the literature on integrating only traditional aspects in mechatronic design. However, they address the design problem across multiple stages that require user interaction to switch from one stage to another. Moreover, examples in the literature do not describe a procedure of formulating the problem from user requirements.