*Article* **Over-Actuated Underwater Robots: Configuration Matrix Design and Perspectives †**

**Tho Dang 1,\*, Lionel Lapierre 1,\*, Rene Zapata 1, Benoit Ropars <sup>2</sup> and Pascal Lepinay <sup>1</sup>**

	- <sup>2</sup> Reeds Company, 199 rue Hélène Boucher, 34170 Castelnau-Le-Lez, France; ropars@lirmm.fr

**Abstract:** In general, for the configuration designs of underwater robots, the positions and directions of actuators (i.e., thrusters) are given and installed in conventional ways (known points, vertically, horizontally). This yields limitations for the capability of robots and does not optimize the robot's resources such as energy, reactivity, and versatility, especially when the robots operate in confined environments. In order to optimize the configuration designs in the underwater robot field focusing on over-actuated systems, in the paper, performance indices (manipulability, energetic, reactive, and robustness indices) are introduced. The multi-objective optimization problem was formulated and analyzed. To deal with different objectives with different units, the goal-attainment method, which can avoid the difficulty of choosing a weighting vector to obtain a good balance among these objectives, was selected to solve the problem. A solution design procedure is proposed and discussed. The efficiency of the proposed method was proven by simulations and experimental results.

**Keywords:** over-actuated underwater robots; multi-objective optimization; underwater robots; performance indices
