## 1 Introduction  
Swarm robotics (SR) [1] is the research field that, combining aspects of artificial intelligence and robotics, studies the use of many simple distributed robots that collectively cooperate in order to solve complex tasks. The tasks addressed by swarm robotics can be either intrinsically collective problems, that can uniquely be solved through interaction, or single agent problems whose results can be boosted in multi-agent setups. SR is widely inspired by how biological swarms work in nature [2], exposing the emergence of complex collective behaviors from local interactions. Some examples remarkably recurrent in swarm robotics are ant colonies, bee colonies, flocks of birds, fish schools or slime molds, among others. In [3], the authors defined a set of conditions that a robotics system must fulfill in order to be considered a swarm robotics system: Autonomy, large swarm sizes, homogeneity, inefficiency and simplicity of single agents, local communication and sensing of the environment. Moreover, apart from efficiency in solving the task, scalability, robustness and flexibility are highly desirable properties in SR systems (see [3]). In contrast to behavior-based design methods, automatic design methods find suitable robot's controllers through an optimization process. The most important and widely used example of automatic design method is Evolutionary Robotics (ER) [4], and in particular, Evolutionary Algorithms (EA) to evolve the parameters of Artificial Neural Networks (ANN). The optimization of ANN parameters by means of evolutionary computation is called neuroevolution, see e.g., [5]. Nonetheless, the use of Recurrent Neural Networks (RNN) is of special interest in swarm robotics. The main reason is that they allow action generation not only based on current stimuli being measured but also based on past experience and events. Specifically, Continuous-Time Recurrent Neural Networks (CTRNN), see [6], have been employed as neuro-controllers in multiple works [7; 8; 9; 10]. In [7], a CTRNN is evolved using a generational EA for the flocking of a swarm. They designed a fitness function that reflects cohesion, separation and alignment of the swarm, as in Reynolds' rules. [PERSON] et al. [8] also optimize CTRNN controllers using an EA. In this case, they address a foraging problem, with a single nest and a single food area, in which robots have to decide whether they assume the role of foraging or nest patrolling. Moreover the task that they define imposes role switching within simulation to be completed correctly. [PERSON] et al., proposed in [9] the evolution of CTRNNs using a generational genetic algorithm for the task of heading alignment of robots. The study is firstly analyzed in simulated environments and validated with real robots. In [10] the authors use a simple EA with roulette wheel selection and a CTRNN controller in order to solve the problem of cooperative transportation of heavy objects. The works listed above, in the context of evolutionary computation tools applied to the optimization of ANNs, are either Genetic Algorithms (GA) or Evolutionary Algorithms (EA) [11]. Other algorithms from evolutionary computation have also been employed in swarm robotics and collective robotics, such as differential evolution [12] or neuroevolution of augmenting topologies (NEAT) [13; 14]. Besides, a family of algorithms that has gained research interest in the context of single agent controllers are Natural Evolution Strategies (NES) (see [15]). NES algorithms have recently proved to be competitive alternatives to deep reinforcement learning, tested in known benchmark problems such as Atari games or humanoid locomotion (see [16; 17]). In NES, the population individuals are randomly sampled from a search distribution whose parameters are optimized in order to maximize the expected fitness (see Section 3.3), following the natural gradient direction. However, up to our knowledge, NES algorithms have not been applied to the field of swarm robotics yet.