Abstract. Using discrete-time dynamics of a two neuron network with recurrent connectivity it is shown that for specific parameter configurations the output signals of neurons can be of almost sinusoidal shape. These networks live near the Sacker-Neimark bifurcation set, and are termed SO(2)-networks, because their weight matrices correspond to rotations in the plane. The discretized sinus-shaped waveform is due to the existence of quasi-periodic attractors. It is shown that the frequency of the oscillators can be controlled by only one parameter. Signals from the neurons have a phase shift of π/2 and may be useful for various kinds of applications; for instance controlling the gait of legged robots.

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SUMMARYMyon is a humanoid robot where each joint is controlled independently by a supervised bio-inspired artificial neural network inducing the correction of a number of distinct actions depending on the excitation. One of the control strategies, which the network, located within a certain joint, may implement, allows a controlled motion of the limb connected to the joint from a stable state up to a prescribed height and the maintenance of the new position afterwards. The original approach adopted for this control operation is stable and robust but results in slow and energy-inefficient limb movements. This work proposes a novel, low-power, timeefficient and adaptive memristor-centred control strategy for the aforementioned robot action. The idea is based upon the exploitation of the combined ability of memristors to store and process data in the same physical location. The part I paper sets the theoretic foundations for the memcomputing paradigm to robot motion control, while the part II manuscript shall demonstrate its benefits over the original approach in terms of energy, and speed, and the inheritance from the standard strategy of a good level of adaptability to changes in the limb load on the basis of the analysis of circuit-theoretic models adopting an ideal and a real memristor, respectively.

Controlling a biped robot with a high degree of freedom to achieve stable movement patterns is still an open and complex problem, in particular within the RoboCup community. Thus, the development of control mechanisms for biped locomotion have become an important field of research. In this paper we introduce a model-free approach of biped motion generation, which specifies target angles for all driven joints and is based on a neural oscillator. It is potentially capable to control any servo motor driven biped robot, in particular those with a high degree of freedom, and requires only the identification of the robot's physical constants in order to provide an adequate simulation. The approach was implemented and successfully tested within a physical simulation of our target system -the 19-DoF Bioloid robot. The crucial task of identifying and optimizing appropriate parameter sets for this method was tackled using evolutionary algorithms. We could show, that the presented approach is applicable in generating walking patterns for the simulated biped robot. The work demonstrates, how the important parameters may be identified and optimized when applying evolutionary algorithms. Several so evolved controllers were capable of generating a robust biped walking behavior with relatively high walking speeds, even without using sensory information. In addition we present first results of laboratory experiments, where some of the evolved motions were tried to transfer to real hardware.

Summary Neuromorphic circuits shall be considered in electronics to perform complex computing tasks in a time‐efficient and energy‐efficient fashion and to adapt their problem‐solving methodologies to changes in initial conditions and parameters. One of the key biological paradigms at the basis of their operation, allowing them to exhibit higher performance levels as compared with state‐of‐the‐art electronic systems, is the mem‐computing functionality, i.e. the capability to process and store data in the same physical location, which represents the core principle to overcome the time inefficiency of von Neumann machine architectures. With the advent of memristors, the interest in the exploitation of this principle to develop dynamic circuits for the implementation of innovative signal processing strategies has grown considerably. Here, we leverage the mem‐computing capability inherent in these devices to propose an innovative control system for motion control in a humanoid robot. In the part I paper, we introduced the paradigm theoretic foundations. In this part II manuscript, we propose circuit‐theoretic models for the new control system based upon an ideal and upon a physical memristor model and demonstrate through numerical simulations how it outperforms the old approach in terms of time‐efficiency and energy‐efficiency, maintaining a good degree of adaptability to changes in environmental conditions.