Developmental acquisition of entrainment skills in robot swinging using van der Pol oscillators Paschalis Veskos Department of Electrical and Electronic Engineering Imperial College London SW7 2BT paschalis.veskos@imperial.ac.uk Yiannis Demiris Department of Electrical and Electronic Engineering Imperial College London SW7 2BT y.demiris@imperial.ac.uk Abstract In this study we investigated the effects of different morphological configurations on a robot swinging task using van der Pol oscillators. The task was examined using two separate degrees of freedom (DoF), both in the presence and absence of neural entrainment. Neural entrainment stabilises the system, reduces time-to-steady state and relaxes the requirement for a strong coupling with the environment in order to achieve mechanical entrainment. It was found that staged release of the distal DoF does not have any benefits over using both DoF from the onset of the experimentation. On the contrary, it is less efficient, both with respect to the time needed to reach a stable oscillatory regime and the maximum amplitude it can achieve. The same neural architecture is successful in achieving neuromechanical entrainment for a robotic walking task. 1. Introduction Non-linear differential equations have been used in robotics as central pattern generators (CPGs) for a multitude of tasks such as robot swinging (Lungarella and Berthouze 2002), arm motion (Williamson 1998) and locomotion (Taga 1991; Zielinska 1996; Lewis, Etienne- Cummings et al. 2003), both in simulation and robotic experiments. CPGs have become increasingly popular as they provide biologically-inspired, robust and adaptive motion. With the use of CPGs in robot swinging, an interesting range of rhythmical behaviours can be explored. Thus, what might seem as an uncomplicated task offers the right amount of complexity to investigate and make comparisons with theoretical findings and different oscillators, while at the same time maintaining a controlled experimental environment. An increasingly strong case has been made for embodiment and hence the use of real robots instead of simulations, initially with (Brooks 1991) and now many others such as (Thelen and Smith 1994; Beer, Chiel et al. 1998). The main argument is that the body, “which mediates perception and affects behaviour, plays an integral role in the emergence of human cognition, […] the central tenet of embodied cognition is that cognitive and behavioural processes emerge from the reciprocal and dynamic coupling between the brain, body and environment” (Lungarella, Metta et al. 2003). We endorse this school of thought and have thus made use of an embodied robotic platform to investigate our problem. In a previous study (Lungarella and Berthouze 2002), the same task was investigated using a different non-linear oscillator (Matsuoka 1985). In this paper, we explore the behaviour of the system and its ability to achieve entrainment with the natural dynamics under different morphological configurations, with and without neural entrainment. The van der Pol oscillator (Strogatz 2001) was chosen for the smaller number of parameters requiring tuning, robustness (Matsuoka is a near-harmonic oscillator that does not feature an asymptotically stable limit cycle) and straightforward computational implementation. 2. The Degrees of Freedom Problem The degrees of freedom problem was first attacked theoretically by Nikolai Bernstein in a series of papers, published collectively in The coordination and regulation of movements (Bernstein 1967). The main theme of his framework was the staged acquisition of control, in the proximal-to-distal direction. This is a three-staged process: 1. Distal (peripheral) degrees of freedom (DoF) are decreased (frozen) to a minimum. 2. Once control of the more proximal ones has been mastered, the frozen degrees of freedom are released and the process continues. 3. Once the organism can control its morphology in its entirety, it can begin to exploit any reactive phenomena that occur to its advantage. This process is intuitive, e.g. the reduction of variables to be controlled is reasonably expected to accelerate acquisition of control and also draws a parallel to Piaget’s notion of stages of cognitive development. As such, it has been widely accepted for a long time. There is some experimental verification of the process, with the most widely cited example being that of the disappearing infant stepping/kicking reflex. Exhibited by infants as young as 12 weeks in utero, this reflex disappears by the age of four or five months. It only reappears much later when the child learns how to walk at around 12 months. This is viewed as freezing of a distal DoF because the infant 87 Berthouze, L., Kaplan, F., Kozima, H., Yano, H., Konczak, J., Metta, G., Nadel, J., Sandini, G., Stojanov, G. and Balkenius, C. (Eds.) Proceedings of the Fifth International Workshop on Epigenetic Robotics: Modeling Cognitive Development in Robotic Systems Lund University Cognitive Studies, 123. ISBN 91-974741-4-2