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Generating Spatiotemporal Joint Torque Patterns from Dynamical Synchronization of Distributed Pattern Generators Alexandre Pitti, Max Lungarella, Yasuo Kuniyoshi

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Generating Spatiotemporal Joint Torque Patterns from Dynamical Synchronization of Distributed Pattern Generators Alexandre Pitti, Max Lungarella, Yasuo Kuniyoshi Generating spatiotemporal joint torque patterns from dynamical synchronization of distributed pattern generators Alexandre Pitti, Max Lungarella, Yasuo Kuniyoshi To cite this version: Alexandre Pitti, Max Lungarella, Yasuo Kuniyoshi. Generating spatiotemporal joint torque patterns from dynamical synchronization of distributed pattern generators. Frontiers in Neurorobotics, Fron- tiers, 2009, 3 (2), pp.1-14. 10.3389/neuro.12.002.2009. hal-00656930 HAL Id: hal-00656930 https://hal.archives-ouvertes.fr/hal-00656930 Submitted on 6 Jan 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. ORIGINAL RESEARCH ARTICLE published: 29 October 2009 NEUROROBOTICS doi: 10.3389/neuro.12.002.2009 Generating spatiotemporal joint torque patterns from dynamical synchronization of distributed pattern generators Alexandre Pitti1*, Max Lungarella2 and Yasuo Kuniyoshi1 1 ERATO Synergistic Project, JST, Laboratory for Intelligent Systems and Informatics, Department of Mechano-Informatics, Graduate School of Information Science and Technology, University of Tokyo, Bunkyo-ku, Tokyo, Japan 2 Artifi cial Intelligence Laboratory, University of Zurich, Zurich, Switzerland Edited by: Pattern generators found in the spinal cord are no more seen as simple rhythmic oscillators for Jun Tani, RIKEN Brain Science Institute, motion control. Indeed, they achieve fl exible and dynamical coordination in interaction with the Japan body and the environment dynamics giving to rise motor synergies. Discovering the mechanisms Reviewed by: Fumiya Iida, ETH Zurich, Switzerland underlying the control of motor synergies constitutes an important research question not only Hiroshi Kimura, Kyoto Institute of for neuroscience but also for robotics: the motors coordination of high dimensional robotic Technology, Japan systems is still a drawback and new control methods based on biological solutions may reduce *Correspondence: their overall complexity. We propose to model the fl exible combination of motor synergies in Alexandre Pitti, Laboratory for embodied systems via partial phase synchronization of distributed chaotic systems; for specifi c Intelligent Systems and Informatics, Department of Mechano-Informatics, coupling strength, chaotic systems are able to phase synchronize their dynamics to the resonant Graduate School of Information frequencies of one external force. We take advantage of this property to explore and exploit Science and Technology, the intrinsic dynamics of one specifi ed embodied system. In two experiments with bipedal University of Tokyo, Eng. Bldg.2, 7-3-1, walkers, we show how motor synergies emerge when the controllers phase synchronize to Hongo, Bunkyo-ku, Tokyo 113-8656, Japan. the body’s dynamics, entraining it to its intrinsic behavioral patterns. This stage is characterized e-mail: [email protected] by directed information fl ow from the sensors to the motors exhibiting the optimal situation when the body dynamics drive the controllers (mutual entrainment). Based on our results, we discuss the relevance of our fi ndings for modeling the modular control of distributed pattern generators exhibited in the spinal cord, and for exploring the motor synergies in robots. Keywords: motor synergies, phase synchronization, sensorimotor coordination, causal information fl ow INTRODUCTION Motor synergy, the muscles grouping by few order parameters, During the 1960s and 1970s, central pattern generators (CPGs) has been an answer for Bernstein to explain how infants, dur- were considered to be neural circuits capable of producing sin- ing their early development, face the enormous dimensionality gle patterned motor output in the absence of sensory feedback. problem of linking sensors and motors activities for producing However, more recent investigations have demonstrated that they coordinated movements. Although CPGs can autonomously can adapt to a large variety of tasks scenarios and environmental establish some regular rhythmic fi ring patterns, they are under the conditions (Bizzi and Clarac, 1999; Ivanenko et al., 2005; Ting and constant supervision of descending chemical substances known as MacPherson, 2005). Such adaptability and continuous adjustment neuromodulators (Selverston et al., 2000; Rabinovich et al., 2006). of behavior is made possible by specifi c activations of muscles As neuromodulators control the activity of CPGs, they are in a groups, also known as muscle synergies (Bernstein, 1967). Given sense the meta-controllers that realize the CPGs’ coordination or that each muscle can be also activated by several synergies, it refl ects separation (Doya, 2002). We hypothesize that they do not only the considerable fl exibility and complexity in the motor systems’ regulate the partial synchronization of CPGs to each other, but dynamics (see Figure 1). Hence, the rhythmical patterns found also to the body dynamics to create one specifi c rhythm dynami- in CPGs are more likely to be created dynamically by interacting cally. Hence, a better image is perhaps to view the neuromodula- with other signals rather than stored. As the motor system com- tors governing the global coordination (or synergy) between the bines modularity, plasticity (Bizzi et al., 1995; Rabinovich et al., body dynamics and the pattern generators to the generation of the 2006; Choi and Bastian, 2007; Miall, 2007), but also robustness ongoing motion (Wolf and Pearson, 1988; Calabrese, 1995; Marder to perturbations (Torres-Oviedo et al., 2006), one might ask how and Calabrese, 1996). this complexity could be organized? Despite all the progresses We propose to model this mechanism of dynamical phase syn- done, little is known about the mechanisms regulating the fl exible chronization (PS) between the body dynamics and its nonlinear coordination of the motor synergies (Ting, 2007), how they inte- controllers for the discovery and the control of its motor synergies. grate the body dynamics, and how animals acquire them (if so). It is known that chaotic systems are capable to phase synchronize Understanding these mechanisms is important for neuroscience their dynamics to the resonant frequencies of any weak external since it underlines the so-called Bernstein’s problem (Bernstein, force coupled to them. Within an embodied system, we exploit this 1967) – how do we face the enormous dimensionality to control our property to transiently match the resonant frequencies of the body’s body – but also for robotics to control high dimensional systems. limbs and to coordinate their dynamics with each other (Lungarella Frontiers in Neurorobotics www.frontiersin.org October 2009 | Volume 3 | Article 2 | 1 Pitti et al. Dynamical synchronization of pattern generators PHASE SYNCHRONIZATION IN COUPLED CHAOTIC SYSTEMS To explain the principle of PS, let us consider the discrete nonlinear dynamical system F(x) where x = x(t)∈Rd is the system’s d dimen- sional vector sampled at the discrete time step t. The system is perturbed with a weak external periodic force P such that: =+ xxFP() , (1) ω + δ ω + δ … ω + δ where P(t) = [A1cos( t 1), A2cos( t 2), ,Adcos( t d)]. The applied periodic force has the frequency ω and is weighted by the coeffi cients Aj = 1,2,…,d. Under these conditions, it is possible to observe PS (see Rosenblum et al., 1996; Pikovsky et al., 1997). This means that although the system’s amplitude remains chaotic, FIGURE 1 | Concept of motor synergies. One motor synergy constitutes its dynamics change in such a way that the phase ψ of the chaotic particular grouping of muscles for certain weights confi gurations (Bizzi and attractor meets the one of the external force φ. Clarac, 1999). In the same time, one muscle can be activated by several synergies (Ting, 2007); this demonstrates how modular and fl exible the motor ψ()tt=φ () ±m ω t , (2) n system is. with m and n as integer and Ω the frequency of the oscillator such that: and Berthouze, 2002, 2004; Kuniyoshi and Suzuki, 2004; Pitti et al., Ω − ω 2005, 2006; Kuniyoshi and Sangawa, 2006). Such scenario permits |n m | = 0. (3) to incorporate the body dynamics within the control loop, repro- Therefore, PS means that the phase of the oscillator always stays ducing the modular and bottom-up aspects of the biological motor close enough to the phase of the force (m = n = 1), or to the one of synergies (Schoner et al., 1988; Kelso and Haken, 1995; Taga, 1995; its harmonics (m > n); or, alternatively, the frequency of the oscil- Seo and Slotine, 2007) whereas other methods account more on the lator, Ω, is close to a harmonic of the force’s frequency (m < n). role of internal dynamics over the body for motion generation (cf. Whether we obtain PS or not, depends on the properties of the Nakanishi et al., 2004; Buchli et al., 2006). In two experiments with force applied (i.e. its coupling strength vector A) which drives the bipedal walkers, we show that at PS, the body and the controllers system’s dynamics into the neighborhood of ω (Gonzalez-Miranda, mutually and dynamically entrain themselves to each other yield- 2004). Moreover, P in our example is a compound
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