Abstract

The aim of this thesis is to propose an integrated framework based on synchronization in dynamical systems for robotics and embodied AI. Our contribution includes: (i) A methodology that exploits the property of nonlinear oscillators to match (synchronize) and amplify the resonant frequencies of any given system (feedback resonance) to explore, quantify and categorize the natural dynamics of a robotic system, independent of its dimensionality and morphology. (ii) A methodology that exploits the property of phase synchronization in chaotic systems for information processing purposes. Our novel model based on this property - a multi-layer Coupled Map Lattices (CML) - has the memory function based on the phase-locking of chaotic systems, and can be used for dynamical learning i.e. pattern recognition of scene images, or for the learning and the control of simple robotic motion behaviors. (iii) This mechanism permits the dynamical linkage between the internal dynamics of an embodied robot and the external dynamics of the environment. Simple skill transfer (dynamical learning of coordinated body limbs motion) is possible without algorithmic optimization technique. (iv) We develop novel measuring tools to quantify dynamical behavior in high dimensional systems: the wavelet bifurcation diagram (spatio-temporal correlations among units and groups of units), two multi-scale causality measure variants (a measure of the causal relationship occuring at different temporal scales between two signals and a measure of the causal relationship occuring between the different temporal scales in one signal).

The thesis is organized in eight chapters as follows:

Chapter 1, Introduction, We present our main thesis, the phenomenon of synchronization in dynamical systems can serve as a framework for robotics toward exploration and exploitation of body dynamics, the learning and the recognition of dynamical patterns, the acquisition of external information in an embodied sytem toward development.

Chapter 2, Synchronization, a Central Role for Cognition, we cover briefly the state of the art in cognitive sciences to point out on the central role played by synchronization. We underline the researches done in neurology on the mechanism of phase synchronization between neural assemblies for communication and perception processes, in physiology in the study of corresponding activity between brain processes dynamics with motion behavior which indicates synergy and synchronization, and in developmental psychology, we focus on the importance for infants development to detect, to learn and to reproduce synchronous and coincidental events i.e. contingency and imitation, social interaction.

Chapter 3, Phase synchronization in nonlinear dynamical systems, we present the mechanism of phase synchronization in nonlinear oscillators and its capabilites for control, stabilization, communication, information transfer, detection and learning. We propose a novel architecture of coupled assemblies of chaotic maps to store dynamically external information as phase delay between the units. We give a simple example of its properties for a pattern recognition application to store and discriminate several patterns into the dynamics of the oscillators. The detection process is based on the distance measure between the internal dynamics and the presented stimulus.

Chapter 4, Analysis methods, this chapter treats about the measures that we employed with the novel ones that we propose to quantify and classify spatio-temporal patterns in high dimensional complex systems, and the causal relationships occuring between them. We expose the three novel measuring tools that we developed: the wavelet bifurcation diagram (spatio-temporal correlations among units and groups of units), and two multi-scale causality measure variants.

Chapter 5, Exploration of behavioral patterns, stability and bifurcation, we present the methodology that exploits the property of nonlinear oscillators to match (synchronize) and amplify the resonant frequencies of any given system (mechanism of feedback resonance) to explore, quantify, and categorize the natural dynamics of a robotic system independent of its dimensionality and morphology. We perform experimental analysis on three qualitatively different mechanical system simulations: a compass biped model (one degree of freedom), (2) a dog-like model (two d.o.f.), and (3) a ring-like mass-spring model possessing thirty degrees of freedom. We show that for specific coupling values corresponding to synchronized states, the internal system (nonlinear oscillators) discovers the natural dynamics of the systems i.e. The biped walker performs stable and periodic walking locomotion, the dog-like model explores its stable motions as well as its most impulsive ones like crawling, hopping, walking, and jumping; and the ring-like model shows complex behaviors depending on the level of coordination between the sub-parts that constitutes it, like rolling, fast accelerating, and breaking.

Chapter 6, Implication of synchronization for development and embodiment, in this chapter we expose how the mechanism of synchronization can serve to drive the dynamical learning of sensori-motor patterns and the skills acquisition in an embodied robot. We show that externally imposed dynamics can affect the internal dynamics only when the state of phase synchronization occurs. The rationale is that for only certain coupling values between the internal system and the body, the linkage between the two systems is possible even though they are working at different time scales, it follows the dynamical exchange of information between the external and the internal dynamics. The level of synchronization between the sensor system and the motor system rules their coordination and the amount of information exchanged.

Chapter 7 Control, the dual view of synchronization, this chapter is a synthesis of the previous chapters on coordination dynamics and on information processing. It describes some experiments that we have done to study the causal sensori-motor information flow between the internal dynamics of a chaotic oscillator coupled to the body dynamics in a compass-like biped walker. It shows that synchronization between the two systems permits the linkage, the exploitation of the body dynamics and the dynamical stabilization over time of their coupling. In a final experience, we integrate exploration, learning and control of the sensori-motor information flow for a developmental issue using the biped model and the multi-layer CML map. Through the effect of the sensor signal during walking on the internal dynamics of the chaotic elements, clusters are formed and retained dynamically. Although the patterns were not designed but emerged from the interaction, they are informational i.e. They correspond to adaptive filters of the sensori-motor coordination.

Chapter 8, Conclusion, in the conclusion of thesis, we explain how we have explored the range that goes from the physics (interactions, friction, elasticity, resonance) toward information (gait, patterns, memory effects, etc...) using the framework of synchronization in dynamical systems. Three parts can be distinguished on (i) body dynamics exploration and coordination, (ii) learning and storage of information with the multi-layered maps model, and (iii) learning and acquisition of information in an embodied system. We contribute also by providing quantifying tools, three novel analysis methods to measure the multi-scale spatial and temporal phase transition in complex and high dimensional systems that we named the wavelet bifurcation diagram, and two multi-scaled causal relationship between and within the systems. These methods are general methods for the study of complex and dynamical systems that can be applied in biology or physics.

本論文は,Phase Synchronization Between Internal and Body Dynamics for Exploration, Memory, and Control of Embodied Behavior(和訳:身体行動の探索・記憶・制御のための内部および身体ダイナミクス間の位相同期)と題し,8章からなる.本論文は,身体性に基づく知能のため,ダイナミカルシステム間の同期現象に基づき,探索,記憶,制御を統一的に扱うメカニズムを提示することを目指した研究である.まず,カオス振動子系と帰還共鳴による位相同期現象に基づき,脚歩行型や30自由度リング型などを含む任意の自由度と形態のロボット機構の未知の固有ダイナミクスに対し,固有モードを顕在化,分離して多様な行動を創発させる方法を提示した後,その原理を発展させて新たに提案した多層カオス結合格子(Multi-Layer CML)モデルが,位相同期現象に基づく適応的記憶・再生機能を有することを示し,これをテレビカメラ画像の記憶,人間型身体モデルでの運動の教示と再生,二脚ロボットモデルの歩行モードの自発探索と記憶と制御,に順次適用・解析することで,同モデルがダイナミクス構造の探索・記憶・制御の機能を併せ持つことを示した.また,これら実験の解析のため,高次元力学系の振る舞いの全体的構造の分析手法として,1)各自由度間の時空間相関構造を一括して抽出・表現するウェーブレット分岐ダイアグラム法,2)2信号間の各時間尺度ごと,および単一信号内の各時間尺度間,の因果関係測度を抽出する時間階層型因果解析法,を提案し活用している.

第1章,　Introduction(序論)では,本研究の背景,立場,目的について述べている.

第2章,　Synchronization, a Central Role for Cognition(認知において中心的な役割を果たす同期現象)においては,近年の認知科学の知見を踏まえ,認知の中で同期現象が果たす役割について論じている.特に,神経科学で知られる,神経集団間のコミュニケーション,生理学で知られる,脳活動と身体運動の協調,および,発達心理学で知られる,社会的相互作用等において,位相同期現象が重要な役割を果たしているとの知見を引用し検討している.

第3章,　Emergence in Nonlinear Systems(非線形系における創発)では,複数のカオス写像を双方向結合して,連鎖構造とネットワーク構造の両方の特性を併せ持つようにした新たなモデルを提案している.そして,位相同期時には,このモデルが位相固定ネットワークとして振る舞うことで,各要素が情報の入出力と記憶の機能を有することを示している.

第4章,　Analysis Methods(解析手法)では,高次元複雑系に現れる時空間パタンとサブシステム間の動的因果関係を解析する手法を提示,提案している.新規提案としては,要素間および要素集団間の時空間相関を抽出表示するウェーブレット分岐ダイアグラム法,および,2種類の多階層因果性指標がある.

第5章,　Emergence and Exploration of Behavioral Patterns, Stability and Bifurcation(行動パタンの創発と探索,安定性と分岐)では,カオス振動子群の特性を活用して,任意の対象システムの固有振動数に同期し励起する方法を提案し,実験的に検証している.これにより,任意のロボット機構について,その固有ダイナミクスを探索し,カテゴリ化することができる.実験では,コンパス型2脚モデル(1自由度)の歩行,犬型2脚モデル(2自由度)の歩行や跳躍,環型バネマスダンパモデル(30自由度)の多様なロコモーションなどの行動創発が,対象システムに関する詳細知識なしに起こることを示した.

第6章,　Implication of Synchronization for Development and Embodiment(発達と身体性における同期の意味)では,提案したカオスネットワークモデルを人体型モデルに適用し,他者が外部から四肢を動かす教示が,位相同期時にのみ,内部記憶に反映し,その後のネットワーク動作により様々な動作パタンに発展することを示した.これを踏まえて,発達論的な見解を展開した.

第7章,　Control, the Dual View of Synchronization(制御:同期のもう一つの側面)では,前述の内部モデルを再びコンパス型2脚歩行モデルに適用し,歩行モードの探索,記憶,制御(安定化)が同一のモデルで実現されることを示した.運動パタンは,特定の位相関係を保持した内部振動パタンによって記憶されている.これにより,前章までの内容が統合され,身体性に基づく認知発達の基本要素(探索,記憶,制御)を提案モデルで統一的に扱えることを示した.

第8章,　Conclusion(結論)では,上述の結果を総括し,身体の物理現象から記憶などの情報現象までを一貫した力学系的モデルで扱えたことを主張している.また,提案した解析手法が一般の高次元力学系の振る舞いの解析に有用であることを主張している.

　以上要するに,本論文は,対象システムに関する詳細知識なしに,その物理特性を活用した運動を探索し,記憶し,制御することのできる統一的モデルを提示し実験的に検証し,また,その解析手段として高次元力学系の挙動を明快に抽出表示する新規手法を提案し,もって創発的知能システムに関する新たな知見を加え,知能機械情報学の発展に貢献したものである.

　よって本論文は博士(情報理工学)の学位請求論文として合格と認められる.