Symmetry-breaking in a rate model for a biped locomotion central pattern generator

The timing patterns of animal gaits are produced by a network of spinal neurons called a Central Pattern Generator (CPG). Pinto and Golubitsky studied a four-node CPG for biped dynamics in which each leg is associated with one flexor node and one extensor node, with Ζ2 x Ζ2 symmetry. They used symmetric bifurcation theory to predict the existence of four primary gaits and seven secondary gaits. We use methods from symmetric bifurcation theory to investigate local bifurcation, both steady-state and Hopf, for their network architecture in a rate model. Rate models incorporate parameters corresponding to the strengths of connections in the CPG: positive for excitatory connections and negative for inhibitory ones. The three-dimensional space of connection strengths is partitioned into regions that correspond to the first local bifurcation from a fully symmetric equilibrium. The partition is polyhedral, and its symmetry group is that of a tetrahedron. It comprises two concentric tetrahedra, subdivided by various symmetry planes. The tetrahedral symmetry arises from the structure of the eigenvalues of the connection matrix, which is involved in, but not equal to, the Jacobian of the rate model at bifurcation points. Some of the results apply to rate equations on more general networks

Neural Control of Interlimb Coordination and Gait Timing in Bipeds and Quadrupeds

1) A large body of behavioral data conceming animal and human gaits and gait transitions is simulated as emergent properties of a central pattern generator (CPG) model. The CPG model incorporates neurons obeying Hodgkin-Huxley type dynamics that interact via an on-center off-surround anatomy whose excitatory signals operate on a faster time scale than their inhibitory signals. A descending cornmand or arousal signal called a GO signal activates the gaits and controL their transitions. The GO signal and the CPG model are compared with neural data from globus pallidus and spinal cord, among other brain structures. 2) Data from human bimanual finger coordination tasks are simulated in which anti-phase oscillations at low frequencies spontaneously switch to in-phase oscillations at high frequencies, in-phase oscillations can be performed both at low and high frequencies, phase fluctuations occur at the anti-phase in-phase transition, and a "seagull effect" of larger errors occurs at intermediate phases. When driven by environmental patterns with intermediate phase relationships, the model's output exhibits a tendency to slip toward purely in-phase and anti-phase relationships as observed in humans subjects. 3) Quadruped vertebrate gaits, including the amble, the walk, all three pairwise gaits (trot, pace, and gallop) and the pronk are simulated. Rapid gait transitions are simulated in the order--walk, trot, pace, and gallop--that occurs in the cat, along with the observed increase in oscillation frequency. 4) Precise control of quadruped gait switching is achieved in the model by using GO-dependent modulation of the model's inhibitory interactions. This generates a different functional connectivity in a single CPG at different arousal levels. Such task-specific modulation of functional connectivity in neural pattern generators has been experimentally reported in invertebrates. Phase-dependent modulation of reflex gain has been observed in cats. A role for state-dependent modulation is herein predicted to occur in vertebrates for precise control of phase transitions from one gait to another. 5) The primary human gaits (the walk and the run) and elephant gaits (the amble and the walk) are sirnulated. Although these two gaits are qualitatively different, they both have the same limb order and may exhibit oscillation frequencies that overlap. The CPG model simulates the walk and the run by generating oscillations which exhibit the same phase relationships. but qualitatively different waveform shapes, at different GO signal levels. The fraction of each cycle that activity is above threshold quantitatively distinguishes the two gaits, much as the duty cycles of the feet are longer in the walk than in the run. 6) A key model properly concerns the ability of a single model CPG, that obeys a fixed set of opponent processing equations to generate both in-phase and anti-phase oscillations at different arousal levels. Phase transitions from either in-phase to anti-phase oscillations, or from anti-phase to in-phase oscillations, can occur in different parameter ranges, as the GO signal increases.Air Force Office of Scientific Research (90-0128, F49620-92-J-0225, 90-0175); National Science Foundation (IRI-90-24877); Office of Naval Research (N00014-92-J-1309); Army Research Office (DAAL03-88-K-0088); Advanced Research Projects Agency (90-0083

Development of behaviors for a simulated humanoid robot

Mestrado em Engenharia de Computadores e TelemáticaControlar um robô bípede com vários graus de liberdade é um desafio que recebe a atenção de vários investigadores nas áreas da biologia, física, electrotecnia, ciências de computadores e mecânica. Para que um humanóide possa agir em ambientes complexos, são necessários comportamentos rápidos, estáveis e adaptáveis. Esta dissertação está centrada no desenvolvimento de comportamentos robustos para um robô humanóide simulado, no contexto das competições de futebol robótico simulado 3D do RoboCup, para a equipa FCPortugal3D. Desenvolver tais comportamentos exige o desenvolvimento de métodos de planeamento de trajectórias de juntas e controlo de baixo nível. Controladores PID foram implementados para o controlo de baixo nível. Para o planeamento de trajectórias, quatro métodos foram estudados. O primeiro método apresentado foi implementado antes desta dissertação e consiste numa sequência de funções degrau que definem o ângulo desejado para cada junta durante o movimento. Um novo método baseado na interpolação de um seno foi desenvolvido e consiste em gerar uma trajectória sinusoidal durante um determinado tempo, o que resulta em transições suaves entre o ângulo efectivo e o ângulo desejado para cada junta. Um outro método que foi desenvolvido, baseado em séries parciais de Fourier, gera um padrão cíclico para cada junta, podendo ter múltiplas frequências. Com base no trabalho desenvolvido por Sven Behnke, um CPG para locomoção omnidireccional foi estudado em detalhe e implementado. Uma linguagem de definição de comportamentos é também parte deste estudo e tem como objectivo simplificar a definição de comportamentos utilizando os vários métodos propostos. Integrando o controlo de baixo nível e os métodos de planeamento de trajectórias, vários comportamentos foram criados para permitir a uma versão simulada do humanóide NAO andar em diferentes direcções, rodar, chutar a bola, apanhar a bola (guarda-redes) e levantar do chão. Adicionalmente, a optimização e geração automática de comportamentos foi também estudada, utilizado algoritmos de optimização como o Hill Climbing e Algoritmos Genéticos. No final, os resultados são comparados com as equipas de simulação 3D que reflectem o estado da arte. Os resultados obtidos são bons e foram capazes de ultrapassar uma das três melhores equipas simuladas do RoboCup em diversos aspectos como a velocidade a andar, a velocidade de rotação, a distância da bola depois de chutada, o tempo para apanhar a bola e o tempo para levantar do chão. ABSTRACT: Controlling a biped robot with several degrees of freedom is a challenging task that takes the attention of several researchers in the fields of biology, physics, electronics, computer science and mechanics. For a humanoid robot to perform in complex environments, fast, stable and adaptable behaviors are required. This thesis is concerned with the development of robust behaviors for a simulated humanoid robot, in the scope of the RoboCup 3D Simulated Soccer Competitions, for FCPortugal3D team. Developing such robust behaviors requires the development of methods for joint trajectory planning and low-level control. PID control were implemented to achieve low-level joint control. For trajectory planning, four methods were studied. The first presented method was implemented before this thesis and consists of a sequence of step functions that define the target angle of each joint during the movement. A new method based on the interpolation of a sine function was developed and consists of generating a sinusoidal shape during some amount of time, leading to smooth transitions between the current angle and the target angle of each joint. Another method developed, based on partial Fourier Series, generates a multi-frequency cyclic pattern for each joint. This method is very flexible and allows to completely control the angular positions and velocities of the joints. Based on the work of developed by Sven Behnke, a CPG for omnidirectional locomotion was studied in detail and implemented. A behavior definition language is also part of this study and aims at simplifying the definition of behaviors using the several proposed methods. By integrating the low-level control and the trajectory planning methods, several behaviors were created to allow a simulated version of the humanoid NAO to walk in different directions, turn, kick the ball, catch the ball (goal keeper) and get up from the ground. Furthermore, the automatic generation of gaits, through the use of optimization algorithms such as hill climbing and genetic algorithms, was also studied and tested. In the end, the results are compared with the state of the art teams of the RoboCup 3D simulation league. The achieved results are good and were able to overcome one of the state of the art simulated teams of RoboCup in several aspects such as walking velocity, turning velocity, distance of the ball when kicked, time to catch the ball and the time to get up from the ground

Self-organized adaptive legged locomotion in a compliant quadruped robot

In this contribution we present experiments of an adaptive locomotion controller on a compliant quadruped robot. The adaptive controller consists of adaptive frequency oscillators in different configurations and produces dynamic gaits such as bounding and jumping. We show two main results: (1)The adaptive controller is able to track the resonant frequency of the robot which is a function of different body parameters (2)controllers based on dynamical systems as we present are able to "recognize” mechanically intrinsic modes of locomotion, adapt to them and enforce them. More specifically the main results are supported by several experiments, showing first that the adaptive controller is constantly tracking body properties and readjusting to them. Second, that important gait parameters are dependent on the geometry and movement of the robot and the controller can account for that. Third, that local control is sufficient and the adaptive controller can adapt to the different mechanical modes. And finally, that key properties of the gaits are not only depending on properties of the body but also the actual mode of movement that the body is operating in. We show that even if we specify the gait pattern on the level of the CPG the chosen gait pattern does not necessarily correspond to the CPG's pattern. Furthermore, we present the analytical treatment of adaptive frequency oscillators in closed feedback loops, and compare the results to the data from the robot experiment

Neurobiologically Inspired Control of Engineered Flapping Flight

This article presents a new control approach for engineered flapping flight with many interacting degrees of freedom. This paper explores the applications of neurobiologically inspired control systems in the form of Central Pattern Generators (CPG) to generate wing trajectories for potential flapping flight MAVs. We present a rigorous mathematical and control theoretic framework to design complex three dimensional motions of flapping wings. Most flapping flight demonstrators are mechanically limited in generating the wing trajectories. Because CPGs lend themselves to more biological examples of flight, a novel robotic model has been developed to emulate the flight of bats. This model has shoulder and leg joints totaling 10 degrees of freedom for control of wing properties. Results of wind tunnel experiments and numerical simulation of CPG-based flight control validate the effectiveness of the proposed neurobiologically inspired control approach

System Identification of Bipedal Locomotion in Robots and Humans

The ability to perform a healthy walking gait can be altered in numerous cases due to gait disorder related pathologies. The latter could lead to partial or complete mobility loss, which affects the patients’ quality of life. Wearable exoskeletons and active prosthetics have been considered as a key component to remedy this mobility loss. The control of such devices knows numerous challenges that are yet to be addressed. As opposed to fixed trajectories control, real-time adaptive reference generation control is likely to provide the wearer with more intent control over the powered device. We propose a novel gait pattern generator for the control of such devices, taking advantage of the inter-joint coordination in the human gait. Our proposed method puts the user in the control loop as it maps the motion of healthy limbs to that of the affected one. To design such control strategy, it is critical to understand the dynamics behind bipedal walking. We begin by studying the simple compass gait walker. We examine the well-known Virtual Constraints method of controlling bipedal robots in the image of the compass gait. In addition, we provide both the mechanical and control design of an affordable research platform for bipedal dynamic walking. We then extend the concept of virtual constraints to human locomotion, where we investigate the accuracy of predicting lower limb joints angular position and velocity from the motion of the other limbs. Data from nine healthy subjects performing specific locomotion tasks were collected and are made available online. A successful prediction of the hip, knee, and ankle joints was achieved in different scenarios. It was also found that the motion of the cane alone has sufficient information to help predict good trajectories for the lower limb in stairs ascent. Better estimates were obtained using additional information from arm joints. We also explored the prediction of knee and ankle trajectories from the motion of the hip joints

Humanoid Robots

For many years, the human being has been trying, in all ways, to recreate the complex mechanisms that form the human body. Such task is extremely complicated and the results are not totally satisfactory. However, with increasing technological advances based on theoretical and experimental researches, man gets, in a way, to copy or to imitate some systems of the human body. These researches not only intended to create humanoid robots, great part of them constituting autonomous systems, but also, in some way, to offer a higher knowledge of the systems that form the human body, objectifying possible applications in the technology of rehabilitation of human beings, gathering in a whole studies related not only to Robotics, but also to Biomechanics, Biomimmetics, Cybernetics, among other areas. This book presents a series of researches inspired by this ideal, carried through by various researchers worldwide, looking for to analyze and to discuss diverse subjects related to humanoid robots. The presented contributions explore aspects about robotic hands, learning, language, vision and locomotion

Locomotion Trajectory Generation and Dynamic Control for Bipedal Walking Robots

Ph.DDOCTOR OF PHILOSOPH

Intelligent System Synthesis for Dynamic Locomotion Behavior in Multi-legged Robots

Robot technology has been implemented in many fields of our life, such as entertainment, security, rescue, rehabilitation, social life, the military, and etc. Multi-legged robot always exist in many fields, therefore it is important to be developed. Motion capabilities of the robot will be a main focus to be developed. Current development or conventional model of motion capabilities have several issues in saturation of development. There are some limitation in dynamic factors such as, locomotion generator, flexibility of motion planning, and smoothness of movement. Therefore, in this research, natural based computation are implemented as the basic model. There are three subsystems to be developed and integrated, (1) locomotion behavior model, (2) stability behavior model, and (3) motion planning model. Since individual people has different walking behavior in each walking direction and walking speed, locomotion behavior learning model of omni-directional bio-inspired locomotion which is generating different walking behavior in different walking provision are required to be developed. Step length in sagital and coronal direction, and degree of turning are considered parameters in walking provision. In proposed omni-directional walking model, interconnection structures composed by 16 neurons where 1 leg is represented by 4 joints and 1 joint is represented by 2 motor neurons. In order to acquire walking behavior in certain walking provision, the interconnection structure is optimized by multi-objectives evolutionary algorithm. For acquiring the diversity of references, several optimized interconnection structures are generated in optimization processes in different walking provisions. Learning models are proposed for solving non-linearity of relationship between walking input and walking output representing the synaptic weight of interconnection structure, where one learning model representing one walking parameter. Furthermore, by using optimized model, walking behavior can be generated with unsealed walking provision. Smooth walking transition with low error of desired walking provision was proved based on several numerical experiments in physical computer simulation. In stability behavior model, neuro-based push recovery controller is applied in multi-legged robot in order to keep the stability with minimum energy required. There are three motion patterns in individual people behavior when it gets external perturbation, those are ankle behavior, hip behavior, and step behavior. We propose a new model of Modular Recurrent Neural Network (MRNN) for performing online learning system in each motion behavior. MRNN consists of several recurrent neural networks (RNNs) working alternatively depending on the condition. MRNN performs online learning process of each motion behavior controller independently. The aim of push recovery controller is to manage the motion behavior controller by minimizing the energy required for responding to the external perturbation. This controller selects the appropriate motion behavior and adjusts the gain that represent the influence of the motion behavior to certain push disturbance based on behavior graphs which is generated by adaptive regression spline. We applied the proposed controller to the humanoid robot that has small footprint in open dynamics engine. Experimental result shows the effectiveness of the push controller stabilizing the external perturbation with minimum energy required. Proposed motion planning model presents a natural mechanism of the human brain for generating a dynamic path planning in 3-D rough terrain. The proposed model not only emphasizes the inner state process of the neuron but also the development process of the neurons in the brain. There are two information transmission processes in this proposed model, the forward transmission activity for constructing the neuron connections to find the possible way and the synaptic pruning activity with backward neuron transmission for finding the best pathway from current position to target position and reducing inefficient neuron with its synaptic connections. In order to respond and avoid the unpredictable obstacle, dynamic path planning is also considered in this proposed model. An integrated system for applying the proposed model in the actual experiments is also presented. In order to confirm the effectiveness of the proposed model, we applied the integrated system in the pathway of a four-legged robot on rough terrain in computer simulation. For analyzing and proving the flexibility of proposed model, unpredictable collision is also performed in those experiments. The model can find the best pathway and facilitate the safe movement of the robot. When the robot found an unpredictable collision, the path planner dynamically changed the pathway. The proposed path planning model is capable to be applied in further advance implementation. In order to implement the motion capabilities in real cases, all subsystem should be integrated into one interconnected motion capabilities model. We applied small quadruped robot equipped with IMU, touch sensor, and dual ultrasonic sensor for performing motion planning in real terrain from starting point to goal point. Before implemented, topological map is generated by Kinect camera. In this implementation, all subsystem were analyzed and performed well and the robot able to stop in the goal point. These implementation proved the effectiveness of the system integration, the motion planning model is able to generate safe path planning, the locomotion model is able to generate flexible movement depending on the walking provision from motion planning model, and the stability model can stabilize the robot on rough terrain. Generally, the proposed model can be expected to bring a great contribution to the motion capabilities development and can be used as alternative model for acquiring the dynamism and efficient model in the future instead of conventional model usage. In the future, the proposed model can be applied into any legged robot as navigation, supporter, or rescue robot in unstable environmental condition. In addition, we will realize a cognitive locomotion that generates multiple gaits depending on the 3 aspects, embodiment, locomotion generator, and cognition model. A dynamic neuro-locomotion integrated with internal and external sensory information for correlating with the environmental condition will be designed.ロボット技術は、エンターテイメント、セキュリティ、救助、リハビリ、社会生活、軍事などの様々な生活分野に実現さている。多脚ロポットは常に多くの分野に存在するため開発することが重要である。ロボットの運動能力が開発の主要となっている。現状の開発されている動作能力は,飽和状態にある。いくつかの動的な要因により、歩行生成器、動作計画の柔軟性、および動作の滑らかさ等に制限がある。そこで、本研究では、基本的なモデルとして自然計算に基づく方法論を実装する、また、本研究では、歩行動作モデル、安定動作モデル、や運動計画モデルからなる3つのサブシステムを開発し統合する。人間は歩行方向と速度に応じて歩行動作が異なるため、異なる歩行軸では異なる歩行動作を生成するという全方位生物的な運動の歩行動作学習モデルが開発には要求される。球欠および制御方向のステップ長や旋回の度合いは,歩行軸のパラメータとして考慮される。提案した全方位歩行モデルでは,1肢につき16個のニューロンによって構成される相互接続構造を4つの関節によって表現する。また、1つの関節は,2個のモータニューロンによって表現する。一定の歩行軸での歩行動作を獲得するために,本研究では,多目的進化アルゴリズムによって最適化を行う。提案手法では、参照点の多様性を獲得するために,異なる歩行軸においていくつかの最適な相互接続構造が生成される。相互接続構造のシナプス重みを表現している歩行入力と出力間の非線形な関係を解くための学習モデルを構築する。本手法では,1つの学習モデルが1つの歩行パラメータで表現され、最適化されたモデルを用いることにより,歩行動作は,スケーリングされていない歩行軸を生成することが可能となる,物理演算シミュレーションを用いた実験により,誤差の少ない歩行軸の滑らかな歩行遷移を本実験では示している。安定動作モデルでは、必要最小限のエネルギーで安定性を維持するため多足歩行ロボットにニューロベースプッシュリカバリ制御器を適用した。外力をを受けたとき,人間の行動には足首の動作・股関節の動作・踏み動作の3つの動作パターンが存在する。本研究では,各運動動作におけるオンライン学習システムを実現するために、モジュラーリカレントニューラルネットワーク(MRNN)を用いた新たな学習モデルを提案する。MRNNは状況に応じて選択される複数のリカレントニューラルネットワーク(RNN)によって構成される。MRNNは各運動動作コントローラのオンライン学習プロセスを独立して実行する。プッシュリカバリ制御器の目的は、外乱に応じてエネルギー最小化を行うことによって運動動作制御器を管理することである。この制御器は適切な運動動作を選択し,適応回帰スプラインにより生成された動作グラフに基づき押し動作に対して最も影響を及ぼす運動動作のゲインの調整を行う。提案した制御器をOpen Dynamics Engine(ODE)上で小さな足の長さを持つヒューマノイドロボットに適用し,必要最小限のエネルギーで外力に対して安定させるプッシュリカバリ制御器の有効性を示している。3次元の不整地における動的な経路計画を生成するために,人間の自然な脳機能に基づいた動作計画手法を提案する。本モデルは、ニューロンの内部状態過程だけでなく、脳内のニューロンの発達過程も重視している。本モデルは二つのアルゴリズムに構成される。1つは、通過可能な道を見つけるために構築される接続的なニューロン活動である順方向伝達活動であり,もう1つは、現在位置から最適経路を見つけるために、シナプス結合を用いて非効率的なニューロンを減少させる逆方向にニューロン伝達を行うシナプスプルーニング活動である。また,予測不可能な衝突を回避するために,動的な経路計画も実行される。さらに、実環境において提案されたモデルを実現するための統合システムも提示される。提案モデルの有効性を検証するために,コンピュータシミュレーション上で、不整地環境の4足歩行ロボットに関するシミュレーション環境を実装した。これらの実験では,予測不能な衝突に関する実験も行った。本モデルは、最適経路を見つけ出しロボットの安全な移動を実現できた。さらに、ロボットが予測できない衝突を検出した場合,経路計画アルゴリズムが経路を動的に変更可能であることを示している。これらのことから、提案された経路計画モデルはさらなる先進的な展開が実現可能であると考えられる。実環境における運動能力を実装するためには、すべてのサブシステムを1つの運動能力モデルに統合する必要がある。そこで本研究では、IMU、タッチセンサ、2つの超音波センサを搭載した小型の4足歩行ロポットを用いた実環境において出発地点から目的地点までの運動計画を行った、本実装では、3次元距離計測センサであるKinecを用い3次元空間の位相構造を生成する。また、本実装では、すべてのサブシステムが分析され、ロボットは目的地点で停止することができた。さらに、安全な経路計画を生成することができたことからシステム統合の有効性が確認できた。また、歩行モデルにより歩行軸に応じた柔軟な動きが生成されることで、この安定性モデルは不整地環撹でもロボットの歩行を安定させることができた。これらのことから、本提案モデルは運動能力への多大な貢献が期待され、ダイナミクスを獲得するための代替モデルとして使用することができ,現在よく使用されているモデルに代わる効率的なモデルとなることが考えられる。今後の課題としては,不安定な環境下におけるナビゲーション・支援・レスキューロボットといった任意の肢の数を持つ多足歩行ロボットへの本提案モデルの適用があげられる。さらに,身体性,歩行生成,認知モデルの3つの観点から複数の歩容を生成する認知的歩行を実現することを考えている。環境と相互作用するためのモデルとして、内界センサと外界センサ情報を統合した動的ニューロ歩行を実現する予定である。首都大学東京, 2018-03-25, 修士（工学）首都大学東