Biped Locomotion Control through a Biomimetic CPG-based Controller

Modern concepts of motor learning favour intensive training directed to the neural networks stimulation and reorganization within the spinal cord, the central pattern generator, by taking advantage of the neural plasticity. In the present work, a biomimetic controller using a system of adaptive oscillators is proposed to understand the neuronal principles underlying the human locomotion. A framework for neural control is presented, enabling the following contributions: a) robustness to external perturbations; b) flexibility to variations in the environmental constraints; and c) incorporation of volitional mechanisms for self-adjustment of gait dynamics. Phase modulation of adaptive oscillators and postural balance control are proposed as main strategies for stable locomotion. Simulations of the locomotion model with a biped robot in closed-loop control are presented to validate the implemented neuronal principles. Specifically, the proposed system for online modulation of previous learnt gait patterns was verified in terrains with different slopes. The proposed phase modulation method and postural balanced control enabled robustness enhancement considering a broader range of slope angles than recent studies. Furthermore, the system was also verified for tilted ground including different slopes in the same experiment and uneven terrain with obstacles. Adaptive Frequency Oscillators, under Dynamic Hebbian Learning Adaptation mechanism, are proposed to build a hierarchical control architecture with spinal and supra spinal centers with multiple rhythm-generating neural networks that drive the legs of a biped model. The proposed neural oscillators are based on frequency adaptation and can be entrained by sensory feedback to learn specific patterns. The proposed biomimetic controller intrinsically generates patterns of rhythmic activity that can be induced to sustain CPG function by specific training. This method provides versatile control, paving the way for the design of experimental motor control studies, optimal rehabilitation procedures and robot-assisted therapeutic outcomes.     

Learning model for coupled neural oscillators.

Neurophysiological experiments have shown that many motor commands in living systems are generated by coupled neural oscillators. To coordinate the oscillators and achieve a desired phase relation with desired frequency, the intrinsic frequencies of component oscillators and coupling strengths between them must be chosen appropriately. In this paper we propose learning models for coupled neural oscillators to acquire the desired intrinsic frequencies and coupling weights based on the instruction of the desired phase pattern or an evaluation function. The abilities of the learning rules were examined by computer simulations including adaptive control of the hopping height of a hopping robot. The proposed learning rule takes a simple form like a Hebbian rule. Studies on such learning models for neural oscillators will aid in the understanding of the learning mechanism of motor commands in living bodies.     

Global dynamics of two coupled parametrically excited van der Pol oscillators

Using a combination of analytical and numerical methods, the global bifurcations and chaotic dynamics of two non-linearly coupled parametrically excited van der Pol oscillators are investigated in detail. With the aid of the method of multiple scales, the slow flow equations are obtained. Based on the slow flow equations, normal form theory and the techniques of choosing complementary space are applied to find the explicit expressions of the simpler normal form associated with a double zero and a pair of pure imaginary eigenvalues. By the simpler normal form, using the global perturbation method developed by Kovacic and Wiggins, the analysis of global bifurcation and chaotic dynamics of two non-linearly coupled parametrically excited van der Pol oscillators is given. The results indicate that there exists a Silnikov type single-pulse homoclinic orbit for this class of system which implies the chaotic motions can occur. Numerical simulations are also given and verify the analytical predictions.     

Neural network-based synchronization of uncertain chaotic systems with unknown states

In this paper, synchronization of chaotic systems with unknown parameters and unmeasured states is investigated. Two nonidentical chaotic systems in the framework of a master and a slave are considered for synchronization. It is assumed that both systems have uncertain dynamics, and states of the slave system are not measured. To tackle this challenging synchronization problem, a novel neural network-based adaptive observer and an adaptive controller have been designed. Moreover, a neural network is utilized to approximate the unknown dynamics of the slave system. The proposed method imposes neither restrictive assumption nor constraint on the dynamics of the systems. Furthermore, the stability of the entire closed-loop system in the presence of the observer dynamics has been established. Finally, effectiveness of the proposed scheme is demonstrated via computer simulation.     

Partial synchronization and clustering in a system of diffusively coupled chaotic oscillators

We examine the problem of partial synchronization (or clustering) in diffusively coupled arrays of identical chaotic oscillators with periodic boundary conditions. The term partial synchronization denotes a dynamic state in which groups of oscillators synchronize with one another, but there is no synchronization among the groups. By combining numerical and analytical methods we prove the existence of partially synchronized states for systems of three and four oscillators. We determine the stable clustering structures and describe the dynamics within the clusters. Illustrative examples are presented for coupled Rössler systems. At the end of the paper, synchronization in larger arrays of chaotic oscillators is discussed.     

Generation of bipedal walking through interactions among the robot dynamics,the oscillator dynamics,and the environment: Stability characteristics of a five-link planar biped robot

We previously developed a locomotion control system for a biped robot using nonlinear oscillators and verified the performance of this system in order to establish adaptive walking through the interactions among the robot dynamics, the oscillator dynamics, and the environment. In order to clarify these mechanisms, we investigate the stability characteristics of walking using a five-link planar biped robot with a torso and knee joints that has an internal oscillator with a stable limit cycle to generate the joint motions. Herein we conduct numerical simulations and a stability analysis, where we analytically obtain approximate periodic solutions and examine local stability using a Poincaré map. These analyses reveal (1) stability characteristics due to locomotion speed, torso, and knee motion, (2) stability improvement due to the modulation of oscillator states based on phase resetting using foot-contact information, and (3) the optimal parameter in the oscillator dynamics for adequately exploiting the interactions among the robot dynamics, the oscillator dynamics, and the environment in order to increase walking stability. The results of the present study demonstrate the advantage and usefulness of locomotion control using oscillators through mutual interactions.     

Firing patterns transition induced by system size in coupled Hindmarsh-Rose neural system

The effect of system size on the different dynamical states in coupled cell system is numerically investigated, by using the Hindmarsh-Rose (HR) model. We select the external current as a controlling parameter, for the proper coupling intensity, it is found that the system undergoes the transition of neural firing patterns from one state to another one, when the number of neurons in coupled system is set to be a proper value. And if the coupled system is turned below the bifurcation point, we find that such transition behavior can occur both between two different periodic states, or periodic state and chaotic one. These phenomena imply the occurrence of firing patterns transition (FPT) induced by system size in this coupled system. Furthermore, if we select r as a controlling parameter, we can also find the similar transition behavior can also be observed, and find that such transition behaviors may have some inherent relevance with the activity degree. Finally, we simply gave the reason for difference direction of FPT. Our results indicate the HR system may make an effective response to external stimulus by adjusting itself parameter, and using this transition mode.     

一种混沌Hopfiele网络及其在优化计算中的应用

文章讨论了神经网络算法在约束优化问题中的应用,提出了一种混沌神经网络模型。在Hopfield网络中引入混沌机制,首先在混沌动态下搜索,然后利用HNN梯度优化搜索。对非线性函数的优化问题仿真表明算法具有很强的克服陷入局部极小能力。     

一种混沌Hopfield网络及其在优化计算中的应用

文章讨论了神经网络算法在约束优化问题中的应用,提出了一种混沌神经网络模型。在Hopfield网络中引入混沌机制,首先在混沌动态下搜索,然后利用HNN梯度优化搜索。对非线性函数的优化问题仿真表明算法具有很强的克服陷入局部极小能力。     

A transient-chaotic autoassociative network (TCAN) based on Lee oscillators.

In the past few decades, neural networks have been extensively adopted in various applications ranging from simple synaptic memory coding to sophisticated pattern recognition problems such as scene analysis. Moreover, current studies on neuroscience and physiology have reported that in a typical scene segmentation problem our major senses of perception (e.g., vision, olfaction, etc.) are highly involved in temporal (or what we call "transient") nonlinear neural dynamics and oscillations. This paper is an extension of the author's previous work on the dynamic neural model (EGDLM) of memory processing and on composite neural oscillators for scene segmentation. Moreover, it is inspired by the work of Aihara et al. and Wang on chaotic neural oscillators in pattern association. In this paper, the author proposes a new transient chaotic neural oscillator, namely the "Lee oscillator," to provide temporal neural coding and an information processing scheme. To illustrate its capability for memory association, a chaotic autoassociative network, namely the Transient-Chaotic Auto-associative Network (TCAN) was constructed based on the Lee oscillator. Different from classical autoassociators such as the celebrated Hopfield network, which provides a "time-independent" pattern association, the TCAN provides a remarkable progressive memory association scheme [what we call "progressive memory recalling" (PMR)] during the transient chaotic memory association. This is exactly consistent with the latest research in psychiatry and perception psychology on dynamic memory recalling schemes.     

Rewiring-induced chaos in pulse-coupled neural networks

The dependence of the dynamics of pulse-coupled neural networks on random rewiring of excitatory and inhibitory connections is examined. When both excitatory and inhibitory connections are rewired, periodic synchronization emerges with a Hopf-like bifurcation and a subsequent period-doubling bifurcation; chaotic synchronization is also observed. When only excitatory connections are rewired, periodic synchronization emerges with a saddle node-like bifurcation, and chaotic synchronization is also observed. This result suggests that randomness in the system does not necessarily contaminate the system, and sometimes it even introduces rich dynamics to the system such as chaos.     

Dynamics of relay relaxation oscillators

Relaxation oscillators can usually be represented as a feedback system with hysteresis. The relay relaxation oscillator consists of relay hysteresis and a linear system in feedback. The objective of this work is to study the existence of periodic orbits and the dynamics of coupled relay oscillators. In particular, we give a complete analysis for the case of unimodal periodic orbits, and illustrate the presence of degenerate and asymmetric orbits. We also discuss how complex orbits can arise from bifurcation of unimodal orbits. Finally, we focus on oscillators with an integrator as the linear component, and study the entrainment under external forcing, and phase locking when such oscillators are coupled in a ring     

A Network of Neural Oscillators for Fractal Pattern Recognition

Biological neural networks are high dimensional nonlinear systems, which presents complex dynamical phenomena, such as chaos. Thus, the study of coupled dynamical systems is important for understanding functional mechanism of real neural networks and it is also important for modeling more realistic artificial neural networks. In this direction, the study of a ring of phase oscillators has been proved to be useful for pattern recognition. Such an approach has at least three nontrivial advantages over the traditional dynamical neural networks: first, each input pattern can be encoded in a vector instead of a matrix; second, the connection weights can be determined analytically; third, due to its dynamical nature, it has the ability to capture temporal patterns. In the previous studies of this topic, all patterns were encoded as stable periodic solutions of the oscillator network. In this paper, we continue to explore the oscillator ring for pattern recognition. Specifically, we propose algorithms, which use the chaotic dynamics of the closed loops of Stuart–Landau oscillators as artificial neurons, to recognize randomly generated fractal patterns. We manipulate the number of neurons and initial conditions of the oscillator ring to encode fractal patterns. It is worth noting that fractal pattern recognition is a challenging problem due to their discontinuity nature and their complex forms. Computer simulations confirm good performance of the proposed algorithms.     

Specificity enhancement in classification of breast MRI lesion based on multi-classifier

In the conventional CMAC-based adaptive controller design, a switching compensator is designed to guarantee system stability in the Lyapunov stability sense but the undesirable chattering phenomenon occurs. This paper proposes a CMAC-based smooth adaptive neural control (CSANC) system that is composed of a neural controller and a saturation compensator. The neural controller uses a CMAC neural network to online mimic an ideal controller and the saturation compensator is designed to dispel the approximation error between the ideal controller and neural controller without any chattering phenomena. The parameter adaptive algorithms of the CSANC system are derived in the sense of Lyapunov stability, so the system stability can be guaranteed. Finally, the proposed CSANC system is applied to a Chua’s chaotic circuit and a DC motor driver. Simulation and experimental results show the CSANC system can achieve a favorable tracking performance. It should be emphasized that the development of the proposed CSANC system doesn’t need the knowledge of the system dynamics.     

非均匀气隙永磁同步电机的自适应混沌同步

提出了一种非均匀气隙永磁同步电机(PMSM)混沌系统的同步控制方法. 首先通过多时标变换, 将转子磁场定向坐标系下的PMSM模型, 变换成一种简单的无量纲模型. 之后采用相图和分岔图的方法, 对PMSM的混沌动态行为进行了分析. 指出了倍周期分岔是非均匀气隙PMSM通向混沌的主要途径. 最后基于Lyapunov稳定性理论,设计自适应控制器, 实现了PMSM系统的混沌同步. 数字仿真结果验证了理论分析的正确性和控制方法的有效性.     

SLF混沌神经网络及其应用

针对混沌神经网络的单调激励函数,引入Legendre函数和Sigmoid函数组合作为非单调激励函数,构造了一种新的暂态混沌神经元模型（SLF模型）,并给出了此混沌神经元的倒分岔图和最大Lyapunov指数时间演化图,利用该模型构建了一种暂态混沌神经网络,通过对非线性函数优化和TSP问题的求解验证了该模型的有效性。     

一种基于退火策略的混沌神经网络优化算法

Ｈｏｐｆｉｅｌｄ网络（ＨＮＮ）中引入混沌机制,首先在混沌动态下粗搜索,并利用退火策略控制混沌动态退出和逆分贫出现,进而ＨＮＮ梯度优化搜索,提出了一种具有随机性和确定性并存的优化算法,对经典旅行商（ＴＳＰ）的研究,表明算法具有很强的克服陷入局部极小能力,较大程度提高了优化、时间和对初值的鲁棒性能,同时给出了模型参数对性能影响的一些结论。     

Intrinsic adaptation in autonomous recurrent neural networks

A massively recurrent neural network responds on one side to input stimuli and is autonomously active, on the other side, in the absence of sensory inputs. Stimuli and information processing depend crucially on the quality of the autonomous-state dynamics of the ongoing neural activity. This default neural activity may be dynamically structured in time and space, showing regular, synchronized, bursting, or chaotic activity patterns. We study the influence of nonsynaptic plasticity on the default dynamical state of recurrent neural networks. The nonsynaptic adaption considered acts on intrinsic neural parameters, such as the threshold and the gain, and is driven by the optimization of the information entropy. We observe, in the presence of the intrinsic adaptation processes, three distinct and globally attracting dynamical regimes: a regular synchronized, an overall chaotic, and an intermittent bursting regime. The intermittent bursting regime is characterized by intervals of regular flows, which are quite insensitive to external stimuli, interceded by chaotic bursts that respond sensitively to input signals. We discuss these findings in the context of self-organized information processing and critical brain dynamics.     

基于混沌神经网络的发电机定子绕组匝间短路故障诊断

本文采用耦合的混沌振荡子作为单个混沌神经元构造混沌神经网络模型，用改进Hebb算法设计网络的连接权值。在此基础上，实现了混沌神经网络的动态联想记忆并应用该混沌神经网络模型对发电机定子绕组匝间短路故障进行诊断。结果表明，该种方法有助于故障模式的记