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This paper aims to use the Matsuoka’s neural oscillators as the basic units of central pattern generator (CPG), and to offer a new CPG architecture consisting of a dual neural CPG of circular three links responsible for oscillator phase adjustment, to which an external neural oscillator is added, which is responsible for oscillator amplitude adjustment, to control foot depth to balance itself when treading on an obstacle.

It is equipped with a triaxial accelerometer and a triaxial gyroscope to obtain a real-time robot attitude, and to disintegrate the foot tilt in each direction as feedback signals to CPG to restore the robot’ horizontal attitude on an uneven terrain. The CPG controller is a distributed control method, with each foot controller consisting of a group of reciprocally coupling neural oscillators and sensors to generate different locomotion by different coupling patterns.

The experiment results indicated that the gait design method succeeded in enabling a steady hexapod walking on a rugged terrain, the mode of response is such that adjustments can only be made when the tilt occurs.

The overall control mechanism uses individual foot tilts as the feedback signal input to the neural oscillators to change the amplitude and compare against the reference oscillators of fixed amplitude to generate the foot height reference signals that can balance the body, and then convert the control signals, through a trajectory generator, to foot trajectories from which the actual rotation angle of servo motors can be obtained through inverse kinematics to achieve the effect of restoring the balance when traveling.

The controller design based on the bionic CPG model has the ability to restore its balance when its body tilts. In addition to the model’s ability to control locomotion, from the response waveforms of this experiment, it can also be noticed that it can control the foot depth to balance itself when treading on an obstacle, and it can adapt to a changing environment. When the obstacle is removed, the robot can quickly regain its balance.

The purpose of this paper is to extend an analysis presented in earlier work which investigated the dynamical behavior of a network of oscillatory units described by the amplitude of and phase of oscillations, and to present an objective function that can be successfully applied to multi‐layer networks.

In this paper, an objective function is presented that can be successfully applied to multi‐layer networks. The behavior of the objective function is explained through its ability to achieve a sparse representation of the inputs in complex‐valued space.

It is found that if the activity of each network unit is represented by a phasor in the complex plane, then sparsity is achieved when there is maximal phase separation in the complex plane. Increasing the spread of feedback connections is shown to improve segmentation performance significantly but does not affect separation performance. This enables a quantitative approach to characterizing and understanding cortical function.

The formulation of the multi‐layer objective function and the interpretation of its behavior through sparsity in complex space are novel contributions of this paper.

To achieve stable gait planning and enhance the motion performance of quadruped robot, this paper aims to propose a motion control strategy based on central pattern generator (CPG) and back-propagation neural network (BPNN).

First, the Kuramoto phase oscillator is used to construct the CPG network model, and a piecewise continuous phase difference matrix is designed to optimize the duty cycle of walk gait, so as to realize the gait planning and smooth switching. Second, the mapper between CPG output and joint drive is established based on BP neural network, so that the quadruped robot based on CPG control has better foot trajectory to enhance the motion performance. Finally, to obtain better mapping effect, an evaluation function is resigned to evaluate the proximity between the actual foot trajectory and the ideal foot trajectory. Genetic algorithm and particle swarm optimization are used to optimize the initial weights and thresholds of BPNN to obtain more accurate foot trajectory.

The method provides a solution for the smooth gait switching and foot trajectory of the robot. The quintic polynomial trajectory is selected to testify the validity and practicability of the method through simulation and prototype experiment.

The paper solved the incorrect duty cycle under the walk gait of CPG network constructed by Kuramoto phase oscillator, and made the robot have a better foot trajectory by mapper to enhance its motion performance.

The purpose of this paper is to introduce a motion control method for WFF-AmphiRobot, which can effectively realize the flexible motion of the robot on land, underwater and in the transition zone between land and water.

Based on the dynamics model, the authors selected the appropriate state variables to construct the state space model of the robot and estimated the feedback state of the robot through the maximum a posteriori probability estimation. The nonlinear predictive model controller of the robot is constructed by local linearization of the model to perform closed-loop control on the overall motion of the robot. For the control problem of the terminal trajectory, using the neural rhythmic movement theory in bionics to construct a robot central pattern generator (CPG) for real-time generation of terminal trajectory.

In this paper, the motion state of WFF-AmphiRobot is estimated, and a model-based overall motion controller for the robot and an end-effector controller based on neural rhythm control are constructed. The effectiveness of the controller and motion control algorithm is verified by simulation and physical prototype motion experiments on land and underwater, and the robot can ideally complete the desired behavior.

The paper designed a controller for WFF-AmphiRobot. First, when constructing the robot state estimator in this paper, the robot dynamics model is introduced as the a priori estimation model, and the error compensation of the a priori model is performed by the method of maximum a posteriori probability estimation, which improves the accuracy of the state estimator. Second, for the underwater oscillation motion characteristics of the flipper, the Hopf oscillator is used as the basis, and the flipper fluctuation equation is modified and improved by the CPG signal is adapted to the flipper oscillation demand. The controller effectively controls the position error and heading angle error within the desired range during the movement of the WFF-AmphiRobot.

An image contrast enhancement is one of the most important low‐level image pre‐processing tasks required by the vision‐based advanced driver assistance systems (ADAS). This paper seeks to address this important issue keeping the real time constraints in focus, which is especially vital for the ADAS.

The approach is based on a paradigm of nonlinear‐coupled oscillators in image processing. Each layer of the colored images is treated as an independent grayscale image and is processed separately by the paradigm. The pixels with the lowest and the highest gray levels are chosen and their difference is enhanced to span all the gray levels in an image over the entire gray level range, i.e. [0 1]. This operation enhances the contrast in each layer and the enhanced layers are finally combined to produce a color image of a much improved quality.

The approach performs robust contrast enhancement as compared to other approaches available in the relevant literature. Generally, other approaches do need a new setting of parameters for every new image to perform its task, i.e. contrast enhancement. These approaches are not useful for real‐time applications such as ADAS. Whereas, the proposed approach presented in this paper performs contrast enhancement for different images under the same setting of parameters, hence giving rise to the robustness in the system. The unique setting of parameters is derived through a bifurcation analysis explained in the paper.

The proposed approach is novel in different aspects. First, the proposed paradigm comprises of coupled differential equations, and therefore, offers a continuous model as opposed to other approaches in the relevant literature. This continuity in the model is an inherent feature of the proposed approach, which could be useful in realizing real‐time image processing with an analog implemented circuit of the approach. Furthermore, a novel framework combining coupled oscillatory paradigm and cellular neural network is also possible to achieve ultra‐fast solution in image contrast enhancement.

This study aims to establish a bio-inspired controller for realizing the bounding gait of a quadruped robot system presented in this paper.

The bio-inspired controller is divided into three levels to mimic the biological patterns of animals. First, the high-level sub-controller is equivalent to the cerebellum, which could plan and control the motion of animals. Second, the effect of the middle-level sub-controller corresponds to the central nervous system. The central pattern generators in the spine generate the stable and cyclic signals as the fundamental rhythm for periodic motion of the leg and spine joints. Third, the low-level sub-controller is equal to the end effector, which adopts the simple proportional-derivative (PD) control to realize the specific motion trajectory of the legs and spine.

Combined with the stability criterion presented previously and the delayed feedback control method, the bounding gait of the cheetah virtual prototype could be actuated and stabilized by the bio-inspired controller. Moreover, the bio-inspired controller is applied to realize the bounding gait of an SQBot, which is a quadruped robot with a spine joint. Meanwhile, the validity and practicability of the bio-inspired controller for the control of quadruped robot have been verified against different forward velocities.

The bio-inspired controller and bionic quadruped robot system are instructive for the designing and actuating of the real quadruped robot.

The purpose of this paper is to generate a virtual knee angle reference to be followed by a knee prosthesis control, using an adaptive central pattern generator (CPG). Also, to study the feasibility of this approach to implement a continuous control strategy on the prosthesis.

A CPG based on amplitude controlled phase oscillators (ACPOs) to track the current percentage of gait cycle on the prosthesis is proposed. Then, the virtual knee angle reference is generated along gait cycle, by interpolation with the corresponding angle of a sound knee. The structure and coupling of the CPG, as well as the control strategy are presented.

The coupling of the CPG with real gait on the prosthesis was proven, regardless of gait speed. Also, it was found that the maximum knee angle reached during walking is proportional to gait speed. Finally, generation of virtual knee angle reference to be followed by a prosthesis is demonstrated.

As only one event detected along gait cycle was used to update the CPG phase, the response to gait speed changes might be slow. Updating the CPG with more events remains for a future work.

The coupling of the CPG with real gait on the prosthesis results in a continuous gait cycle tracker, useful for any control strategy to be applied.

It is the first time a bio‐inspired concept as CPGs is applied to the prosthetic field. This could mean the beginning of a new era of cybernetic prostheses, which reproduce the lost limb and also the control functions of it.

This paper aims to develop a robofish with oscillating pectoral fins, and control it to mimic the bionic prototype by central pattern generators (CPGs).

First, the oscillation characteristics of the cownose ray were analyzed quantitatively. Second, a robofish with multi-joint pectoral fins was developed according to the bionic morphology and kinematics. Third, the improved phase oscillator was established, which contains a spatial asymmetric coefficient and a temporal asymmetric coefficient. Moreover, the CPG network is created to mimic the cownose ray and accomplish three-dimensional (3D) motions. Finally, the experiments were done to test the authors ' works.

The results demonstrate that the CPGs is effective to control the robofish to imitate the cownose ray realistically. In addition, the robofish is able to accomplish 3D motions of high maneuverability, and change among different swimming modes quickly and smoothly.

The research provides the method to develop a robofish from both 3D morphology and kinematics. The motion analysis and CPG control make sure that the robofish has the features of high maneuverability and camouflage. It is useful for military underwater applications and underwater detections in narrow environments. Second, this work lays the foundation for the autonomous 3D control. Moreover, the robotic fish can be taken as a scientific tool for the fluid bionics research.

The purpose of this paper is to present an analytical approximate technique to solve nonlinear conservative oscillator based on the He’s energy balance method (improved version recently presented by Khan and Mirzabeigy). The method is illustrated by solving double well Duffing oscillator.

The Duffing equation with a double-well potential (with a negative linear stiffness) is an important model of a mass particle moving in a symmetric double well potential. This form of the equation also appears in the transverse vibrations of a beam when the transverse and longitudinal deflections are coupled (Thompsen, 2003).

The approximate solutions obtained by the present technique have good agreement with the numerical solution and also provide better results than other existing methods.

The results are more accurate than those obtained by other existing methods. The relative errors obtained by the present paper are less than those obtained by other existing methods. Therefore, the present technique is very effective and convenient for solving nonlinear conservative oscillator.

The purpose of this paper is to present an analytical technique, based on the He’s energy balance method (an improved version recently presented by Khan et al.), to obtain the approximate solution of quadratic nonlinear oscillator (QNO).

This oscillator (QNO) is used as a mathematical model of the human eardrum oscillation.

It has been shown that the results by the present technique are very close to the numerical solution.

The results obtained in this paper are compared with those obtained by Hu (harmonic balance method) and Khan et al. The result shows that the method is more accurate and effective than harmonic balance as well as improved energy balance methods.