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To control one of the joints during the actual movement of the hydraulically driven quadruped robot, all the other joints in the leg need to be locked. Once the joints are unlocked, there is a coupling effect among the joints. Therefore, during the normal exercise of the robot, the movement of each joint is affected by the coupling of other joints. This brings great difficulties to the coordinated motion control of the multi-joints of the robot. Therefore, it is necessary to reduce the influence of the coupling of the hydraulically driven quadruped robot.

To solve the coupling problem with the joints of the hydraulic quadruped robot, based on the principle of mechanism dynamics and hydraulic control, the dynamic mathematical model of the single leg mechanism of the hydraulic quadruped robot is established. On this basis, the coupling dynamics model of the two joints of the thigh and the calf is derived. On the basis of the multivariable decoupling theory, a neural network (NN) model reference decoupling controller is designed.

The simulation and prototype experiment are carried out between the thigh joint and the calf joint of the hydraulic quadruped robot, and the results show that the proposed NN model reference decoupling control method is effective, and this method can reduce the cross-coupling between the thigh and the calf and improve the dynamic characteristics of the single joint of the leg.

The proposed method provides technical support for the mechanical–hydraulic cross-coupling among the joints of the hydraulic quadruped robot, achieving coordinated movement of multiple joints of the robot and promoting the performance and automation level of the hydraulic quadruped robot.

On the basis of the theory of multivariable decoupling, a new decoupling control method is proposed, in which the mechanical–hydraulic coupling is taken as the coupling behavior of the hydraulic foot robot. The method reduces the influence of coupling of system, improves the control precision, realizes the coordinated movement among multiple joints and promotes the popularization and use of the hydraulically driven quadruped robot.

This paper aims to introduce a novel design of the biomimetic quadruped robot, including its body structure, three structural modes and respective workspace.

By taking a metamorphic 8-bar linkage as the body of a quadruped robot, the authors propose a reconfigurable walking robot that can imitate three kinds of animals: mammals (e.g. dog), arthropods (e.g. stick insect) and reptiles (e.g. lizard). Furthermore, to analyze the three structural modes of this quadruped robot, the workspace is calculated and studied.

Based on experimental data analyses, it is revealed that the metamorphic quadruped robot can walk in all its three structural modes and adapt to different terrains.

Because the body of the quadruped robot is deformable and reconfigurable, the location of payload is not considered in the current stage.

The relative positions and postures of legs of the metamorphic robot can be rearranged during its body reconfiguration in such a way to combine all the features of locomotion of the three kinds of animals into one robot. So, the metamorphic quadruped robot is capable of maintaining wider stability margins than conventional rigid-body quadruped robots and conducting operations in different environments, particularly the extreme and restricted occasions due to the changeable and adaptable trunk.

The main contribution is the development of a reconfigurable biomimetic quadruped robot, which uses the metamorphic 8-bar linkage. This robot can easily reshape to three different structural modes and mimic the walking patterns of all mammals, arthropods and reptiles.

The purpose of this paper is to introduce a quadruped robot strategy to avoid tipping down because of side impact disturbance and a control algorithm that guarantees the strategy can be controlled stably even in the presence of disturbances or model uncertainties.

A quadruped robot was developed. Trot gait is applied so the quadruped can be modelled as a compass biped model. The algorithm to find a correct stepping position after an impact was developed. A particle swarm optimization-based structure-specified mixed sensitivity (H₂/H_∞) robust is applied to reach the stepping position.

By measuring the angle and speed of the side tipping after an impact disturbance, a point location for the robot to step or the foothold recovery point (FRP) was successfully generated. The proposed particle swarm optimization-based structure-specified mixed sensitivity H₂/H_∞ robust control also successfully brought the legs to the desired point.

A traditional H_∞ controller synthesis usually results in a very high order of controller. This makes implementation on an embedded controller very difficult. The proposed controller is just a second-order controller but it can handle the uncertainties and disturbances that arise and guarantee that FRP can be reached.

The first contribution is the proposed low-order robust H₂/H_∞ controller so it is easy to be programmed on a small embedded system. The second is FRP, a stepping point for a quadruped robot after receiving side impact disturbance so the robot will not fall.

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.

Legged walking robots have numerous advantages over the wheel or tracked robots due to their strong operational ability and exposure to the complex environment. This paper aims to present details about the mechanical formation and a new conceptual elliptical trajectory generation discussed throughout the paper of the quadruped robot.

Initially, a realistic CAD model of the four-legged robot is developed in Solidwork-2019. The proposed model’s forward and inverse kinematics equations are deduced using Denavit–Hartenberg parameters. Based on geometry and kinematics, manipulability and obstacle avoidance are investigated. A method of galloping trajectory is proposed for aiming the increase of upright direction impulse, which is produced by ground reaction force at each step frequency. Furthermore, the locomotion equation of the ellipse trajectory is derived by setting transition angle polynomial of free-fall phase, stance phase and swing phase and the constraints.

Finally, a successive simulation on a 2D sagittal plane is performed to check and verify the usefulness of the proposed trajectory. Before the development of the full quadruped, a single prototype leg is generated for experimental verification of the dynamic simulations.

The proposed trajectory is novel in that it uses force tracking control, which is intended to improve the quadruped robot’s robustness and stability.

The computing power of the legged robot is not enough to perform high-frequency updates for the full-body model predictive control (MPC) of the robot, which is a common problem encountered in the gait research of the legged robot. The purpose of this paper is to propose a high-frequency MPC control method for the bounding gait of a parallel quadruped robot.

According to the bounding gait characteristics of the robot, the quadruped robot model is simplified to an equivalent plane bipedal model. Under the biped robot model, the forces between the robot’s feet and the ground are calculated by MPC. Then, the authors apply a proportional differential controller to distribute these forces to the four feet of the quadruped robot. The robot video can be seen at www.bilibili.com/video/BV1je4y1S7Rn.

To verify the feasibility of the controller, a prototype was made, and the controller was deployed on the actual prototype and then fully analyzed through experiments. Experiments show that the update frequency of MPC could be stabilized at 500 Hz while the robot was running in the bounding gait stably and efficiently.

This paper proposes a high-frequency MPC controller under the simplified model, which has a higher working efficiency and more stable control performance.

This study proposes a predictive neural network model reference decoupling control method for the coupling problem between the leg joints of hydraulic quadruped robots, and verifies its decoupling effect..

The machine–hydraulic cross-linking coupling is studied as the coupling behavior of the hydraulically driven quadruped robot, and the mechanical dynamics coupling force of the robot system is controlled as the disturbance force of the hydraulic system through the Jacobian matrix transformation. According to the principle of multivariable decoupling, a prediction-based neural network model reference decoupling control method is proposed; each module of the control algorithm is designed one by one, and the stability of the system is analyzed by the Lyapunov stability theorem.

The simulation and experimental research on the robot joint decoupling control method is carried out, and the prediction-based neural network model reference decoupling control method is compared with the decoupling control method without any decoupling control method. The results show that taking the coupling effect experiment between the hip joint and knee joint as an example, after using the predictive neural network model reference decoupling control method, the phase lag of the hip joint response line was reduced from 20.3° to 14.8°, the amplitude attenuation was reduced from 1.82% to 0.21%, the maximum error of the knee joint coupling line was reduced from 0.67 mm to 0.16 mm and the coupling effect between the hip joint and knee joint was reduced from 1.9% to 0.48%, achieving good decoupling.

The prediction-based neural network model reference decoupling control method proposed in this paper can use the neural network model to predict the next output of the system according to the input and output. Finally, the weights of the neural network are corrected online according to the predicted output and the given reference output, so that the optimization index of the neural network decoupling controller is extremely small, and the purpose of decoupling control is achieved.

Jumping robots with coordinated multiple legs have been a hot research subject during the past years because of their excellent abilities in fast moving and obstacle-climbing. However, dynamics of jumping process of these coordinated legged robots are complex because of collisions between coordinated legs and the ground. This paper aims to analyze features of jumping process and to present the kinematic and dynamic models of a novel sole-type quadruped jumping robot with variable coordinated joints.

A complete jumping period of is divided into several subphases according to contact status of different coordinated legs to the ground. Continuous dynamics and discrete dynamics are established in different subphases. Simulations are performed in MATLAB software and ADAMS environment.

Comparison between two-set simulated results acquired from ADAMS and MATLAB demonstrates the validity of kinematic and dynamic equations.

The established dynamics establish the foundation of further research in motion planning and controller design of coordinated multiple legs.

This paper presents an evolutionary algorithm (EA) for Sony legged robots to learn good walking behaviours with little or no interaction with the designers. Once the learning method is put into place, the module can learn through its interaction with the real world.

An EA for developing locomotion gaits of quadruped walking robots is presented in this paper. It is based on a hybrid approach that changes the probability of genetic operators in respect to the performance of the operator's offspring.

The mutating and combination behaviours of the genetic algorithms allow the process to develop a useful behaviour over time. The resulting gait from this training proved to be a better solution than the non‐interference training for movements over all types of surfaces, pointing to a local optima being discovered in the non‐environmental interference situation.

The behaviour of these algorithms is stochastic so that they may potentially present different solutions in different runs of the same algorithm. The mechanism described here has several features that should be noted. It allows rapid parameterisation of operator probabilities across the range of potential genetic algorithms and operator set. It is tailored to a steady state reproduction scheme. It would not be literally applicable to problems with noisy evaluation functions.

Provides novel application of genetic algorithms to a potentially practical application area.

The paper aims to present a new mechanical scheme for a leg to be included in legged vehicles that simplifies the control actuations along the stride.

The scheme includes three four‐bar links grouped in two mechanisms. The first one decouples the vertical and horizontal foot movements. The second one produces a constant horizontal foot velocity when the corresponding motor is given a constant speed. A hybrid robot with wheels at the end of the hind legs has been simulated and constructed to validate the leg performance.

The gait control requires only five commands for the electronic cards to control the leg. Decoupling vertical and horizontal movements allows a more adequate selection of actuators, a reduction of energy consumption, and higher load capacity and robot velocity. Additional mechanical benefits, such as improved robustness and lower inertia, are obtained. The hind legs can also be articulated, allowing the robot to overcome an obstacle and to climb up and down stairs.

A hybrid robot offers greater stability with respect to a legged robot. This way the lateral movement is not a concern, and therefore it has not been tested yet during the walking cycle.

This new scheme obtains a quasi‐Cartesian behaviour for the foot movement that drastically simplifies the control of the walking cycle. Although the decoupling between movements has already been obtained in previous configurations, these follow a pantograph structure and suffer from blocking problems when they are subject to lateral forces. These schemes were suitable for crab‐like gaits. The proposed leg moves according to a mammal‐like gait.