Central Pattern Generator Parameters Research Articles

Robot motor learning shows emergence of frequency-modulated, robust swimming with an invariant Strouhal number.

Fish locomotion emerges from diverse interactions among deformable structures, surrounding fluids and neuromuscular activations, i.e. fluid-structure interactions (FSI) controlled by fish's motor systems. Previous studies suggested that such motor-controlled FSI may possess embodied traits. However, their implications in motor learning, neuromuscular control, gait generation, and swimming performance remain to be uncovered. Using robot models, we studied the embodied traits in fish-inspired swimming. We developed modular robots with various designs and used central pattern generators (CPGs) to control the torque acting on robot body. We used reinforcement learning to learn CPG parameters for maximizing the swimming speed. The results showed that motor frequency converged faster than other parameters, and the emergent swimming gaits were robust against disruptions applied to motor control. For all robots and frequencies tested, swimming speed was proportional to the mean undulation velocity of body and caudal-fin combined, yielding an invariant, undulation-based Strouhal number. The Strouhal number also revealed two fundamental classes of undulatory swimming in both biological and robotic fishes. The robot actuators were also demonstrated to function as motors, virtual springs and virtual masses. These results provide novel insights in understanding fish-inspired locomotion.

Zero-shot model-free learning of periodic movements for a bio-inspired soft-robotic arm

In recent years, soft robots gain increasing attention as a result of their compliance when operating in unstructured environments, and their flexibility that ensures safety when interacting with humans. However, challenges lie on the difficulty to develop control algorithms due to various limitations induced by their soft structure. In this paper, we introduce a novel technique that aims to perform motion control of a modular bio-inspired soft-robotic arm, with the main focus lying on facilitating the qualitative reproduction of well-specified periodic trajectories. The introduced method combines the notion behind two previously developed methodologies both based on the Movement Primitive (MP) theory, by exploiting their capabilities while coping with their main drawbacks. Concretely, the requested actuation is initially computed using a Probabilistic MP (ProMP)-based method that considers the trajectory as a combination of simple movements previously learned and stored as a MP library. Subsequently, the key components of the resulting actuation are extracted and filtered in the frequency domain. These are eventually used as input to a Central Pattern Generator (CPG)-based model that takes over the generation of rhythmic patterns at the motor level. The proposed methodology is evaluated on a two-module soft arm. Results show that the first algorithmic component (ProMP) provides an immediate estimation of the requested actuation by avoiding time-consuming training, while the latter (CPG) further simplifies the execution by allowing its control through a low-dimensional parameterization. Altogether, these results open new avenues for the rapid acquisition of periodic movements in soft robots, and their compression into CPG parameters for long-term storage and execution.

Central Pattern Generator (CPG)-Based Locomotion Control and Hydrodynamic Experiments of Synergistical Interaction between Pectoral Fins and Caudal Fin for Boxfish-like Robot.

Locomotion control of synergistical interaction between fins has been one of the key problems in the field of robotic fish research owing to its contribution to improving and enhancing swimming performance. In this paper, the coordinated locomotion control of the boxfish-like robot with pectoral and caudal fins is studied, and the effects of different control parameters on the propulsion performance are quantitatively analyzed by using hydrodynamic experiments. First, an untethered boxfish-like robot with two pectoral fins and one caudal fin was designed. Second, a central pattern generator (CPG)-based controller is used to coordinate the motions of the pectoral and caudal fins to realize the bionic locomotion of the boxfish-like robot. Finally, extensive hydrodynamic experiments are conducted to explore the effects of different CPG parameters on the propulsion performance under the synergistic interaction of pectoral and caudal fins. Results show that the amplitude and frequency significantly affect the propulsion performance, and the propulsion ability is the best when the frequency is 1 Hz. Different phase lags and offset angles between twisting and flapping of the pectoral fin can generate positive and reverse forces, which realize the forward, backward, and pitching swimming by adjusting these parameters. This paper reveals for the first time the effects of different CPG parameters on the propulsion performance in the case of the synergistic interaction between the pectoral fins and the caudal fin using hydrodynamic experimental methods, which sheds light on the optimization of the design and control parameters of the robotic fish.

유전 알고리즘을 이용한 뱀형 로봇 주행 패턴 생성

This paper presents a novel method of designing an efficient locomotion pattern generating algorithm for snake robots by a genetic algorithm (GA). In search and rescue operations in disaster areas, a snake robot requires multiple locomotion patterns. To overcome the complexity of snake robot control, we used a central pattern generator (CPG)-based control method which mimics the motion of a biological snake. GA was used to optimize CPG parameters to maximize locomotion performance. The locomotion performance according to the CPG parameters change was analyzed using the snake robot simulator. The proposed locomotion pattern generation algorithm evolved quickly for the target performance and obtained CPG parameters for the desired locomotion.

CPG-Based Hierarchical Locomotion Control for Modular Quadrupedal Robots Using Deep Reinforcement Learning

Modular robots have the potential for an unmatched ability to perform versatile and robust locomotion. However, designing effective and adaptive locomotion controllers for modular robots is challenging, resulting in a number of model-based methods that typically require various forms of prior knowledge. Deep reinforcement learning (DRL) provides a promising model-free approach for locomotion control by trial-and-error. However, current DRL methods often require extensive interaction data, hindering many possible applications. In this letter, a novel two-level hierarchical locomotion framework for modular quadrupedal robots is proposed. The approach combines a low-level central pattern generator (CPG)-based controller with a high-level neural network to learn a variety of locomotion tasks using DRL. The low-level CPG controller is pre-optimized to generate stable rhythmic walking gaits, while the high-level network is trained to modulate the CPG parameters for achieving task goals based on high-dimensional inputs, including the robot states and user commands. The proposed approach is employed on a simulated modular quadruped. With a limited amount of prior knowledge, the proposed method is demonstrated to be capable of learning a variety of locomotion skills such as velocity tracking, path following, and navigating to a target. Simulation results show that the proposed method can achieve higher sample efficiency than the model-free DRL method and are substantially more robust than the baseline methods to external disturbances and irregular terrain.

A Pathological Condition Affects Motor Modules in a Bipedal Locomotion Model.

Bipedal locomotion is a basic motor activity that requires simultaneous control of multiple muscles. Physiological experiments suggest that the nervous system controls bipedal locomotion efficiently by using motor modules of synergistic muscle activations. If these modules were merged, abnormal locomotion patterns would be realized as observed in patients with neural impairments such as chronic stroke. However, sub-acute patients have been reported not to show such merged motor modules. Therefore, in this study, we examined what conditions in the nervous system merges motor modules. we built a two-dimensional bipedal locomotion model that included a musculoskeletal model with 7 segments and 18 muscles, a neural system with a hierarchical central pattern generator (CPG), and various feedback inputs from reflex organs. The CPG generated synergistic muscle activations comprising 5 motor modules to produce locomotion phases. Our model succeeded to acquire stable locomotion by using the motor modules and reflexes. Next, we examined how a pathological condition altered motor modules. Specifically, we weakened neural inputs to muscles on one leg to simulate a stroke condition. Immediately after the simulated stroke, the model did not walk. Then, internal parameters were modified to recover stable locomotion. We refitted either (a) reflex parameters or (b) CPG parameters to compensate the locomotion by adapting (a) reflexes or (b) the controller. Stable locomotion was recovered in both conditions. However the motor modules were merged only in (b). These results suggest that light or sub-acute stroke patients, who can compensate stable locomotion by just adapting reflexes, would not show merge of motor modules, whereas severe or chronic patients, who needed to adapt the controller for compensation, would show the merge, as consistent with experimental findings.

Parallel Spine Design and CPG Motion Test of Quadruped Robot

The spine of mammals aids in the stability of locomotion. Central Pattern Generators (CPGs) located in spinal cord can rapidly provide a rhythmic output signal during loss of sensory feedback on the basis of a simulated quadruped agent. In this paper, active spine of quadruped robot is shown to be extremely effective in motion. An active spine model based on the Parallel Kinematic Mechanism (PKM) system and biological phenomena is described. The general principles involved in constructing a neural network coupled with limbs and spine to solve specific problems are discussed. A CPG mathematical model based on Hopf nonlinear oscillators produces rhythmic signal during locomotion is described, where many parameters to be solved must be formulated in terms of desired stability, often subject to vertical stability analysis. Our simulations demonstrate that active spine with setting reasonable CPG parameters can reduce unnecessary lateral displacement during trot gait, improving the stability of quadruped robot. In addition, we demonstrate that physical prototype mechanism provides a framework which shows correctness of simulation, and stability can thus be easily embodied within locomotion.

Kinematic study on a self-propelled bionic underwater robot with undulation and jet propulsion modes

SUMMARYThis paper proposed a novel type of bionic underwater robot (BUR). The undulation and jet propulsion modes on the self-propelled BUR were combined, and the kinematic characteristics of the two propulsion modes were thoroughly compared. First, the prototype and swimming strategy of the BUR were presented, and a dynamic model of the BUR was established based on several assumptions. Then, a central pattern generator (CPG) model allowing free adjustment of frequency and amplitude was employed to achieve the undulation propulsion of carangiform fish and the jet propulsion of jellyfish. Also, the kinematic characteristics of the two propulsion modes were investigated through experiments under different caudal fin actuation parameters. The experimental results indicate that the developed prototype can realize the undulation and jet propulsion by the means of the coordinated movement of the multi-caudal fins. By adjusting the CPG parameters, the BUR can switch the propulsion mode smoothly. Furthermore, the propulsion velocity of the BUR initially increased rapidly with the frequency and then slowed down when the frequency was greater than 0.8 Hz in both propulsion modes. The undulation propulsion velocity increased with the amplitude in the measurement ranges, however, the jet propulsion velocity initially increased quickly with the amplitude and then kept constant and even decreased when the amplitude was greater than 11 cm. Under the same caudal fin actuation parameters, the average velocity in undulation propulsion mode was higher than that in jet propulsion mode.

Optimizing central pattern generators (CPG) controller for one legged hopping robot by using genetic algorithm (GA)

This paper presents the optimization process of Central Pattern Generator (CPG) controller for one legged hopping robot by using Genetic Algorithm (GA). To control the one legged hopping robot, a CPG controller is designed and integrated with a conventional Proportional-Integral (PI) controller. Conventionally, the CPG parameters are tuned manually. But by using this method, the parameters produced are not exactly the optimum parameters for the CPG. Therefore, a computational stochastic optimization method; GA is designed to optimize the CPG controller parameters. The GA is designed based on minimizing the error produced towards achieving the reference height. The re-sponse of the one legged hopping robot is compared and the results of the error towards reference height are analyzed.

Consideration for application of central pattern generator to pneumatic anti-vibration apparatus (Parameter setting of CPG, change of switch input, and comparison of both inversion and non-inversion CPG)

For pneumatic anti-vibration apparatus (AVA) used in the precision positioning field, the authors have pursued the possibility of applying Central Pattern Generator (CPG) and realized its application in order to suppress flow disturbance caused by the pressure variation of the compressed air supplied to the pneumatic AVA. In the past, CPG has been mainly used for generation of desired values, such as analysis of biological movement and motion control of a quadruped walking robot. On the other hand, CPG has been implemented in the loop of the control system to improve the damping ability of the structure by the mass damper. The authors have also tried to improve the suppression effect of the disturbance by implementing CPG in the same way. However, the background of determining the parameters of CPG is not shown in any relevant documents. Therefore, this paper describes the parameter setting method for implementing CPG to the pneumatic AVA in detail. In addition, the characteristics and performances of CPG which have not been mentioned so far are revealed. Concretely, when switch input and signs for CPG input stage are changed, the influence of these is verified. These are summarized as consideration for application of CPG to the pneumatic AVA.

Model of a bilateral Brown-type central pattern generator for symmetric and asymmetric locomotion.

The coordinated activity of muscles is produced in part by spinal rhythmogenic neural circuits, termed central pattern generators (CPGs). A classical CPG model is a system of coupled oscillators that transform locomotor drive into coordinated and gait-specific patterns of muscle recruitment. The network properties of this conceptual model can be simulated by a system of ordinary differential equations with a physiologically inspired coupling locus of interactions capturing the timing relationship for bilateral coordination of limbs in locomotion. Whereas most similar models are solved numerically, it is intriguing to have a full analytical description of this plausible CPG architecture to illuminate the functionality within this structure and to expand it to include steering control. Here, we provided a closed-form analytical solution contrasted against the previous numerical method. The evaluation time of the analytical solution was decreased by an order of magnitude when compared with the numerical approach (relative errors, <0.01%). The analytical solution tested and supported the previous finding that the input to the model can be expressed in units of the desired limb locomotor speed. Furthermore, we performed parametric sensitivity analysis in the context of controlling steering and documented two possible mechanisms associated with either an external drive or intrinsic CPG parameters. The results identify specific propriospinal pathways that may be associated with adaptations within the CPG structure. The model offered several network configurations that may generate the same behavioral outcomes. NEW & NOTEWORTHY Using a simple process of leaky integration, we developed an analytical solution to a robust model of spinal pattern generation. We analyzed the ability of this neural element to exert locomotor control of the signal associated with limb speeds and tested the ability of this simple structure to embed steering control using the velocity signal in the model's inputs or within the internal connectivity of its elements.

Arm motion control model based on central pattern generator

According to the theory of Matsuoka neural oscillators and with the consideration of the fact that the human upper arm mainly consists of six muscles, a new kind of central pattern generator (CPG) neural network consisting of six neurons is proposed to regulate the contraction of the upper arm muscles. To verify effectiveness of the proposed CPG network, an arm motion control model based on the CPG is established. By adjusting the CPG parameters, we obtain the neural responses of the network, the angles of joint and hand of the model with MATLAB. The simulation results agree with the results of crank rotation experiments designed by Ohta et al., showing that the arm motion control model based on a CPG network is reasonable and effective.

A central pattern generator approach to footstep transition for biped navigation

Existing sampling-based footstep planning method for biped navigation used an intermediate static posture for footstep transition. However, when adopting this approach, the robot is sensitive to modeling error and external environments, and also the transition between different gait patterns is unnatural. This article presents a central pattern generator approach to footstep transition for biped navigation. First, this approach decomposes the biped walking motion into five motion types and designs central pattern generator network for all joints of legs accordingly. Then, the central pattern generator parameters are simplified and the relationship between these parameters and footstep transition is formulated. By modifying the central pattern generator parameters, different walking gaits can be obtained. With sensing feedbacks, self-adaption walking on irregular terrains, such as walking on unknown sloped terrains and flat floor with tiny obstacles, is realized. Experiments were conducted both in simulator and on a physical biped robot. Results have shown that the proposed approach is able to generate gesture transition trajectory for biped robot navigation and realize a self-adaption walking for irregular terrains.

パラサイクリング競技における最適クリート位置の探索

Para-cyclists that use below-knee prosthesis in both legs do not have the healthy characteristic information of their feet. To decide the cleat position, they have to consider the relation between the position and pedaling performance. In this study, angular velocity and kinetic energy were evaluated when the cleat position was changed. Two dimensional lower extremity model was used in this study. The joint torque was generated using a central pattern generator (CPG), and the parameters of CPG at a certain cleat position were optimized by a genetic algorithm. As a result, there were some conditions where higher angular velocity and lower work were obtained. Therefore, an adequate cleat position could be decided to suit to a physical characteristic of a para-cyclist, and consider the other kinematic or kinetic quantities in pedaling performance.

CPGと強化学習を用いた多脚ロボットの目標到達行動の獲得

The effectiveness of reinforcement learning for the real robots such as crawling robot and six-legged robot was demonstrated in our early studies. However, the acquired movements of those robots were the repetition of one step move and wait for observation at every time step. In other words, the acquired patterns were not smooth forward movements. In this paper, we realize that the multi-legged robots such as six-legged robot and four-legged robot acquire the smooth movements to the target direction and to reach the target area. In order to realize these tasks, we apply reinforcement learning to the multi-legged robots in which Central Pattern Generators (CPG) are implemented. CPG parameters to generate efficient walking patterns are optimized by using reinforcement learning. Through the experiments using the real multi-legged robots, we confirm the effectiveness of our method using CPG and reinforcement learning.

CPG Network Optimization for a Biomimetic Robotic Fish via PSO.

In this brief, we investigate the parameter optimization issue of a central pattern generator (CPG) network governed forward and backward swimming for a fully untethered, multijoint biomimetic robotic fish. Considering that the CPG parameters are tightly linked to the propulsive performance of the robotic fish, we propose a method for determination of relatively optimized control parameters. Within the framework of evolutionary computation, we use a combination of dynamic model and particle swarm optimization (PSO) algorithm to seek the CPG characteristic parameters for an enhanced performance. The PSO-based optimization scheme is validated with extensive experiments conducted on the actual robotic fish. Noticeably, the optimized results are shown to be superior to previously reported forward and backward swimming speeds.

Parameter Synthesis of Coupled Nonlinear Oscillators for CPG-Based Robotic Locomotion

This paper presents a numerical method for parameter synthesis of a central pattern generator (CPG) network to acquire desired locomotor patterns. The CPG network is modeled as a chain of unidirectionally or bidirectionally coupled Hopf oscillators with a novel coupling scheme that eliminates the influence of afferent signals on amplitude of the oscillator. The method converts the related CPG parameters into dynamic systems that evolve as part of the CPG network dynamics. The frequency, amplitude, and phase relations of teaching signals can be encoded by the CPG network with the proposed learning rules. The ability of the method to learn instructed locomotor pattern is proven with simulations. Application of the proposed method to online gait synthesis of a robotic fish is also presented.

Real-time Walking Pattern Generation for a Biped Robot with Hybrid CPG-ZMP Algorithm

Biped robots have better mobility than conventional wheeled robots. The bio-inspired method based on a central pattern generator (CPG) can be used to control biped robot walking in a manner like human beings. However, to achieve stable locomotion, it is difficult to modulate the parameters for the neural networks to coordinate every degree of freedom of the walking robot. The zero moment point (ZMP) method is very popular for the stability control of biped robot walking. However, the reference trajectories have low energy efficiency, lack naturalness and need significant offline calculation. This paper presents a new method for biped real-time walking generation using a hybrid CPG-ZMP control algorithm. The method can realize a stable walking pattern by combining the ZMP criterion with rhythmic motion control. The CPG component is designed to generate the desired motion for each robot joint, which is modulated by phase resetting according to foot contact information. By introducing the ZMP location, the activity of the CPG output signal is adjusted to coordinate the limbs’ motion and allow the robot to maintain balance during the process of locomotion. The numerical simulation results show that, compared with the CPG method, the new hybrid CPG-ZMP algorithm can enhance the robustness of the CPG parameters and improve the stability of the robot. In addition, the proposed algorithm is more energy efficient than the ZMP method. The results also demonstrate that the control system can generate an adaptive walking pattern through interactions between the robot, the CPG and the environment.

Simulation platform for the underwater snake-like robot swimming based on Kane’s dynamic model and central pattern generator

A systematic method for swimming control of the underwater snake-like robot is still lacking. We construct a simulation platform of the underwater snake-like robot swimming based on Kane’s dynamic model and central pattern generator (CPG). The partial velocity is deduced. The forces which contribute to dynamics are determined by Kane’s approach. Hydrodynamic coefficients are determined by experiments. Then, we design a CPG-based control architecture implemented as the system of coupled nonlinear oscillators. The CPG, like its biological counterpart, can produce coordinated patterns of rhythmic activity while being modulated by simple control parameters. The relations between the CPG parameters and the speed of the underwater snake-like robot swimming are investigated. Swimming in a straight line, turning, and switching between swimming modes are implemented in our simulation platform to prove the feasibility of the proposed simulation platform. The results show that the simulation platform can imitate different swimming modes of the underwater snake-like robot.

Coupling effect analysis between the central nervous system and the CPG network with proprioception

SUMMARYHuman rhythmic movement is generated by central pattern generators (CPGs), and their application to robot control has attracted interest of many scientists. But the coupling relationship between the central nervous system and the CPG network with external inputs is still not unveiled. According to biological experiment results, the CPG network is controlled by the neural system; in other words, the interaction between the central nervous system and the CPG network can control human movement effectively. This paper offers a complex human locomotion model, which illustrates the coupling relationship between the central nervous system and the CPG network with proprioception. Based on Matsuoka's CPG model (K. Matsuoka, Biol. Cybern. 52(6), 367–376 (1985)), the stability and robustness of the CPG network are analyzed with external inputs. In order to simulate the coupling relationship, the Radial Basis Function (RBF) neural network is used to simulate the cerebral cortex, and the Credit-Assignment Cerebellar Model Articulation Controller algorithm is employed to realize the locomotion mode conversion. A seven-link biped robot is chosen to simulate the walking gait. The main discoveries include: (1) the output of a new CPG network, which is stable and robust, can be treated as proprioception. Proprioception provides the central nervous system with the information about all joint angles; (2) analysis on a new locomotion model reveals that the cerebral cortex can modulate CPG parameters, leading to adjustment in walking gait.