Analysis of the gait generation principle by a simulated quadruped model with a CPG incorporating vestibular modulation

This study aims to understand the principles of gait generation in a quadrupedal model. It is difficult to determine the essence of gait generation simply by observation of the movement of complicated animals composed of brains, nerves, muscles, etc. Therefore, we build a planar quadruped model with simplified nervous system and mechanisms, in order to observe its gaits under simulation. The model is equipped with a mathematical central pattern generator (CPG), consisting of four coupled neural oscillators, basically producing a trot pattern. The model also contains sensory feedback to the CPG, measuring the body tilt (vestibular modulation). This spontaneously gives rise to an unprogrammed lateral walk at low speeds, a transverse gallop while running, in addition to trotting at a medium speed. This is because the body oscillation exhibits a double peak per leg frequency at low speeds, no peak (little oscillation) at medium speeds, and a single peak while running. The body oscillation autonomously adjusts the phase differences between the neural oscillators via the feedback. We assume that the oscillations of the four legs produced by the CPG and the body oscillation varying according to the current speed are synchronized along with the varied phase differences to keep balance during locomotion through postural adaptation via the vestibular modulation, resulting in each gait. We succeeded in determining a single simple principle that accounts for gait transition from walking to trotting to galloping, even without brain control, complicated leg mechanisms, or a flexible trunk.     

An Efficient Gait-generating Method for Electrical Quadruped Robot Based on Humanoid Power Planning Approach

The research field of legged robots has always relied on the bionic robotic research,especially in locomotion regulating approaches,such as foot trajectory planning,body stability regulating and energy efficiency prompting.Minimizing energy consumption and keeping the stability of body are considered as two main characteristics of human walking.This work devotes to develop an energy-efficient gait control method for electrical quadruped robots with the inspiration of human walking pattern.Based on the mechanical power distribution trend,an efficient humanoid power redistribution approach is established for the electrical quadruped robot.Through studying the walking behavior acted by mankind,such as the foot trajectory and change of mechanical power,we believe that the proposed controller which includes the bionic foot movement trajectory and humanoid power redistribution method can be implemented on the electrical quadruped robot prototype.The stability and energy efficiency of the proposed controller are tested by the simulation and the single-leg prototype experi-ment.The results verify that the humanoid power planning approach can improve the energy efficiency of the electrical quadruped robots.     

Development of a Biomimetic Quadruped Robot

This paper presents the design and prototype of a small quadruped robot whose walking motion is realized by two piezocomposite actuators. In the design, biomimetic ideas are employed to obtain the agility of motions and sustainability of a heavy load. The design of the robot legs is inspired by the leg configuration of insects, two joints （hip and knee） of the leg enable two basic motions, lifting and stepping. The robot frame is designed to have a slope relative to the horizontal plane, which makes the robot move forward. In addition, the bounding locomotion of quadruped animals is implemented in the robot. Experiments show that the robot can carry an additional load of about 100 g and run with a fairly high velocity. The quadruped prototype can be an important step towards the goal of building an autonomous mobile robot actuated by piezocomposite actuators.     

An Approach for Adaptive Limbless Locomotion Using a CPG-Based Reflex Mechanism

Animals＇ free movement in natural environments has attracted many researchers to explore control methods for bio-inspired robots. This paper presents a novel reflex mechanism based on a Central Pattern Generator （CPG） for adaptive locomotion of limbless robots. First, inspired by the concept of reflex arc, the reflex mechanism is designed on a connectionist CPG model. Since the CPG model inspired by the spinal cord of lampreys is developed at the neuron level, it provides a possible natural solution for sensory reflex integration. Therefore, sensory neurons that bridge the external stimuli and the CPG model, together with the concept of reflex arc, are utilized for designing the sensory reflex mechanism. Then, a border reflex and a body reflex are further developed and applied on the ends and the middle part of a limbless robot, respectively. Finally, a ball hitting scenario and a corridor passing scenario are designed to verify the proposed method. Results of simulations and on-site experiments show the feasibility and effectiveness of the reflex mechanism in realizing fast response and adaptive limbless locomotion.     

Sensory feedback in CNN-based central pattern generators

Central Pattern Generators (CPGs) are a suitable paradigm to solve the problem of locomotion control in walking robots. CPGs are able to generate feed-forward signals to achieve a proper coordination among the robot legs. In literature they are often modelled as networks of coupled nonlinear systems. However the topic of feedback in these systems is rarely addressed. On the other hand feedback is essential for locomotion. In this paper the CPG for a hexapod robot is implemented through Cellular Neural Networks (CNNs). Feedback is included in the CPG controller by exploiting the dynamic properties of the CPG motor-neurons, such as synchronization issue and local bifurcations. These universal paradigms provide the essential issues to include sensory feedback in CPG architectures based on coupled nonlinear systems. Experiments on a dynamic model of a hexapod robot are presented to validate the approach introduced.     

Extended Evolutionary Fast Learn-to-Walk Approach for Four-Legged Robots

Robot locomotion is an active research area. In this paper we focus on the locomotion of quadruped robots. An effective walking gait of quadruped robots is mainly concerned with two key aspects, namely speed and stability. The large search space of potential parameter settings for leg joints means that hand tuning is not feasible in general. As a result walking parameters are typically determined using machine learning techniques. A major shortcoming of using machine learning techniques is the significant wear and tear of robots since many parameter combinations need to be evaluated before an optimal solution is found.This paper proposes a direct walking gait learning approach, which is specifically designed to reduce wear and tear of robot motors, joints and other hardware. In essence we provide an effective learning mechanism that leads to a solution in a faster convergence time than previous algorithms. The results demonstrate that the new learning algorithm obtains a faster convergence to the best solutions in a short run. This approach is significant in obtaining faster walking gaits which will be useful for a wide range of applications where speed and stability are important. Future work will extend our methods so that the faster convergence algorithm can be applied to a two legged humanoid and lead to less wear and tear whilst still developing a fast and stable gait.     

Multi-layered multi-pattern CPG for adaptive locomotion of humanoid robots

In this paper, we present an extended mathematical model of the central pattern generator (CPG) in the spinal cord. The proposed CPG model is used as the underlying low-level controller of a humanoid robot to generate various walking patterns. Such biological mechanisms have been demonstrated to be robust in locomotion of animal. Our model is supported by two neurophysiological studies. The first study identified a neural circuitry consisting of a two-layered CPG, in which pattern formation and rhythm generation are produced at different levels. The second study focused on a specific neural model that can generate different patterns, including oscillation. This neural model was employed in the pattern generation layer of our CPG, which enables it to produce different motion patterns—rhythmic as well as non-rhythmic motions. Due to the pattern-formation layer, the CPG is able to produce behaviors related to the dominating rhythm (extension/flexion) and rhythm deletion without rhythm resetting. The proposed multi-layered multi-pattern CPG model (MLMP-CPG) has been deployed in a 3D humanoid robot (NAO) while it performs locomotion tasks. The effectiveness of our model is demonstrated in simulations and through experimental results.     

Effects of Pendular Waist on Gecko's Climbing: Dynamic Gait,Analytical Model and Bio-inspired Robot

Most quadruped reptiles,such as lizards,salamanders and crocodiles,swing their waists while climbing on horizontal or vertical surfaces.Accompanied by body movement,the centroid trajectory also becomes more of a zigzag path rather than a straight line.Inspired by gecko's gait and posture on a vertical surface,a gecko inspired model with one pendular waist and four active axil legs,which is called GPL model,is proposed.Relationship between the waist position,dynamic gait,and driving forces on supporting feet is analyzed.As for waist trajectory planning,a singular line between the supporting feet is found and its effects on driving forces are discussed.Based on the GPL model,it is found that a sinusoidal waist trajectory,rather than a straight line,makes the driving forces on the supporting legs smaller.Also,a waist close to the pygal can reduce the driving forces compared to the one near middle vertebration,which is in accord with gecko's body bending in the process of climbing.The principles of configuration design and gait planning are proposed based on theoretical analyses.Finally,a bio-inspired robot DracoBot is developed and both of the driving force measurements and climbing experiments reinforce theoretical analysis and the rationality of gecko's dynamic gait.     

Virtual Constraint Based Control of Bounding Gait of Quadruped Robots

This paper presents a control approach for bounding gait of quadruped robots by applying the concept of Virtual Constraints (VCs).A VC is a relative motion relation between two related joints imposed to the robots in terms of a specified gait,which can drive the robot to run with desired gait.To determine VCs for highly dynamic bounding gait,the limit cycle motions of the passive dynamic model of bounding gait are analyzed.The leg length and hip/shoulder angle trajectories corresponding to the limit cycles are parameterized by leg angles using 4 th-order polynomials.In order to track the calculated periodic motions,the polynomials are imposed on the robot as virtual motion constraints by a high-level state machine controller.A bounding speed feedback strategy is introduced to stabilize the robot running speed and enhance the stability.The control approach was applied to a newly designed lightweight bioinspired quadruped robot,AgiDog.The experimental results demonstrate that the robot can bound at a frequency up to 5 Hz and bound at a maximum speed of 1.2 m·s-1 in sagittal plane with a Froude number approximating to 1.     

Computational Models to Synthesize Human Walking

The synthesis of human walking is of great interest in biomechanics and biomimetic engineering due to its predictive capabilities and potential applications in clinical biomechanics, rehabilitation engineering and biomimetic robotics. In this paper, the various methods that have been used to synthesize humanwalking are reviewed from an engineering viewpoint. This involves a wide spectrum of approaches, from simple passive walking theories to large-scale computational models integrating the nervous, muscular and skeletal systems. These methods are roughly categorized under four headings： models inspired by the concept of a CPG （Central Pattern Generator）, methods based on the principles of control engineering, predictive gait simulation using optimisation, and models inspired by passive walking theory. The shortcomings and advantages of these methods are examined, and future directions are discussed in the context of providing insights into the neural control objectives driving gait and improving the stability of the predicted gaits. Future advancements are likely to be motivated by improved understanding of neural control strategies and the subtle complexities of the musculoskeletal system during human locomotion. It is only a matter of time before predictive gait models become a practical and valuable tool in clinical diagnosis, rehabilitation engineering and robotics.     

Control of a Quadruped Robot with Bionic Springy Legs in Trotting Gait

Legged robots have better performance on discontinuous terrain than that of wheeled robots. However, the dynamic trotting and balance control of a quadruped robot is still a challenging problem, especially when the robot has multi-joint legs. This paper presents a three-dimensional model of a quadruped robot which has 6 Degrees of Freedom （DOF） on torso and 5 DOF on each leg. On the basis of the Spring-Loaded Inverted Pendulum （SLIP） model, body control algorithm is discussed in the first place to figure out how legs work in 3D trotting. Then, motivated by the principle of joint function separation and introducing certain biological characteristics, two joint coordination approaches are developed to produce the trot and provide balance. The robot reaches the highest speed of 2.0 m.s-1, and keeps balance under 250 Kg.m.s-1 lateral disturbance in the simulations. The effectiveness of these approaches is also verified on a prototype robot which runs to 0.83 m.s-1 on the treadmill, The simulations and experiments show that legged robots have good biological properties, such as the ground reaction force, and spring-like leg behavior.     

Models of central pattern generators for quadruped locomotion II. Secondary gaits

We continue the analysis of the network of symmetrically coupled cells modeling central pattern generators (CPG) for quadruped locomotion proposed by Golubitsky, Stewart, Buono and Collins by studying secondary gaits. Secondary gaits are modeled by output signals from the CPG where each cell emits one of two different output signals along with exact phase shifts. Examples of secondary gaits are transverse gallop, rotary gallop, and canter. We classify secondary gaits that bifurcate when the Poincaré map of a primary gait has a real eigenvalue crossing the unit circle. In particular, we show that periodic solutions modeling transverse gallop and rotary gallop bifurcate from primary gaits. Moreover, we find gaits from period-doubling bifurcations and analyze plausible footfall patterns. Numerical simulations are performed using the Morris-Lecar equations as cell dynamics.     

Visually guided gait modifications for stepping over an obstacle: a bio-inspired approach

There is an increasing interest in conceiving robotic systems that are able to move and act in an unstructured and not predefined environment, for which autonomy and adaptability are crucial features. In nature, animals are autonomous biological systems, which often serve as bio-inspiration models, not only for their physical and mechanical properties, but also their control structures that enable adaptability and autonomy—for which learning is (at least) partially responsible. This work proposes a system which seeks to enable a quadruped robot to online learn to detect and to avoid stumbling on an obstacle in its path. The detection relies in a forward internal model that estimates the robot’s perceptive information by exploring the locomotion repetitive nature. The system adapts the locomotion in order to place the robot optimally before attempting to step over the obstacle, avoiding any stumbling. Locomotion adaptation is achieved by changing control parameters of a central pattern generator (CPG)-based locomotion controller. The mechanism learns the necessary alterations to the stride length in order to adapt the locomotion by changing the required CPG parameter. Both learning tasks occur online and together define a sensorimotor map, which enables the robot to learn to step over the obstacle in its path. Simulation results show the feasibility of the proposed approach.     

Velocity Control of a Bounding Quadruped via Energy Control and Vestibular Reflexes

In this paper a bio-inspired approach of velocity control for a quadruped robot running with a bounding gait on compliant legs is set up. The dynamic properties ofa sagittal plane model of the robot are investigated. By analyzing the stable fixed points based on Poincare map, we find that the energy change of the system is the main source for forward velocity adjustment. Based on the analysis of the dynamics model of the robot, a new simple linear running controller is proposed using the energy control idea, which requires minimal task level feedback and only controls both the leg torque and ending impact angle. On the other hand, the functions of mammalian vestibular reflexes are discussed, and a reflex map between forward velocity and the pitch movement is built through statistical regression analysis. Finally, a velocity controller based on energy control and vestibular reflexes is built, which has the same structure as the mammalian nervous mechanism for body posture control. The new con- troller allows the robot to run autonomously without any other auxiliary equipment and exhibits good speed adjustment capa- bility. A series simulations and experiments were set to show the good movement agility, and the feasibility and validity of the robot system.     

Hard-wired central pattern generators for quadrupedal locomotion

Animal locomotion is generated and controlled, in part, by a central pattern generator (CPG), which is an intraspinal network of neurons capable of producing rhythmic output. In the present work, it is demonstrated that a hard-wired CPG model, made up of four coupled nonlinear oscillators, can produce multiple phase-locked oscillation patterns that correspond to three common quadrupedal gaits — the walk, trot, and bound. Transitions between the different gaits are generated by varying the network's driving signal and/or by altering internal oscillator parameters. The above in numero results are obtained without changing the relative strengths or the polarities of the system's synaptic interconnections, i.e., the network maintains an invariant coupling architecture. It is also shown that the ability of the hard-wired CPG network to produce and switch between multiple gait patterns is a model-independent phenomenon, i.e., it does not depend upon the detailed dynamics of the component oscillators and/or the nature of the inter-oscillator coupling. Three different neuronal oscillator models — the Stein neuronal model, the Van der Pol oscillator, and the FitzHugh-Nagumo model -and two different coupling schemes are incorporated into the network without impeding its ability to produce the three quadrupedal gaits and the aforementioned gait transitions.     

Energy efficient walking with central pattern generators: from passive dynamic walking to biologically inspired control

Like human walking, passive dynamic walking—i.e. walking down a slope with no actuation except gravity—is energy efficient by exploiting the natural dynamics. In the animal world, neural oscillators termed central pattern generators (CPGs) provide the basic rhythm for muscular activity in locomotion. We present a CPG model, which automatically tunes into the resonance frequency of the passive dynamics of a bipedal walker, i.e. the CPG model exhibits resonance tuning behavior. Each leg is coupled to its own CPG, controlling the hip moment of force. Resonance tuning above the endogenous frequency of the CPG—i.e. the CPG’s eigenfrequency—is achieved by feedback of both limb angles to their corresponding CPG, while integration of the limb angles provides resonance tuning at and below the endogenous frequency of the CPG. Feedback of the angular velocity of both limbs to their corresponding CPG compensates for the time delay in the loop coupling each limb to its CPG. The resonance tuning behavior of the CPG model allows the gait velocity to be controlled by a single parameter, while retaining the energy efficiency of passive dynamic walking.     

A passive dynamic walking robot that has a deterministic nonlinear gait

There is a growing body of evidence that the step-to-step variations present in human walking are related to the biomechanics of the locomotive system. However, we still have limited understanding of what biomechanical variables influence the observed nonlinear gait variations. It is necessary to develop reliable models that closely resemble the nonlinear gait dynamics in order to advance our knowledge in this scientific field. Previously, Goswami et al. [1998. A study of the passive gait of a compass-like biped robot: symmetry and chaos. International Journal of Robotic Research 17(12)] and Garcia et al. [1998. The simplest walking model: stability, complexity, and scaling. Journal of Biomechanical Engineering 120(2), 281-288] have demonstrated that passive dynamic walking computer models can exhibit a cascade of bifurcations in their gait pattern that lead to a deterministic nonlinear gait pattern. These computer models suggest that the intrinsic mechanical dynamics may be at least partially responsible for the deterministic nonlinear gait pattern; however, this has not been shown for a physical walking robot. Here we use the largest Laypunov exponent and a surrogation analysis method to confirm and extend Garcia et al.'s and Goswami et al.'s original results to a physical passive dynamic walking robot. Experimental outcomes from our walking robot further support the notion that the deterministic nonlinear step-to-step variations present in gait may be partly governed by the intrinsic mechanical dynamics of the locomotive system. Furthermore the nonlinear analysis techniques used in this investigation offer novel methods for quantifying the nature of the step-to-step variations found in human and robotic gait.     

Symmetrical gaits of primates

Walking and symmetrical running gaits of 26 genera of primates are analyzed using numerical and graphical methods described previously. The raw data are 1701 feet of 16 mm motion picture film mostly exposed at 64 frames per second. Adult monkeys and apes usually use the walking trot or diagonal-sequence walks. Individual monkeys occasionally use lateral-sequence walks resembling those that are usual for human infants. Human children moving on hands and feet use gaits ranging from the walking pace through the lateral-sequence walks to the walking trot. An infant macaque studied from age 17 hours to 96 days first walked with a lateral-sequence, diagonal-couplets gait and then gradually shifted to the diagonal-sequence, diagonal-couplets gait of the adult. Few non-primates use the diagonal-sequence walks which are typical of primates. Typical support sequences are figured. Relative placement of feet and consequent slight asymmetry are described.     

Cavemen Were Better at Depicting Quadruped Walking than Modern Artists: Erroneous Walking Illustrations in the Fine Arts from Prehistory to Today

The experts of animal locomotion well know the characteristics of quadruped walking since the pioneering work of Eadweard Muybridge in the 1880s. Most of the quadrupeds advance their legs in the same lateral sequence when walking, and only the timing of their supporting feet differ more or less. How did this scientific knowledge influence the correctness of quadruped walking depictions in the fine arts? Did the proportion of erroneous quadruped walking illustrations relative to their total number (i.e. error rate) decrease after Muybridge? How correctly have cavemen (upper palaeolithic Homo sapiens) illustrated the walking of their quadruped prey in prehistoric times? The aim of this work is to answer these questions. We have analyzed 1000 prehistoric and modern artistic quadruped walking depictions and determined whether they are correct or not in respect of the limb attitudes presented, assuming that the other aspects of depictions used to determine the animals gait are illustrated correctly. The error rate of modern pre-Muybridgean quadruped walking illustrations was 83.5%, much more than the error rate of 73.3% of mere chance. It decreased to 57.9% after 1887, that is in the post-Muybridgean period. Most surprisingly, the prehistoric quadruped walking depictions had the lowest error rate of 46.2%. All these differences were statistically significant. Thus, cavemen were more keenly aware of the slower motion of their prey animals and illustrated quadruped walking more precisely than later artists.