Behaviour-based modelling of hexapod locomotion: linking biology and technical application

Walking in insects and most six-legged robots requires simultaneous control of up to 18 joints. Moreover, the number of joints that are mechanically coupled via body and ground varies from one moment to the next, and external conditions such as friction, compliance and slope of the substrate are often unpredictable. Thus, walking behaviour requires adaptive, context-dependent control of many degrees of freedom. As a consequence, modelling legged locomotion addresses many aspects of any motor behaviour in general. Based on results from behavioural experiments on arthropods, we describe a kinematic model of hexapod walking: the distributed artificial neural network controller walknet. Conceptually, the model addresses three basic problems in legged locomotion. (I) First, coordination of several legs requires coupling between the step cycles of adjacent legs, optimising synergistic propulsion, but ensuring stability through flexible adjustment to external disturbances. A set of behaviourally derived leg coordination rules can account for decentralised generation of different gaits, and allows stable walking of the insect model as well as of a number of legged robots. (II) Second, a wide range of different leg movements must be possible, e.g. to search for foothold, grasp for objects or groom the body surface. We present a simple neural network controller that can simulate targeted swing trajectories, obstacle avoidance reflexes and cyclic searching-movements. (III) Third, control of mechanically coupled joints of the legs in stance is achieved by exploiting the physical interactions between body, legs and substrate. A local positive displacement feedback, acting on individual leg joints, transforms passive displacement of a joint into active movement, generating synergistic assistance reflexes in all mechanically coupled joints.     

Bio-Inspired Controller for a Robot Cheetah with a Neural Mechanism Controlling Leg Muscles

The realization of a high-speed running robot is one of the most challenging problems in developing legged robots.The excellent performance of cheetahs provides inspiration for the control and mechanical design of such robots.This paper presents a three-dimensional model of a cheetah that predicts the locomotory behaviors of a running cheetah.Applying biological knowledge of the neural mechanism,we control the muscle flexion and extension during the stance phase,and control the positions of the joints in the flight phase via a PD controller to minimize complexity.The proposed control strategy is shown to achieve similar locomotion of a real cheetah.The simulation realizes good biological properties,such as the leg retraction,ground reaction force,and spring-like leg behavior.The stable bounding results show the promise of the controller in high-speed locomotion.The model can reach 2.7 m·s- 1 as the highest speed,and can accelerate from 0 to 1.5 m·s -1 in one stride cycle.A mechanical structure based on this simulation is designed to demonstrate the control approach,and the most recently developed hindlimb controlled by the proposed controller is presented in swinging-leg experiments and jump-force experiments.     

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.     

How locomotion sub-functions can control walking at different speeds?

Inspired from template models explaining biological locomotory systems and Raibert׳s pioneering legged robots, locomotion can be realized by basic sub-functions: elastic axial leg function, leg swinging and balancing. Combinations of these three can generate different gaits with diverse properties. In this paper we investigate how locomotion sub-functions contribute to stabilize walking at different speeds. Based on this trilogy, we introduce a conceptual model to quantify human locomotion sub-functions in walking. This model can produce stable walking and also predict human locomotion sub-function control during swing phase of walking. Analyzing experimental data based on this modeling shows different control strategies which are employed to increase speed from slow to moderate and moderate to fast gaits.     

Three‐Legged Locomotion and the Constraints on Limb Number: Why Tripeds Don’t Have a Leg to Stand On

Three‐legged animals do not exist today and such an animal is not found in the fossil record. Which constraints operate to result in the lack of a triped phenotype? Consideration of animal locomotion and robotic studies suggests that physical constraints would not prevent a triped from being functional or advantageous. As is reviewed here, the strongest constraint on the evolution of a triped is phylogenetic: namely, the early genetic adoption of a bilaterally symmetrical body plan occurring before the advent of limbs. Presumably, this would greatly constrain any three‐legged animal from ever evolving. Tripedalism is employed only by a few animals, but many use a tripod stance while engaged in a variety of activities. Because terms are often used interchangeably in the literature, a standardization of locomotion terminology is proposed. Understanding the constraints behind “forbidden” phenotypes forces us to confront gaps in our evolutionary understanding of which we may be unaware.     

Legged insects select the optimal locomotor pattern based on the energetic cost

 The gait transition in legged animals has attracted many researchers, and its relation to metabolic cost and mechanical work has been discussed in recent decades. We assumed that the energetic cost during locomotion is given by the sum of positive mechanical work and the heat energy loss that is proportional to the square of joint torque and examined the optimal locomotor pattern based on the energetic cost in a simple dynamical model of a hexapod by computer simulations. The obtained results well agree with characteristics in the locomotor patterns in legged animals; for example, the leg protraction time, step length, and the metabolic cost of transport are almost constant for many velocities, the leg cycling period decreases with velocity, and the energetic cost of locomotion induced by carrying loads linearly increases with mass loaded. This correspondence of the results of calculation to experimental results suggest that the heat energy loss for torque generation is proportional to the square of the torque during locomotion, and that the locomotor pattern in legged animals is highly optimized based on the energetic cost. Received: 22 December 1998 / Accepted: 14 April 2000     

Further exploration into the adaptive design of the arthropod "microbrain": I. Sensory and memory-processing systems

Arthropods have small but sophisticated brains that have enabled them to adapt their behavior to a diverse range of environments. In this review, we first discuss some of general characteristics of the arthropod "microbrain" in comparison with the mammalian "megalobrain". Then we discuss about recent progress in the study of sensory and memory-processing systems of the arthropod "microbrain". Results of recent studies have shown that (1) insects have excellent capability for elemental and context-dependent forms of olfactory learning, (2) mushroom bodies, higher olfactory and associative centers of arthropods, have much more elaborated internal structures than previously thought, (3) many genes involved in the formation of basic brain structures are common among arthropods and vertebrates, suggesting that common ancestors of arthropods and vertebrates already had organized head ganglia, and (4) the basic organization of sensori-motor pathways of the insect brain has features common to that of the mammalian brain. These findings provide a starting point for the study of brain mechanisms of elaborated behaviors of arthropods, many of which remain unexplored.     

Candidate gene screen in the red flour beetle Tribolium reveals six3 as ancient regulator of anterior median head and central complex development

Several highly conserved genes play a role in anterior neural plate patterning of vertebrates and in head and brain patterning of insects. However, head involution in Drosophila has impeded a systematic identification of genes required for insect head formation. Therefore, we use the red flour beetle Tribolium castaneum in order to comprehensively test the function of orthologs of vertebrate neural plate patterning genes for a function in insect head development. RNAi analysis reveals that most of these genes are indeed required for insect head capsule patterning, and we also identified several genes that had not been implicated in this process before. Furthermore, we show that Tc-six3/optix acts upstream of Tc-wingless, Tc-orthodenticle1, and Tc-eyeless to control anterior median development. Finally, we demonstrate that Tc-six3/optix is the first gene known to be required for the embryonic formation of the central complex, a midline-spanning brain part connected to the neuroendocrine pars intercerebralis. These functions are very likely conserved among bilaterians since vertebrate six3 is required for neuroendocrine and median brain development with certain mutations leading to holoprosencephaly.     

The integration of locomotion and prey capture in vertebrates: Morphology, behavior, and performance

For most vertebrates, locomotion is a fundamental componentof prey capture. Despite this ubiquitous link, few studies havequantified the integration of these complex systems. Severalvariables related to locomotor performance, including maximumspeed, acceleration, deceleration, maneuverability, accuracy,and approach stability, likely influence feeding performancein vertebrates. The relative importance of these measures ofperformance, however, depends on the ecology of the predator.While factors such as morphology and physiology likely definethe limits of these variables, other factors such as motivationof the predator, prey type, and habitat structure can also influenceperformance. Understanding how these variables relate to feedingunder a given suite of ecological conditions is central to understandingpredator–prey interactions, and ultimately how locomotionand feeding have co-evolved. The goals of this article are todiscuss several variables of locomotor performance related toprey capture, present new data on the relationship between locomotorand feeding morphology in fishes, discuss the evolution of preycapture in cichlid fishes, and outline some future directionsfor research. While suction feeding is a primary mechanism ofprey capture in fishes, swimming is vital for accurately positioningthe mouth relative to the prey item. Many fishes decelerateduring prey capture using their body and fins, but the pectoralfins have a dominant role in maintaining approach stability.This suggests that fishes employing high-performance suctionfeeding (relatively small mouth) will have larger pectoral finsto facilitate accurate and stable feeding. I provide new dataon the relationship between pectoral fin morphology and maximumgape in centrarchid fishes. For seven species, pectoral finarea was significantly, and negatively, correlated with maximumgape. This example illustrates that the demands from one complexsystem (feeding) can influence another complex system (locomotion).Future studies that examine the morphological, physiological,and functional evolution of locomotion involved in prey captureby aquatic and terrestrial vertebrates will provide insightinto the origin and consequences of diversity.     

Running in the real world: adjusting leg stiffness for different surfaces.

A running animal coordinates the actions of many muscles, tendons, and ligaments in its leg so that the overall leg behaves like a single mechanical spring during ground contact. Experimental observations have revealed that an animal''s leg stiffness is independent of both speed and gravity level, suggesting that it is dictated by inherent musculoskeletal properties. However, if leg stiffness was invariant, the biomechanics of running (e.g. peak ground reaction force and ground contact time) would change when an animal encountered different surfaces in the natural world. We found that human runners adjust their leg stiffness to accommodate changes in surface stiffness, allowing them to maintain similar running mechanics on different surfaces. These results provide important insight into mechanics and control of animal locomotion and suggest that incorporating an adjustable leg stiffness in the design of hopping and running robots is important if they are to match the agility and speed of animals on varied terrain.     

Mechanical models for insect locomotion: dynamics and stability in the horizontal plane I. Theory

We study the dynamics and stability of legged locomotion in the horizontal plane. Motivated by experimental studies of insects, we develop two- and three-degree-of freedom rigid body models with pairs of ‘virtual’ elastic legs in intermittent contact with the ground. We focus on conservative compliant-legged models, but we also consider prescribed forces, prescribed leg displacements, and combined strategies. The resulting mechanical systems exhibit periodic gaits whose stability characteristics are due to intermittent foot contact, and are largely determined by geometrical criteria. Most strikingly, we show that mechanics alone can confer asymptotic stability in heading and body orientation. In a companion paper, we apply our results to rapidly running cockroaches. Received: 6 September 1999 / Accepted in revised form: 8 May 2000     

Origins and plasticity of neural crest cells and their roles in jaw and craniofacial evolution

The vertebrate head is a complex assemblage of cranial specializations, including the central and peripheral nervous systems, viscero- and neurocranium, musculature and connective tissue. The primary differences that exist between vertebrates and other chordates relate to their craniofacial organization. Therefore, evolution of the head is considered fundamental to the origins of vertebrates (Gans and Northcutt, 1983). The transition from invertebrate to vertebrate chordates was a multistep process, involving the formation and patterning of many new cell types and tissues. The evolution of early vertebrates, such as jawless fish, was accompanied by the emergence of a specialized set of cells, called neural crest cells which have long held a fascination for developmental and evolutionary biologists due to their considerable influence on the complex development of the vertebrate head. Although it has been classically thought that protochordates lacked neural crest counterparts, the recent identification and characterization of amphioxus and ascidian genes homologous to those involved in vertebrate neural crest development challenges this idea. Instead it suggests thatthe neural crest may not be a novel vertebrate cell population, but could have in fact originated from the protochordate dorsal midline epidermis. Consequently, the evolution of the neural crest cells could be reconsidered in terms of the acquisition of new cell properties such as delamination-migration and also multipotency which were key innovations that contributed to craniofacial development. In this review we discuss recent findings concerning the inductive origins of neural crest cells, as well as new insights into the mechanisms patterning this cell population and the subsequent influence this has had on craniofacial evolution.     

An analytical estimation of the energy cost for legged locomotion

Legged locomotion requires the determination of a number of parameters such as stride period, stride length, order of leg movements, leg trajectory, etc. How are these parameters determined? It has been reported that the locomotor patterns of many legged animals exhibit common characteristics, which suggests that there exists a basic strategy for legged locomotion. In this study we derive an equation to estimate the cost of transport for legged locomotion and examine a criterion of the minimization of the transport cost as a candidate of the strategy. The obtained optimal locomotor pattern that minimizes the cost suitably represents many characteristics of the pattern observed in legged animals. This suggests that the locomotor pattern of legged animals is well optimized with regard to the energetic cost. The result also suggests that the existence of specific gait patterns and the phase transition between them could be the result due to optimization; they are induced by the change in the distribution of ground reaction forces for each leg during locomotion.     

Notch signaling does not regulate segmentation in the honeybee, Apis mellifera

Notch signaling has been implicated in the segmentation of vertebrates but is not involved in segmentation in Drosophila. Recent evidence, however, implies that Notch signaling regulates segmentation in some Arthropods, including an insect, and that Notch signaling regulated segmentation in the common ancestor of Vertebrates and Arthropods. Notch signaling regulates clock-like formation of segments in both groups, a phenomenon not seen in Drosophila. We present evidence that Notch signaling components are expressed in a pattern implying a role in segmentation in honeybees, where the expression of genes involved in segmentation are modulated in a temporal way. Despite this, pharmacological investigation and RNA interference experiments indicate that Notch signaling does not regulate segmentation in honeybees, but instead regulates patterning within segments after segmentation itself has occurred. Notch signaling thus does not regulate segmentation in holometabolous insects, even when segments appear to form in anterior-posterior sequence.     

Running over unknown rough terrain with a one-legged planar robot

The ability to traverse unknown, rough terrain is an advantage that legged locomoters have over their wheeled counterparts. However, due to the complexity of multi-legged systems, research in legged robotics has not yet been able to reproduce the agility found in the animal kingdom. In an effort to reduce the complexity of the problem, researchers have developed single-legged models to gain insight into the fundamental dynamics of legged running. Inspired by studies of animal locomotion, researchers have proposed numerous control strategies to achieve stable, one-legged running over unknown, rough terrain. One such control strategy incorporates energy variations into the system during the stance phase by changing the force-free leg length as a sinusoidal function of time. In this research, a one-legged planar robot capable of implementing this and other state-of-the-art control strategies was designed and built. Both simulated and experimental results were used to determine and compare the stability of the proposed controllers as the robot was subjected to unknown drop and raised step perturbations equal to 25% of the nominal leg length. This study illustrates the relative advantages of utilizing a minimal-sensing, active energy removal control scheme to stabilize running over rough terrain.     

Insects Use Two Distinct Classes of Steps during Unrestrained Locomotion

Background

Adaptive, context-dependent control of locomotion requires modulation of centrally generated rhythmic motor patterns through peripheral control loops and postural reflexes. Thus assuming that the modulation of rhythmic motor patterns accounts for much of the behavioural variability observed in legged locomotion, investigating behavioural variability is a key to the understanding of context-dependent control mechanisms in locomotion. To date, the variability of unrestrained locomotion is poorly understood, and virtually nothing is known about the features that characterise the natural statistics of legged locomotion. In this study, we quantify the natural variability of hexapedal walking and climbing in insects, drawing from a database of several thousand steps recorded over two hours of walking time.

Results

We show that the range of step length used by unrestrained climbing stick insects is large, showing that step length can be changed substantially for adaptive locomotion. Step length distributions were always bimodal, irrespective of leg type and walking condition, suggesting the presence of two distinct classes of steps: short and long steps. Probability density of step length was well-described by a gamma distribution for short steps, and a logistic distribution for long steps. Major coefficients of these distributions remained largely unaffected by walking conditions. Short and long steps differed concerning their spatial occurrence on the walking substrate, their timing within the step sequence, and their prevalent swing direction. Finally, ablation of structures that serve to improve foothold increased the ratio of short to long steps, indicating a corrective function of short steps.

Conclusions

Statistical and functional differences suggest that short and long steps are physiologically distinct classes of leg movements that likely reflect distinct control mechanisms at work.