Neuromechanical simulation of the locust jump

Comparison of water and terrestrial jumping in natural and robotic insects

Jumping requires high actuation power for achieving high speed in a short time. Especially, organisms and robots at the insect scale jump in order to overcome size limits on the speed of locomotion. As small jumpers suffer from intrinsically small power output, efficient jumpers have devised various ingenuous schemes to amplify their power release. Furthermore, semi-aquatic jumpers have adopted specialized techniques to fully exploit the reaction from water. We review jumping mechanisms of natural and robotic insects that jump on the ground and the surface of water, and compare the performance depending on their scale. We find a general trend that jumping creatures maximize jumping speed by unique mechanisms that manage acceleration, force, and takeoff duration under the constraints mainly associated with their size, shape, and substrate.

Control of high-speed jumps in muscle and spring actuated systems: a comparative study of take-off energetics in bush-crickets (Mecopoda elongata) and locusts (Schistocerca gregaria)

The Orthoptera are a diverse insect order well known for their locomotive capabilities. To jump, the bush-cricket uses a muscle actuated (MA) system in which leg extension is actuated by contraction of the femoral muscles of the hind legs. In comparison, the locust uses a latch mediated spring actuated (LaMSA) system, in which leg extension is actuated by the recoil of spring-like structure in the femur. The aim of this study was to describe the jumping kinematics of Mecopoda elongata (Tettigoniidae) and compare this to existing data in Schistocerca gregaria (Acrididae), to determine differences in control of rotation during take-off between similarly sized MA and LaMSA jumpers. 269 jumps from 67 individuals of M. elongata with masses from 0.014 g to 3.01 g were recorded with a high-speed camera setup. In M. elongata, linear velocity increased with mass0.18 and the angular velocity (pitch) decreased with mass-0.13. In S. gregaria, linear velocity is constant and angular velocity decreases with mass-0.24. Despite these differences in velocity scaling, the ratio of translational kinetic energy to rotational kinetic energy was similar for both species. On average, the energy distribution of M. elongata was distributed 98.8% to translational kinetic energy and 1.2% to rotational kinetic energy, whilst in S. gregaria it is 98.7% and 1.3%, respectively. This energy distribution was independent of size for both species. Despite having two different jump actuation mechanisms, the ratio of translational and rotational kinetic energy formed during take-off is fixed across these distantly related orthopterans.

Inside the coupling of ladybird beetle elytra: elastic setae can facilitate swift deployment

The ladybird beetle (Coccinella septempunctata) is known for swift deployment of its elytra, an action that requires considerable power. However, actuation by thoracic muscles alone may be insufficient to deploy elytra at high speed because the maximum mechanical power that elytral muscles can produce is only 70% of that required for initiation of deployment. Nevertheless, the elytra open rapidly, within 3 ms in the initial phase, at a maximum angular velocity of 66.49±21.29 rad s-1, rivaling the strike velocity of antlion (Myrmeleon crudelis) mandibles (65±21 rad s-1). Here we hypothesize that elytra coupling may function as an energy storage mechanism that facilitates rapid opening by releasing elastic strain energy upon deployment. To test this hypothesis and better understand the biomechanics of elytra deployment, we combined micro-computed tomography and scanning electron microscopy to examine the microstructure of the coupling of paired elytra. We found that two rows of setae on the internal edges of the elytra coupling structure undergo elastic deformation when the elytra are locked together. Kinematics observations and mathematical modelling suggest that the elastic potential energy stored in the compressed setae generates 40% of the power required for deployment of elytra. Our findings broaden insights into how ladybirds actuate elytra opening by a strategy of using both muscles and elastic microstructures, and demonstrate a distributed pattern of actuation that adapts to geometrical constraints in elytra locking.

NeuroMechFly, a neuromechanical model of adult Drosophila melanogaster

Animal behavior emerges from an interaction between neural network dynamics, musculoskeletal properties and the physical environment. Accessing and understanding the interplay between these elements requires the development of integrative and morphologically realistic neuromechanical simulations. Here we present NeuroMechFly, a data-driven model of the widely studied organism, Drosophila melanogaster. NeuroMechFly combines four independent computational modules: a physics-based simulation environment, a biomechanical exoskeleton, muscle models and neural network controllers. To enable use cases, we first define the minimum degrees of freedom of the leg from real three-dimensional kinematic measurements during walking and grooming. Then, we show how, by replaying these behaviors in the simulator, one can predict otherwise unmeasured torques and contact forces. Finally, we leverage NeuroMechFly's full neuromechanical capacity to discover neural networks and muscle parameters that drive locomotor gaits optimized for speed and stability. Thus, NeuroMechFly can increase our understanding of how behaviors emerge from interactions between complex neuromechanical systems and their physical surroundings.

A physical model of mantis shrimp for exploring the dynamics of ultrafast systems

Efficient and effective generation of high-acceleration movement in biology requires a process to control energy flow and amplify mechanical power from power density-limited muscle. Until recently, this ability was exclusive to ultrafast, small organisms, and this process was largely ascribed to the high mechanical power density of small elastic recoil mechanisms. In several ultrafast organisms, linkages suddenly initiate rotation when they overcenter and reverse torque; this process mediates the release of stored elastic energy and enhances the mechanical power output of extremely fast, spring-actuated systems. Here we report the discovery of linkage dynamics and geometric latching that reveals how organisms and synthetic systems generate extremely high-acceleration, short-duration movements. Through synergistic analyses of mantis shrimp strikes, a synthetic mantis shrimp robot, and a dynamic mathematical model, we discover that linkages can exhibit distinct dynamic phases that control energy transfer from stored elastic energy to ultrafast movement. These design principles are embodied in a 1.5-g mantis shrimp scale mechanism capable of striking velocities over 26 m [Formula: see text] in air and 5 m [Formula: see text] in water. The physical, mathematical, and biological datasets establish latching mechanics with four temporal phases and identify a nondimensional performance metric to analyze potential energy transfer. These temporal phases enable control of an extreme cascade of mechanical power amplification. Linkage dynamics and temporal phase characteristics are easily adjusted through linkage design in robotic and mathematical systems and provide a framework to understand the function of linkages and latches in biological systems.

Latch-based control of energy output in spring actuated systems

The inherent force-velocity trade-off of muscles and motors can be overcome by instead loading and releasing energy in springs to power extreme movements. A key component of this paradigm is the latch that mediates the release of spring energy to power the motion. Latches have traditionally been considered as switches; they maintain spring compression in one state and allow the spring to release energy without constraint in the other. Using a mathematical model of a simplified contact latch, we reproduce this instantaneous release behaviour and also demonstrate that changing latch parameters (latch release velocity and radius) can reduce and delay the energy released by the spring. We identify a critical threshold between instantaneous and delayed release that depends on the latch, spring, and mass of the system. Systems with stiff springs and small mass can attain a wide range of output performance, including instantaneous behaviour, by changing latch release velocity. We validate this model in both a physical experiment as well as with data from the Dracula ant, Mystrium camillae, and propose that latch release velocity can be used in both engineering and biological systems to control energy output.

Impact of Different Developmental Instars on Locusta migratoria Jumping Performance

Ontogenetic locomotion research focuses on the evolution of locomotion behavior in different developmental stages of a species. Unlike vertebrates, ontogenetic locomotion in invertebrates is poorly investigated. Locusts represent an outstanding biological model to study this issue. They are hemimetabolous insects and have similar aspects and behaviors in different instars. This research is aimed at studying the jumping performance of Locusta migratoria over different developmental instars. Jumps of third instar, fourth instar, and adult L. migratoria were recorded through a high-speed camera. Data were analyzed to develop a simplified biomechanical model of the insect: the elastic joint of locust hind legs was simplified as a torsional spring located at the femur-tibiae joint as a semilunar process and based on an energetic approach involving both locomotion and geometrical data. A simplified mathematical model evaluated the performances of each tested jump. Results showed that longer hind leg length, higher elastic parameter, and longer takeoff time synergistically contribute to a greater velocity and energy storing/releasing in adult locusts, if compared to young instars; at the same time, they compensate possible decreases of the acceleration due to the mass increase. This finding also gives insights for advanced bioinspired jumping robot design.

Hurry Up and Get Out of the Way! Exploring the Limits of Muscle-Based Latch Systems for Power Amplification

Animals can amplify the mechanical power output of their muscles as they jump to escape predators or strike to capture prey. One mechanism for amplification involves muscle-tendon unit (MT) systems in which a spring element (series elastic element [SEE]) is pre-stretched while held in place by a "latch" that prevents immediate transmission of muscle (or contractile element, CE) power to the load. In principle, this storage phase is followed by a triggered release of the latch, and elastic energy released from the SEE enables power amplification (PRATIO=PLOAD/PCE,max >1.0), whereby the peak power delivered from MT to the load exceeds the maximum power limit of the CE in isolation. Latches enable power amplification by increasing the muscle work generated during storage and reducing the duration over which that stored energy is released to power a movement. Previously described biological "latches" include: skeletal levers, anatomical triggers, accessory appendages, and even antagonist muscles. In fact, many species that rely on high-powered movements also have a large number of muscles arranged in antagonist pairs. Here, we examine whether a decaying antagonist force (e.g., from a muscle) could be useful as an active latch to achieve controlled energy transmission and modulate peak output power. We developed a computer model of a frog hindlimb driven by a compliant MT. We simulated MT power generated against an inertial load in the presence of an antagonist force "latch" (AFL) with relaxation time varying from very fast (10 ms) to very slow (1000 ms) to mirror physiological ranges of antagonist muscle. The fastest AFL produced power amplification (PRATIO=5.0) while the slowest AFL produced power attenuation (PRATIO=0.43). Notably, AFLs with relaxation times shorter than ∼300 ms also yielded greater power amplification (PRATIO>1.20) than the system driving the same inertial load using only an agonist MT without any AFL. Thus, animals that utilize a sufficiently fast relaxing AFL ought to be capable of achieving greater power output than systems confined to a single agonist MT tuned for maximum PRATIO against the same load.

Repair of microdamage caused by cyclic loading in insect cuticle

It is well known that repeated loading cycles can reduce the strength of a material and cause eventual failure by the gradual build-up of damage. Previous work has shown that mammalian bone is able to extend its life almost indefinitely by continuously repairing microdamage, preventing the development of macroscopic cracks. However, no study has been conducted until now to investigate repair of microdamage in any other biological material. We applied cyclic bending loads to the hind tibiae of desert locusts (Schistocerca gregaria). We observed a significant decrease in the elastic stiffness (Young's modulus) of the cuticle during the five applied loading cycles, indicating that microdamage had been induced. The tibiae were then left to rest for various time periods: 1 hr, 24 hr, 1 week, and 4 weeks. When tested again after up to 24 hr, there was still a significant decrease in stiffness, showing that some microdamage remained. However, in the samples left for 1 week or 4 weeks before retesting, this decrease in stiffness had disappeared, indicating that the microdamage had been repaired. This is the first ever indication that insects are capable of repairing microdamage. It is a highly significant finding-insects such as locusts rely on the stiffness and strength of their hind legs for jumping. This study suggests that, within a time period of order of a few days, the insect can fully restore the mechanical function of an overloaded leg and thus return to normal activities.

Evolutionary Biomechanics: The Pathway to Power in Snapping Shrimp

The extraordinary snaps of snapping shrimp evolved through simple morphological transitions with remarkable mechanical results.

Extremely fast feeding strikes are powered by elastic recoil in a seahorse relative, the snipefish, Macroramphosus scolopax

Among over 30 000 species of ray-finned fishes, seahorses and pipefishes have a unique feeding mechanism whereby the elastic recoil of tendons allows them to rotate their long snouts extremely rapidly in order to capture small elusive prey. To understand the evolutionary origins of this feeding mechanism, its phylogenetic distribution among closely related lineages must be assessed. We present evidence for elastic recoil-powered feeding in snipefish (Macroramphosus scolopax) from kinematics, dynamics and morphology. High-speed videos of strikes show they achieve extremely fast head and hyoid rotational velocities, resulting in rapid prey capture in as short a duration as 2 ms. The maximum instantaneous muscle-mass-specific power requirement for head rotation in snipefish was above the known vertebrate maximum, which is evidence that strikes are not the result of direct muscle power. Finally, we show that the over-centre conformation of the four-bar linkage mechanism coupling head elevation to hyoid rotation in snipefish can function as a torque reversal latch, preventing the head from rotating and providing the opportunity for elastic energy storage. The presence of elastic recoil feeding in snipefish means that this high-performance mechanism is not restricted to the Syngnathidae (seahorses and pipefish) and may have evolved in parallel.

The principles of cascading power limits in small, fast biological and engineered systems

Mechanical power limitations emerge from the physical trade-off between force and velocity. Many biological systems incorporate power-enhancing mechanisms enabling extraordinary accelerations at small sizes. We establish how power enhancement emerges through the dynamic coupling of motors, springs, and latches and reveal how each displays its own force-velocity behavior. We mathematically demonstrate a tunable performance space for spring-actuated movement that is applicable to biological and synthetic systems. Incorporating nonideal spring behavior and parameterizing latch dynamics allows the identification of critical transitions in mass and trade-offs in spring scaling, both of which offer explanations for long-observed scaling patterns in biological systems. This analysis defines the cascading challenges of power enhancement, explores their emergent effects in biological and engineered systems, and charts a pathway for higher-level analysis and synthesis of power-amplified systems.

Integrating Brain and Biomechanical Models-A New Paradigm for Understanding Neuro-muscular Control

To date, realistic models of how the central nervous system governs behavior have been restricted in scope to the brain, brainstem or spinal column, as if these existed as disembodied organs. Further, the model is often exercised in relation to an in vivo physiological experiment with input comprising an impulse, a periodic signal or constant activation, and output as a pattern of neural activity in one or more neural populations. Any link to behavior is inferred only indirectly via these activity patterns. We argue that to discover the principles of operation of neural systems, it is necessary to express their behavior in terms of physical movements of a realistic motor system, and to supply inputs that mimic sensory experience. To do this with confidence, we must connect our brain models to neuro-muscular models and provide relevant visual and proprioceptive feedback signals, thereby closing the loop of the simulation. This paper describes an effort to develop just such an integrated brain and biomechanical system using a number of pre-existing models. It describes a model of the saccadic oculomotor system incorporating a neuromuscular model of the eye and its six extraocular muscles. The position of the eye determines how illumination of a retinotopic input population projects information about the location of a saccade target into the system. A pre-existing saccadic burst generator model was incorporated into the system, which generated motoneuron activity patterns suitable for driving the biomechanical eye. The model was demonstrated to make accurate saccades to a target luminance under a set of environmental constraints. Challenges encountered in the development of this model showed the importance of this integrated modeling approach. Thus, we exposed shortcomings in individual model components which were only apparent when these were supplied with the more plausible inputs available in a closed loop design. Consequently we were able to suggest missing functionality which the system would require to reproduce more realistic behavior. The construction of such closed-loop animal models constitutes a new paradigm of computational neurobehavior and promises a more thoroughgoing approach to our understanding of the brain's function as a controller for movement and behavior.

Jump stabilization and landing control by wing-spreading of a locust-inspired jumper

Bio-inspired robotics is a promising design strategy for mobile robots. Jumping is an energy efficient locomotion gait for traversing difficult terrain. Inspired by the jumping and flying behavior of the desert locust, we have recently developed a miniature jumping robot that can jump over 3.5 m high. However, much like the non-adult locust, it rotates while in the air and lands uncontrollably. Inspired by the winged adult locust, we have added spreading wings and a tail to the jumper. After the robot leaps, at the apex of the trajectory, the wings unfold and it glides to the ground. The advantages of this maneuver are the stabilization of the robot when airborne, the reduction of velocity at landing, the control of the landing angle and the potential to change the robot's orientation and control its flight trajectory. The new upgraded robot is capable of jumping to a still impressive height of 1.7 m eliminating airborne rotation and reducing landing velocity. Here, we analyze the dynamic and aerodynamic models of the robot, discuss the robot's design, and validate its ability to perform a jump-glide in a stable trajectory, land safely and change its orientation while in the air.

A Survey of Bioinspired Jumping Robot: Takeoff, Air Posture Adjustment, and Landing Buffer

A bioinspired jumping robot has a strong ability to overcome obstacles. It can be applied to the occasion with complex and changeable environment, such as detection of planet surface, postdisaster relief, and military reconnaissance. So the bioinspired jumping robot has broad application prospect. The jumping process of the robot can be divided into three stages: takeoff, air posture adjustment, and landing buffer. The motivation of this review is to investigate the research results of the most published bioinspired jumping robots for these three stages. Then, the movement performance of the bioinspired jumping robots is analyzed and compared quantitatively. Then, the limitation of the research on bioinspired jumping robots is discussed, such as the research on the mechanism of biological motion is not thorough enough, the research method about structural design, material applications, and control are still traditional, and energy utilization is low, which make the robots far from practical applications. Finally, the development trend is summarized. This review provides a reference for further research of bioinspired jumping robots.

Feed-forward motor control of ultrafast, ballistic movements

To circumvent the limits of muscle, ultrafast movements achieve high power through the use of springs and latches. The time scale of these movements is too short for control through typical neuromuscular mechanisms, thus ultrafast movements are either invariant or controlled prior to movement. We tested whether mantis shrimp (Stomatopoda: Neogonodactylus bredini) vary their ultrafast smashing strikes and, if so, how this control is achieved prior to movement. We collected high-speed images of strike mechanics and electromyograms of the extensor and flexor muscles that control spring compression and latch release. During spring compression, lateral extensor and flexor units were co-activated. The strike initiated several milliseconds after the flexor units ceased, suggesting that flexor activity prevents spring release and determines the timing of strike initiation. We used linear mixed models and Akaike's information criterion to serially evaluate multiple hypotheses for control mechanisms. We found that variation in spring compression and strike angular velocity were statistically explained by spike activity of the extensor muscle. The results show that mantis shrimp can generate kinematically variable strikes and that their kinematics can be changed through adjustments to motor activity prior to the movement, thus supporting an upstream, central-nervous-system-based control of ultrafast movement. Based on these and other findings, we present a shishiodoshi model that illustrates alternative models of control in biological ballistic systems. The discovery of feed-forward control in mantis shrimp sets the stage for the assessment of targets, strategic variation in kinematics and the role of learning in ultrafast animals.

A locust-inspired miniature jumping robot

Unmanned ground vehicles are mostly wheeled, tracked, or legged. These locomotion mechanisms have a limited ability to traverse rough terrain and obstacles that are higher than the robot's center of mass. In order to improve the mobility of small robots it is necessary to expand the variety of their motion gaits. Jumping is one of nature's solutions to the challenge of mobility in difficult terrain. The desert locust is the model for the presented bio-inspired design of a jumping mechanism for a small mobile robot. The basic mechanism is similar to that of the semilunar process in the hind legs of the locust, and is based on the cocking of a torsional spring by wrapping a tendon-like wire around the shaft of a miniature motor. In this study we present the jumping mechanism design, and the manufacturing and performance analysis of two demonstrator prototypes. The most advanced jumping robot demonstrator is power autonomous, weighs 23 gr, and is capable of jumping to a height of 3.35 m, covering a distance of 1.37 m.

Passive joint forces are tuned to limb use in insects and drive movements without motor activity

Background

Limb movements are generally driven by active muscular contractions working with and against passive forces arising in muscles and other structures. In relatively heavy limbs, the effects of gravity and inertia predominate, whereas in lighter limbs, passive forces intrinsic to the limb are of greater consequence. The roles of passive forces generated by muscles and tendons are well understood, but there has been little recognition that forces originating within joints themselves may also be important, and less still that these joint forces may be adapted through evolution to complement active muscle forces acting at the same joint.

Results

We examined the roles of passive joint forces in insect legs with different arrangements of antagonist muscles. We first show that passive forces modify actively generated movements of a joint across its working range, and that they can be sufficiently strong to generate completely passive movements that are faster than active movements observed in natural behaviors. We further demonstrate that some of these forces originate within the joint itself. In legs of different species adapted to different uses (walking, jumping), these passive joint forces complement the balance of strength of the antagonist muscles acting on the joint. We show that passive joint forces are stronger where they assist the weaker of two antagonist muscles.

Conclusions

In limbs where the dictates of a key behavior produce asymmetry in muscle forces, passive joint forces can be coadapted to provide the balance needed for the effective generation of other behaviors.

•

Limb movements are assisted by passive forces arising within joints

•

Functional cyclic movements can be generated by a single motor neuron

•

Joint forces are matched to the strength of antagonist muscles across species

•

Passive joint properties can transfer force from a stronger to a weaker muscle

Jumping mechanisms in jumping plant lice (Hemiptera, Sternorrhyncha, Psyllidae)

Jumping mechanisms and performance were analysed in three species of psyllids (Hemiptera, Sternorrhyncha) that ranged from 2 to 4 mm in body length and from 0.7 to 2.8 mg in mass. Jumping was propelled by rapid movements of the short hind legs, which were only 10-20% longer than the other legs and 61-77% of body length. Power was provided by large thoracic muscles that depressed the trochantera so that the two hind legs moved in parallel planes on either side of the body. These movements accelerated the body to take-off in 0.9 ms in the smallest psyllid and 1.7 ms in the largest, but in all species imparted a rapid forward rotation so that at take-off the head pointed downwards, subtending angles of approximately -60 deg relative to the ground. The front legs thus supported the body just before take-off and either lost contact with the ground at the same time as, or even after, the hind legs. In the best jumps from the horizontal, take-off velocity reached 2.7 m s(-1) and the trajectory was steep at 62-80 deg. Once airborne, the body spun rapidly at rates of up to 336 Hz in the pitch plane. In many jumps, the wings did not open to provide stabilisation, but some jumps led directly to sustained flight. In their best jumps, the smallest species experienced a force of 637 g. The largest species had an energy requirement of 13 μJ, a power output of 13 mW and exerted a force of nearly 10 mN. In a rare jumping strategy seen in only two of 211 jumps analysed, the femoro-tibial joints extended further and resulted in the head pointing upwards at take-off and the spin rate being greatly reduced.

Locusts use a composite of resilin and hard cuticle as an energy store for jumping and kicking

Locusts jump and kick by using a catapult mechanism in which energy is first stored and then rapidly released to extend the large hind legs. The power is produced by a slow contraction of large muscles in the hind femora that bend paired semi-lunar processes in the distal part of each femur and store half the energy needed for a kick. We now show that these energy storage devices are composites of hard cuticle and the rubber-like protein resilin. The inside surface of a semi-lunar process consists of a layer of resilin, particularly thick along an inwardly pointing ridge and tightly bonded to the external, black cuticle. From the outside, resilin is visible only as a distal and ventral triangular area that tapers proximally. High-speed imaging showed that the semi-lunar processes were bent in all three dimensions during the prolonged muscular contractions that precede a kick. To reproduce these bending movements, the extensor tibiae muscle was stimulated electrically in a pattern that mimicked the normal sequence of its fast motor spikes recorded in natural kicking. Externally visible resilin was compressed and wrinkled as a semi-lunar process was bent. It then sprung back to restore the semi-lunar process rapidly to its original natural shape. Each of the five nymphal stages jumped and kicked and had a similar distribution of resilin in their semi-lunar processes as adults; the resilin was shed with the cuticle at each moult. It is suggested that composite storage devices that combine the elastic properties of resilin with the stiffness of hard cuticle allow energy to be stored by bending hard cuticle over only a small distance and without fracturing. In this way all the stored energy is returned and the natural shape of the femur is restored rapidly so that a jump or kick can be repeated.

Biomechanics of jumping in the flea

It has long been established that fleas jump by storing and releasing energy in a cuticular spring, but it is not known how forces from that spring are transmitted to the ground. One hypothesis is that the recoil of the spring pushes the trochanter onto the ground, thereby generating the jump. A second hypothesis is that the recoil of the spring acts through a lever system to push the tibia and tarsus onto the ground. To decide which of these two hypotheses is correct, we built a kinetic model to simulate the different possible velocities and accelerations produced by each proposed process and compared those simulations with the kinematics measured from high-speed images of natural jumping. The in vivo velocity and acceleration kinematics are consistent with the model that directs ground forces through the tibia and tarsus. Moreover, in some natural jumps there was no contact between the trochanter and the ground. There were also no observable differences between the kinematics of jumps that began with the trochanter on the ground and jumps that did not. Scanning electron microscopy showed that the tibia and tarsus have spines appropriate for applying forces to the ground, whereas no such structures were seen on the trochanter. Based on these observations, we discount the hypothesis that fleas use their trochantera to apply forces to the ground and conclude that fleas jump by applying forces to the ground through the end of the tibiae.

Control of tumbling during the locust jump

Locust can jump precisely to a target, yet they can also tumble during the trajectory. We propose two mechanisms that would allow the locust to control tumbling during the jump. The first is that prior to the jump, locusts adjust the pitch of their body to move the center of mass closer to the intended thrust vector. The second is that contraction of the dorsolongitudinal muscles during the jump will produce torques that counter the torque produced by thrust. We found that locusts increased their take-off angle as the initial body pitch increased, and that little tumbling occurred for jumps that observed this relationship. Simulations of locust jumping demonstrated that a pitch versus take-off angle relationship that minimized tumbling in simulated jumps was similar to the relationship observed in live locusts. Locusts were strongly biased to pitch head-upward, and performed dorsiflexions far more often than ventral flexions. The direction and magnitude of tumbling could be controlled in simulations by adjusting the tension in the dorsolongitudinal muscles. These mechanisms allowed the simulations to match the data from the live animals. Control of tumbling was also found to influence the control of jump elevation. The bias to pitch head-upwards may have an evolutionary advantage when evading a predator and so make control of tumbling important for the locust.

Neuromechanical simulation

The importance of the interaction between the body and the brain for the control of behavior has been recognized in recent years with the advent of neuromechanics, a field in which the coupling between neural and biomechanical processes is an explicit focus. A major tool used in neuromechanics is simulation, which connects computational models of neural circuits to models of an animal's body situated in a virtual physical world. This connection closes the feedback loop that links the brain, the body, and the world through sensory stimuli, muscle contractions, and body movement. Neuromechanical simulations enable investigators to explore the dynamical relationships between the brain, the body, and the world in ways that are difficult or impossible through experiment alone. Studies in a variety of animals have permitted the analysis of extremely complex and dynamic neuromechanical systems, they have demonstrated that the nervous system functions synergistically with the mechanical properties of the body, they have examined hypotheses that are difficult to test experimentally, and they have explored the role of sensory feedback in controlling complex mechanical systems with many degrees of freedom. Each of these studies confronts a common set of questions: (i) how to abstract key features of the body, the world and the CNS in a useful model, (ii) how to ground model parameters in experimental reality, (iii) how to optimize the model and identify points of sensitivity and insensitivity, and (iv) how to share neuromechanical models for examination, testing, and extension by others.