Modeling locomotion of a soft-bodied arthropod using inverse dynamics

Most bio-inspired robots have been based on animals with jointed, stiff skeletons. There is now an increasing interest in mimicking the robust performance of animals in natural environments by incorporating compliant materials into the locomotory system. However, the mechanics of moving, highly conformable structures are particularly difficult to predict. This paper proposes a planar, extensible-link model for the soft-bodied tobacco hornworm caterpillar, Manduca sexta, to provide insight for biologists and engineers studying locomotion by highly deformable animals and caterpillar-like robots. Using inverse dynamics to process experimentally acquired point-tracking data, ground reaction forces and internal forces were determined for a crawling caterpillar. Computed ground reaction forces were compared to experimental data to validate the model. The results show that a system of linked extendable joints can faithfully describe the general form and magnitude of the contact forces produced by a crawling caterpillar. Furthermore, the model can be used to compute internal forces that cannot be measured experimentally. It is predicted that between different body segments in stance phase the body is mostly kept in tension and that compression only occurs during the swing phase when the prolegs release their grip. This finding supports a recently proposed mechanism for locomotion by soft animals in which the substrate transfers compressive forces from one part of the body to another (the environmental skeleton) thereby minimizing the need for hydrostatic stiffening. The model also provides a new means to characterize and test control strategies used in caterpillar crawling and soft robot locomotion.     

Fully decentralized control of a soft-bodied robot inspired by true slime mold

Animals exhibit astoundingly adaptive and supple locomotion under real world constraints. In order to endow robots with similar capabilities, we must implement many degrees of freedom, equivalent to animals, into the robots’ bodies. For taming many degrees of freedom, the concept of autonomous decentralized control plays a pivotal role. However a systematic way of designing such autonomous decentralized control system is still missing. Aiming at understanding the principles that underlie animals’ locomotion, we have focused on a true slime mold, a primitive living organism, and extracted a design scheme for autonomous decentralized control system. In order to validate this design scheme, this article presents a soft-bodied amoeboid robot inspired by the true slime mold. Significant features of this robot are twofold: (1) the robot has a truly soft and deformable body stemming from real-time tunable springs and protoplasm, the former is used for an outer skin of the body and the latter is to satisfy the law of conservation of mass; and (2) fully decentralized control using coupled oscillators with completely local sensory feedback mechanism is realized by exploiting the long-distance physical interaction between the body parts stemming from the law of conservation of protoplasmic mass. Simulation results show that this robot exhibits highly supple and adaptive locomotion without relying on any hierarchical structure. The results obtained are expected to shed new light on design methodology for autonomous decentralized control system.     

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.     

Deriving neural network controllers from neuro-biological data: implementation of a single-leg stick insect controller

This article presents modular recurrent neural network controllers for single legs of a biomimetic six-legged robot equipped with standard DC motors. Following arguments of Ekeberg et?al. (Arthropod Struct Dev 33:287?C300, 2004), completely decentralized and sensori-driven neuro-controllers were derived from neuro-biological data of stick-insects. Parameters of the controllers were either hand-tuned or optimized by an evolutionary algorithm. Employing identical controller structures, qualitatively similar behaviors were achieved for robot and for stick insect simulations. For a wide range of perturbing conditions, as for instance changing ground height or up- and downhill walking, swing as well as stance control were shown to be robust. Behavioral adaptations, like varying locomotion speeds, could be achieved by changes in neural parameters as well as by a mechanical coupling to the environment. To a large extent the simulated walking behavior matched biological data. For example, this was the case for body support force profiles and swing trajectories under varying ground heights. The results suggest that the single-leg controllers are suitable as modules for hexapod controllers, and they might therefore bridge morphological- and behavioral-based approaches to stick insect locomotion control.     

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.     

Wind-powered wheel locomotion, initiated by leaping somersaults, in larvae of the southeastern beach tiger beetle (Cicindela dorsalis media)

Rapid movement is challenging for elongate, soft-bodied animals with short or no legs. Leaping is known for only a few animals with this "worm-like" morphology. Wheel locomotion, in which the animal's entire body rolls forward along a central axis, has been reported for only a handful of animals worldwide. Here we present the first documented case of wind-powered wheel locomotion, in larvae of the coastal tiger beetle Cicindela dorsalis media. When removed from their shallow burrows, larvae easily can be induced to enter a behavioral sequence that starts with leaping; while airborne, larvae loop their body into a rotating wheel and usually either "hit the ground rolling" or leap again. The direction larvae wheel is closely related to the direction in which winds are blowing; thus, all our larvae wheeled up-slope, as winds at our study site consistently blew from sea to land. Stronger winds increased both the proportion of larvae wheeling, and the distance traveled, exceeding 60 m in some cases. In addition, the proportion of larvae that wheel and the distance traveled by wheeling larvae are significantly greater on smooth sandy beaches than on beach surfaces made rough and irregular by pedestrian, equestrian, and vehicular traffic. Like other coastal species of tiger beetles, C. dorsalis media has suffered major declines in recent years that are clearly correlated with increased human impacts. The present study suggests that the negative effects of beach traffic may be indirect, preventing larvae from escaping from predators using wheel locomotion by disrupting the flat, hard surface necessary for efficient wheeling.     

Piezoelectrically Actuated Biomimetic Self-Contained Quadruped Bounding Robot

This paper presents the development of a mesoscale self-contained quadruped mobile robot that employs two pieces ofpiezocomposite actuators for the bounding locomotion.The design of the robot leg is inspired by legged insects and animals,and the biomimetic concept is implemented in the robot in a simplified form,such that each leg of the robot has only one degreeof freedom.The lack of degree of freedom is compensated by a slope of the robot frame relative to the horizontal plane.For theimplementation of the self-contained mobile robot,a small power supply circuit is designed and installed on the robot.Experimentalresults show that the robot can locomote at about 50 mm·s^-1with the circuit on board,which can be considered as asignificant step toward the goal of building an autonomous legged robot actuated by piezoelectric actuators.     

A Phase-Dependent Hypothesis for Locomotor Functions of Human Foot Complex

The human foot is a very complex structure comprising numerous bones, muscles, ligaments and synovial joints. As the only component in contact with the ground, the foot complex delivers a variety of biomechanical functions during human locomotion, e.g. body support and propulsion, stability maintenance and impact absorption. These need the human foot to be rigid and damped to transmit ground reaction forces to the upper body and maintain body stability, and also to be compliant and resilient to moderate risky impacts and save energy. How does the human foot achieve these apparent conflicting functions？ In this study, we propose a phase-dependent hypothesis for the overall locomotor functions of the human foot complex based on in-vivo measurements of human natural gait and simulation results of a mathematical foot model. We propse that foot functions are highly dependent on gait phase, which is a major characteristics of human locomotion. In early stance just after heel strike, the foot mainly works as a shock absorber by moderating high impacts using the viscouselastic heel pad in both vertical and horizontal directions. In mid-stance phase （-80% of stance phase）, the foot complex can be considered as a springy rocker, reserving external mechanical work using the foot arch whilst moving ground contact point forward along a curved path to maintain body stability. In late stance after heel off, the foot complex mainly serves as a force modulator like a gear box, modulating effective mechanical advantages of ankle plantiflexor muscles using metatarsal-phalangeal joints. A sound under- standing of how diverse functions are implemented in a simple foot segment during human locomotion might be useful to gain insight into the overall foot locomotor functions and hence to facilitate clinical diagnosis, rehabilitation product design and humanoid robot development.     

Jumping robots: a biomimetic solution to locomotion across rough terrain

This paper introduces jumping robots as a means to traverse rough terrain; such terrain can pose problems for traditional wheeled, tracked and legged designs. The diversity of jumping mechanisms found in nature is explored to support the theory that jumping is a desirable ability for a robot locomotion system to incorporate, and then the size-related constraints are determined from first principles. A series of existing jumping robots are presented and their performance summarized. The authors present two new biologically inspired jumping robots, Jollbot and Glumper, both of which incorporate additional locomotion techniques of rolling and gliding respectively. Jollbot consists of metal hoop springs forming a 300 mm diameter sphere, and when jumping it raises its centre of gravity by 0.22 m and clears a height of 0.18 m. Glumper is of octahedral shape, with four 'legs' that each comprise two 500 mm lengths of CFRP tube articulating around torsion spring 'knees'. It is able to raise its centre of gravity by 1.60 m and clears a height of 1.17 m. The jumping performance of the jumping robot designs presented is discussed and compared against some specialized jumping animals. Specific power output is thought to be the performance-limiting factor for a jumping robot, which requires the maximization of the amount of energy that can be stored together with a minimization of mass. It is demonstrated that this can be achieved through optimization and careful materials selection.     

Influence of leg stiffness and its effect on myodynamic jumping performance.

The purposes of this study are: a) to examine the possibility of influencing the leg stiffness through instructions given to the subjects and b) to determine the effect of the leg stiffness on the mechanical power and take-off velocity during the drop jumps. A total of 15 athletes performed a series of drop jumps from heights of 20, 40 and 60 cm. The instructions given to the subjects were a) "jump as high as you can" and b) "jump high a little faster than your previous jump". The jumps were performed at each height until the athlete could not achieve a shorter ground contact time. The ground reaction forces were measured using a "Kistler" force plate (1000 Hz). The athletes body positions were recorded using a high speed (250 Hz) video camera. EMG was used to measure muscle activity in five leg muscles. The data was divided into 5 groups where group 1 was made up of the longest ground contact times of each athlete and group 5 the shortest. The leg and ankle stiffness values were higher when the contact times were shorter. This means that by influencing contact time through verbal instructions it is possible to control leg stiffness. Maximum center of mass take-off velocity the can be achieved with different levels of leg stiffness. The mechanical power acting on the human body during the positive phase of the drop jumps had the highest values in group 3. This means that there is an optimum stiffness value for the lower extremities to maximize mechanical power.     

A proprioceptive neuromechanical theory of crawling

The locomotion of many soft-bodied animals is driven by the propagation of rhythmic waves of contraction and extension along the body. These waves are classically attributed to globally synchronized periodic patterns in the nervous system embodied in a central pattern generator (CPG). However, in many primitive organisms such as earthworms and insect larvae, the evidence for a CPG is weak, or even non-existent. We propose a neuromechanical model for rhythmically coordinated crawling that obviates the need for a CPG, by locally coupling the local neuro-muscular dynamics in the body to the mechanics of the body as it interacts frictionally with the substrate. We analyse our model using a combination of analytical and numerical methods to determine the parameter regimes where coordinated crawling is possible and compare our results with experimental data. Our theory naturally suggests mechanisms for how these movements might arise in developing organisms and how they are maintained in adults, and also suggests a robust design principle for engineered motility in soft systems.     

Kinematic control of walking

The planar law of inter-segmental co-ordination we described may emerge from the coupling of neural oscillators between each other and with limb mechanical oscillators. Muscle contraction intervenes at variable times to re-excite the intrinsic oscillations of the system when energy is lost. The hypothesis that a law of coordinative control results from a minimal active tuning of the passive inertial and viscoelastic coupling among limb segments is congruent with the idea that movement has evolved according to minimum energy criteria (1, 8). It is known that multi-segment motion of mammals locomotion is controlled by a network of coupled oscillators (CPGs, see 18, 33, 37). Flexible combination of unit oscillators gives rise to different forms of locomotion. Inter-oscillator coupling can be modified by changing the synaptic strength (or polarity) of the relative spinal connections. As a result, unit oscillators can be coupled in phase, out of phase, or with a variable phase, giving rise to different behaviors, such as speed increments or reversal of gait direction (from forward to backward). Supra-spinal centers may drive or modulate functional sets of coordinating interneurons to generate different walking modes (or gaits). Although it is often assumed that CPGs control patterns of muscle activity, an equally plausible hypothesis is that they control patterns of limb segment motion instead (22). According to this kinematic view, each unit oscillator would directly control a limb segment, alternately generating forward and backward oscillations of the segment. Inter-segmental coordination would be achieved by coupling unit oscillators with a variable phase. Inter-segmental kinematic phase plays the role of global control variable previously postulated for the network of central oscillators. In fact, inter-segmental phase shifts systematically with increasing speed both in man (4) and cat (38). Because this phase-shift is correlated with the net mechanical power output over a gait cycle (3, 4), phase control could be used for limiting the overall energy expenditure with increasing speed (22). Adaptation to different walking conditions, such as changes in body posture, body weight unloading and backward walk, also involves inter-segmental phase tuning, as does the maturation of limb kinematics in toddlers.     

Mechanical power in running: a comparison of different approaches

The purposes of the present study were: (1) to compare four different methods of calculating mechanical power in running on the basis of comparable data over a wide range of running velocity; (2) to examine the linearity of the relation between mechanical power as calculated with the four methods and running velocity. Eight runners participated in the investigation (height: 1.82 +/- 0.03 m, body mass: 81.05 +/- 4.69 kg). A Kistler force platform registered all components of the ground reaction force (1000 Hz) during one foot ground contact, which was additionally video taped using two high-speed video cameras running at 120 Hz. Four different methods were used to calculate mechanical power. Two methods determined the mechanical power due to the work done on the athletes' center of mass and two were calculated from the motion of the athletes' segments. The four different methods provided different relations between mechanical power and running velocity. The calculations on the basis of kinematic data cannot be recommended to determine efficiency of movement. The methods based on ground reaction force measurements revealed significant linear relations (r = 0.90, r2 = 0.84) between running velocity and mechanical power.     

Gait Study and Pattern Generation of a Starfish-Like Soft Robot with Flexible Rays Actuated by SMAs

This paper presents the design and development of a starfish-like soft robot with flexible rays and the implementation of multi-gait locomotion using Shape Memory Alloy （SMA） actuators. The design principle was inspired by the starfish, which possesses a remarkable symmetrical structure and soft internal skeleton. A soft robot body was constructed by using 3D printing technology. A kinematic model of the SMA spring was built and developed for motion control according to displacement and force requirements. The locomotion inspired from starfish was applied to the implementation of the multi-ray robot through the flexible actuation induced multi-gait movements in various environments. By virtue of the proposed ray control patterns in gait transition, the soft robot was able to cross over an obstacle approximately twice of its body height. Results also showed that the speed of the soft robot was 6.5 times faster on sand than on a clammy rough terrain. These experiments demonstrated that the bionic soft robot with flexible rays actuated by SMAs and multi-gait locomotion in proposed patterns can perform successfully and smoothly in various terrains.     

Locomotion in caterpillars

Most species of caterpillar move around by inching or crawling. Their ability to navigate in branching three‐dimensional structures makes them particularly interesting biomechanical subjects. The mechanism of inching has not been investigated in detail, but crawling is now well understood from studies on caterpillar neural activity, dynamics and structural mechanics. Early papers describe caterpillar crawling as legged peristalsis, but recent work suggests that caterpillars use a tension‐based mechanism that helps them to exploit arboreal niches. Caterpillars are not obligate hydrostats but instead use their strong grip to the substrate to transmit forces, in effect using their environment as a skeleton. In addition, the gut which accounts for a substantial part of the caterpillar's weight, moves independently of the body wall during locomotion and may contribute to crawling dynamics. Work‐loop analysis of caterpillar muscles shows that they are likely to act both as actuators and energy dissipaters during crawling. Because caterpillar tissues are pseudo‐elastic, and locomotion involves large body deformations, moving is energetically inefficient. Possession of a soft body benefits caterpillars by allowing them to grow quickly and to access remote food sources safely.     

Drag force mechanical power during an actual propulsion cycle on a manual wheelchair

The object of this study was to compute the mechanical power of the resultant braking force during an actual propulsion cycle with a manual wheelchair on the field. The resultant braking force was calculated from a mechanical model taking into account the rolling resistances of the front and rear wheels. Both the resultant braking force and the wheelchair velocity were not constant during the propulsion cycle and varied according to the subject's fore-and-aft and vertical movements in the wheelchair. These variations had logical repercussions on the braking force mechanical power, which ranged from 20.6 to 34.5 W (mean = 29.6 W) during the propulsion cycle. The mechanical power was also calculated from the conditions of a classical drag test, by the product of the cycle mean velocity and a constant braking force corresponding to a 60% rear wheels distribution of the subject-and-wheelchair's weight. This second mechanical power (32.4 W) was 10% higher than the average of the instantaneous power. Beyond the need of a clear definition of the two phases of the propulsion cycle, this study showed that the assumption on wheelchair locomotion usually admitted on laboratory ergometers cannot be applied in field studies, and that the kinetic energy variations during the cycle propulsive phase should be considered for evaluating the subject's mechanical work and power.     

A new bi-axial cantilever beam design for biomechanics force measurements

The demand for measuring forces exerted by animals during locomotion has increased dramatically as biomechanists strive to understand and implement biomechanical control strategies. In particular, multi-axial force transducers are often required to capture animal limb coordination patterns. Most existing force transducers employ strain gages arranged in a Wheatstone bridge on a cantilever beam. Bi-axial measurements require duplicating this arrangement in the transverse direction. In this paper, we reveal a method to embed a Wheatstone bridge inside another to allow bi-axial measurements without additional strain gages or additional second beams. This hybrid configuration resolves two force components from a single bridge circuit and simplifies fabrication for the simultaneous assessment of normal and transverse loads. This design can be implemented with two-dimensional fabrication techniques and can even be used to modify a common full bridge cantilever force transducer. As a demonstration of the new design, we built a simple beam which achieved bi-axial sensing capability that outperformed a conventional half-bridge-per-axis bi-axial strain gage design. We have used this design to measure the ground reaction forces of a crawling caterpillar and a caterpillar-mimicking soft robot. The simplicity and increased sensitivity of this method could facilitate bi-axial force measurements for experimental biologists.     

Kinematics of soft-bodied, legged locomotion in Manduca sexta larvae

Caterpillar crawling is distinct from that of worms and molluscs; it consists of a series of steps in different body segments that can be compared to walking and running in animals with stiff skeletons. Using a three-dimensional kinematic analysis of horizontal crawling in Manduca sexta, the tobacco hornworm, we found that the phase of vertical displacement in the posterior segments substantially led changes in horizontal velocity and the segments appeared to pivot around the attached claspers. Both of the motions occur during vertebrate walking. In contrast, vertical displacement and horizontal velocity in the anterior proleg-bearing segments were in phase, as expected for running gaits coupled by elastic storage. We propose that this kinematic similarity to running results from the muscular compression and release of elastic tissues. As evidence in support of this proposal, the compression and extension of each segment were similar to harmonic oscillations in a spring, although changes in velocity were 70 degrees out of phase with displacement, suggesting that the spring was damped. Measurements of segment length within, and across, intersegmental boundaries show that some of these movements were caused by folding of the body wall between segments. These findings demonstrate that caterpillar crawling is not simply the forward progression of a peristaltic wave but has kinetic components that vary between segments. Although these movements can be compared to legged locomotion in animals with stiff skeletons, the underlying mechanisms of caterpillar propulsion, and in particular the contribution of elastic tissues, remain to be discovered.     

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.     

The burrowing of Priapulus caudatus

An account is given of the way in which Priapulus caudatus burrows in the muddy sea-bed in which it lives. Three phases are distinguishable in the muscular activity which is responsible for locomotion. During the first phase the animal is able to feed and defaecate, during the second the proboscis becomes invaginated, and during the third the animal moves forward. The power for locomotion is provided by contraction of the longitudinal and circular muscles of the body wall, not, as has been suggested previously, by the retractor muscles of the praesoma. Invagination of the proboscis is apparently stimulated by the arrival of a wave of contraction in the body wall musculature, propagated from the trunk.
In general the animal burrows in a way common for soft-bodied animals; the anterior and posterior extremities acting in turn as "terminal" and "penetration" anchors in the substratum. The muscular activities of the larva are limited by the presence of a lorica which encases the trunk, and the animal's powers of movement at this stage are very restricted.