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.     

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.     

GoQBot: a caterpillar-inspired soft-bodied rolling robot

Rolling locomotion using an external force such as gravity has evolved many times. However, some caterpillars can curl into a wheel and generate their own rolling momentum as part of an escape repertoire. This change in body conformation occurs well within 100 ms and generates a linear velocity over 0.2 m s(-1), making it one of the fastest self-propelled wheeling behaviors in nature. Inspired by this behavior, we construct a soft-bodied robot to explore the dynamics and control issues of ballistic rolling. This robot, called GoQBot, closely mimics caterpillar rolling. Analyzing the whole body kinematics and 2D ground reaction forces at the robot ground anchor reveals about 1G of acceleration and more than 200 rpm of angular velocity. As a novel rolling robot, GoQBot demonstrates how morphing can produce new modes of locomotion. Furthermore, mechanical coupling of the actuators improves body coordination without sensory feedback. Such coupling is intrinsic to soft-bodied animals because there are no joints to isolate muscle-generated movements. Finally, GoQBot provides an estimate of the mechanical power for caterpillar rolling that is comparable to that of a locust jump. How caterpillar musculature produces such power in such a short time is yet to be discovered.     

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.     

An octopus-bioinspired solution to movement and manipulation for soft robots

Soft robotics is a challenging and promising branch of robotics. It can drive significant improvements across various fields of traditional robotics, and contribute solutions to basic problems such as locomotion and manipulation in unstructured environments. A challenging task for soft robotics is to build and control soft robots able to exert effective forces. In recent years, biology has inspired several solutions to such complex problems. This study aims at investigating the smart solution that the Octopus vulgaris adopts to perform a crawling movement, with the same limbs used for grasping and manipulation. An ad hoc robot was designed and built taking as a reference a biological hypothesis on crawling. A silicone arm with cables embedded to replicate the functionality of the arm muscles of the octopus was built. This novel arm is capable of pushing-based locomotion and object grasping, mimicking the movements that octopuses adopt when crawling. The results support the biological observations and clearly show a suitable way to build a more complex soft robot that, with minimum control, can perform diverse tasks.     

A model for cell motility on soft bio-adhesive substrates

Mechanical stiffness of bio-adhesive substrates has been recognized as a major regulator of cell motility. We present a simple physical model to study the crawling locomotion of a contractile cell on a soft elastic substrate. The mechanism of rigidity sensing is accounted for using Schwarz's two-spring model Schwarz et al. (2006). The predicted dependency between the speed of motility and substrate stiffness is qualitatively consistent with experimental observations. The model demonstrates that the rigidity dependent motility of cells is rooted in the regulation of actomyosin contractile forces by substrate deformation at each anchorage point. On stiffer substrates, the traction forces required for cell translocation acquire larger magnitude but show weaker asymmetry which leads to slower cell motility. On very soft substrates, the model predicts a biphasic relationship between the substrate rigidity and the speed of locomotion, over a narrow stiffness range, which has been observed experimentally for some cell types.     

Soft-cuticle biomechanics: A constitutive model of anisotropy for caterpillar integument

The mechanical properties of soft tissues are important for the control of motion in many invertebrates. Pressurized cylindrical animals such as worms have circumferential reinforcement of the body wall; however, no experimental characterization of comparable anisotropy has been reported for climbing larvae such as caterpillars. Using uniaxial, real-time fluorescence extensometry on millimeter scale cuticle specimens we have quantified differences in the mechanical properties of cuticle to circumferentially and longitudinally applied forces. Based on these results and the composite matrix-fiber structure of cuticle, a pseudo-elastic transversely isotropic constitutive material model was constructed with circumferential reinforcement realized as a Horgan-Saccomandi strain energy function. This model was then used numerically to describe the anisotropic material properties of Manduca cuticle. The constitutive material model will be used in a detailed finite-element analysis to improve our understanding of the mechanics of caterpillar crawling.     

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.     

Task-Level Strategies for Human Sagittal-Plane Running Maneuvers Are Consistent with Robotic Control Policies

The strategies that humans use to control unsteady locomotion are not well understood. A “spring-mass” template comprised of a point mass bouncing on a sprung leg can approximate both center of mass movements and ground reaction forces during running in humans and other animals. Legged robots that operate as bouncing, “spring-mass” systems can maintain stable motion using relatively simple, distributed feedback rules. We tested whether the changes to sagittal-plane movements during five running tasks involving active changes to running height, speed, and orientation were consistent with the rules used by bouncing robots to maintain stability. Changes to running height were associated with changes to leg force but not stance duration. To change speed, humans primarily used a “pogo stick” strategy, where speed changes were associated with adjustments to fore-aft foot placement, and not a “unicycle” strategy involving systematic changes to stance leg hip moment. However, hip moments were related to changes to body orientation and angular speed. Hip moments could be described with first order proportional-derivative relationship to trunk pitch. Overall, the task-level strategies used for body control in humans were consistent with the strategies employed by bouncing robots. Identification of these behavioral strategies could lead to a better understanding of the sensorimotor mechanisms that allow for effective unsteady locomotion.     

Undulatory locomotion of Caenorhabditis elegans on wet surfaces

The physical and biomechanical principles that govern undulatory movement on wet surfaces have important applications in physiology, physics, and engineering. The nematode Caenorhabditis elegans, with its highly stereotypical and functionally distinct sinusoidal locomotory gaits, is an excellent system in which to dissect these properties. Measurements of the main forces governing the C. elegans crawling gait on lubricated surfaces have been scarce, primarily due to difficulties in estimating the physical features at the nematode-gel interface. Using kinematic data and a hydrodynamic model based on lubrication theory, we calculate both the surface drag forces and the nematode's bending force while crawling on the surface of agar gels within a preexisting groove. We find that the normal and tangential surface drag coefficients during crawling are ～222 and 22, respectively, and the drag coefficient ratio is ～10. During crawling, the calculated internal bending force is time-periodic and spatially complex, exhibiting a phase lag with respect to the nematode's body bending curvature. This phase lag is largely due to viscous drag forces, which are higher during crawling as compared to swimming in an aqueous buffer solution. The spatial patterns of bending force generated during either swimming or crawling correlate well with previously described gait-specific features of calcium signals in muscle. Further, our analysis indicates that one may be able to control the motility gait of C. elegans by judiciously adjusting the magnitude of the surface drag coefficients.     

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.     

The influence of soft tissue movement on ground reaction forces, joint torques and joint reaction forces in drop landings

The aim of this study was to determine the effects that soft tissue motion has on ground reaction forces, joint torques and joint reaction forces in drop landings. To this end a four body-segment wobbling mass model was developed to reproduce the vertical ground reaction force curve for the first 100 ms of landing. Particular attention was paid to the passive impact phase, while selecting most model parameters a priori, thus permitting examination of the rigid body assumption on system kinetics. A two-dimensional wobbling mass model was developed in DADS (version 9.00, CADSI) to simulate landing from a drop of 43 cm. Subject-specific inertia parameters were calculated for both the rigid links and the wobbling masses. The magnitude and frequency response of the soft tissue of the subject to impulsive loading was measured and used as a criterion for assessing the wobbling mass motion. The model successfully reproduced the vertical ground reaction force for the first 100 ms of the landing with a peak vertical ground reaction force error of 1.2% and root mean square errors of 5% for the first 15 ms and 12% for the first 40 ms. The resultant joint forces and torques were lower for the wobbling mass model compared with a rigid body model, up to nearly 50% lower, indicating the important contribution of the wobbling masses on reducing system loading.     

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.     

Experimental/analytical analysis of human locomotion using bondgraphs

A new vectorial bondgraph approach for modeling and simulation of human locomotion is introduced. The vectorial bondgraph is applied to an eight-segment gait model to derive the equations of motion for studying ground reaction forces (GRFs) and centers of pressure (COPs) in single and double support phases of ground and treadmill walking. A phase detection technique and accompanying transition equation is proposed with which the GRFs and COPs may be calculated for the transitions from double-to-single and single-to-double support phases. Good agreement is found between model predictions and experimental data obtained from force plate measurements. The bondgraph modeling approach is shown to be both informative and adaptable, in the sense that the model resembles the human body structure, and that modeled body segments can be easily added or removed.     

Elegant‐crested Tinamous Eudromia elegans do not synchronize head and leg movements during head‐bobbing

Head‐bobbing is the fore–aft movement of the head relative to the body during terrestrial locomotion in birds. It is considered to be a behaviour that helps to stabilize images on the retina during locomotion, yet some studies have suggested biomechanical links between the movements of the head and legs. This study analysed terrestrial locomotion and head‐bobbing in the Elegant‐crested Tinamou Eudromia elegans at a range of speeds by synchronously recording high‐speed video and ground reaction forces in a laboratory setting. The results indicate that the timing of head and leg movements are dissociated from one another. Nonetheless, head and neck movements do affect stance duration, ground reaction forces and body pitch and, as a result, the movement of the centre of mass in head‐bobbing birds. This study does not support the hypothesis that head‐bobbing is itself constrained by terrestrial locomotion. Instead, it suggests that visual cues are the primary trigger for head‐bobbing in birds, and locomotion is, in turn, constrained by a need for image stabilization and depth perception.     

An Experimental Analysis of Overcoming Obstacle in Human Walking

In this paper, an experimental analysis of overcoming obstacle in human walking is carried out by means of a motion capture system. In the experiment, the lower body of an adult human is divided into seven segments, and three markers are pasted to each segment with the aim to obtain moving trajectory and to calculate joint variation during walking. Moreover, kinematic data in terms of displacement, velocity and acceleration are acquired as well. In addition, ground reaction forces are measured using force sensors. Based on the experimental results, features of overcoming obstacle in human walking are ana- lyzed. Experimental results show that the reason which leads to smooth walking can be identified as that the human has slight movement in the vertical direction during walking; the reason that human locomotion uses gravity effectively can be identified as that feet rotate around the toe joints during toe-off phase aiming at using gravitational potential energy to provide propulsion for swing phase. Furthermore, both normal walking gait and obstacle overcoming gait are characterized in a form that can provide necessary knowledge and useful databases for the implementation of motion planning and gait planning towards overcoming obstacle for humanoid robots.     

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.     

Comparison of in vivo measured loads in knee,hip and spinal implants during level walking

Walking is a task that we seek to understand because it is the most relevant human locomotion. Walking causes complex loading patterns and high load magnitudes within the human body. This work summarizes partially published load data collected in earlier in vivo measurement studies on 9 patients with telemeterized knee endoprostheses, 10 with hip endoprostheses and 5 with vertebral body replacements. Moreover, for the 19 endoprosthesis patients, additional simultaneously measured and previously unreported ground reaction forces are presented.The ground reaction force and the implant forces in the knee and hip exhibited a double peak during each step. The maxima of the ground reaction forces ranged from 100% to 126% bodyweight. In comparison, the greatest implant forces in the hip (249% bodyweight) and knee (271% bodyweight) were much greater. The mean peak force measured in the vertebral body replacement was 39% bodyweight and occurred at different time points of the stance phase.We concluded that walking leads to high load magnitudes in the knee and hip, whereas the forces in the vertebral body replacement remained relatively low. This indicates that the first peak force was greater in the hip than in the knee joint while this was reversed for the second peak force. The forces in the spinal implant were considerably lower than in the knee and hip joints.     

A mechanical model to determine the influence of masses and mass distribution on the impact force during running

Simple spring-damper-mass models have been widely used to simulate human locomotion. However, most previous models have not accounted for the effect of non-rigid masses (wobbling masses) on impact forces. A simple mechanical model of the human body developed in this study included the upper and lower bodies with each part represented by a rigid and a wobbling mass. Spring-damper units connected different masses to represent the stiffness and damping between the upper and lower bodies, and between the rigid and wobbling masses. The simulated impact forces were comparable to experimentally measured impact forces. Trends in changes of the impact forces due to changes in touch-down velocity reported in previous studies could be reproduced with the model. Simulated results showed that the impact force peaks increased with increasing rigid or wobbling masses of the lower body. The ratio of mass distribution between the rigid and wobbling mass in the lower body was also shown to affect the impact force peak, for example, the impact force peak increased with increasing rigid contribution. The variation in the masses of upper body was shown to have a minimum effect on the impact force peak, but a great effect on the active force peak (the second peak in the ground reaction force). Future studies on the dynamics and neuro-muscular control of human running are required to take into consideration the influence of individual variation in lower body masses and mass distribution.