Studying the Neural Basis of Adaptive Locomotor Behavior in Insects

Studying the neural basis of walking behavior, one often faces the problem that it is hard to separate the neuronally produced stepping output from those leg movements that result from passive forces and interactions with other legs through the common contact with the substrate. If we want to understand, which part of a given movement is produced by nervous system motor output, kinematic analysis of stepping movements, therefore, needs to be complemented with electrophysiological recordings of motor activity. The recording of neuronal or muscular activity in a behaving animal is often limited by the electrophysiological equipment which can constrain the animal in its ability to move with as many degrees of freedom as possible. This can either be avoided by using implantable electrodes and then having the animal move on a long tether (i.e. Clarac et al., 1987; Duch & Pflüger, 1995; Böhm et al., 1997; Gruhn & Rathmayer, 2002) or by transmitting the data using telemetric devices (Kutsch et al, 1993; Fischer et al., 1996; Tsuchida et al. 2004; Hama et al., 2007; Wang et al., 2008). Both of these elegant methods, which are successfully used in larger arthropods, often prove difficult to apply in smaller walking insects which either easily get entangled in the long tether or are hindered by the weight of the telemetric device and its batteries. In addition, in all these cases, it is still impossible to distinguish between the purely neuronal basis of locomotion and the effects exerted by mechanical coupling between the walking legs through the substrate. One solution for this problem is to conduct the experiments in a tethered animal that is free to walk in place and that is locally suspended, for example over a slippery surface, which effectively removes most ground contact mechanics. This has been used to study escape responses (Camhi and Nolen, 1981; Camhi and Levy, 1988), turning (Tryba and Ritzman, 2000a,b; Gruhn et al., 2009a), backward walking (Graham and Epstein, 1985) or changes in velocity (Gruhn et al., 2009b) and it allows the experimenter easily to combine intra- and extracellular physiology with kinematic analyses (Gruhn et al., 2006).We use a slippery surface setup to investigate the timing of leg muscles in the behaving stick insect with respect to touch-down and lift-off under different behavioral paradigms such as straight forward and curved walking in intact and reduced preparations.     

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.     

A passive dynamic walking robot that has a deterministic nonlinear gait

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

Robust and efficient walking with spring-like legs

The development of bipedal walking robots is inspired by human walking. A way of implementing walking could be performed by mimicking human leg dynamics. A fundamental model, representing human leg dynamics during walking and running, is the bipedal spring-mass model which is the basis for this paper. The aim of this study is the identification of leg parameters leading to a compromise between robustness and energy efficiency in walking. It is found that, compared to asymmetric walking, symmetric walking with flatter angles of attack reveals such a compromise. With increasing leg stiffness, energy efficiency increases continuously. However, robustness is the maximum at moderate leg stiffness and decreases slightly with increasing stiffness. Hence, an adjustable leg compliance would be preferred, which is adaptable to the environment. If the ground is even, a high leg stiffness leads to energy efficient walking. However, if external perturbations are expected, e.g. when the robot walks on uneven terrain, the leg should be softer and the angle of attack flatter. In the case of underactuated robots with constant physical springs, the leg stiffness should be larger than k = 14 in order to use the most robust gait. Soft legs, however, lack in both robustness and efficiency.     

A self-organizing model of walking patterns of insects

Insects generate walking patterns which depend upon external conditions. For example, when an insect is exposed to an additional load parallel to the direction in which it is walking, the walking pattern changes according to the magnitude of the load. Furthermore, even after some of its legs have been amputated, an insect will produce walking patterns with its remaining legs. These adaptations in insect walking could not previously be explained by a mathematical model, since the mathemati cal models were based upon the hypothesis that the relationship between walking velocity and walking patterns is fixed under all conditions. We have produced a mathematical model which describes self-organizing insect walking patterns in real-time by using feedback information regarding muscle load (Kimura et al. 1993). As part of this model, we introduced a new rule to coordinate leg movement, in which the information is circulated to optimize the efficiency of the energy transduction of each effector orga n. We describe this mechanism as ‘the least dissatisfaction for the greatest number of elements’. In this paper, we introduce the following aspects of this model, which reflect adaptability to changing circumstances: (1) after one leg is exposed to a transient perturbation, the walking pattern recovers swiftly; (2) when the external load parallel to the walking direction is continuously increased or decreased, the pattern transition point is shifted according to the magnitude of the load increme nt or decrement. This model generates a walking pattern which optimizes energy consumption at a given walking velocity even under these conditions; and (3) when some of the legs are amputated, the model generates walking patterns which are consistent with experimental results. We also discuss the ability of a hierarchical self-organizing model to describe a swift and flexible information processing system. Received: 8 February 1993/Accepted in revised form: 12 November 1993     

Maternal and fetal antibrain antibodies in development and disease

Recent evidence has emerged indicating that the maternal immune response can have a substantial deleterious impact on prenatal development (Croen et al., [2008]: Biol Psychiatry 64:583-588). The maternal immune response is largely sequestered from the fetus. Maternal antibodies, specifically immunoglobulin G (IgG), are passed to the fetus to provide passive immunity throughout much of pregnancy. However, both protective and pathogenic autoantibodies have equal access to the fetus (Goines and Van de Water [2010]: Curr Opin Neurol 23:111-117). If the mother has an underlying autoimmune disease or has reactivity to fetal antigens, autoantibodies produced before or during pregnancy can target tissues in the developing fetus. One such tissue is the fetal brain. The blood brainbarrier (BBB) is developing during the fetal period allowing maternal antibodies to have direct access to the brain during gestation (Diamond et al. [2009]: Nat Rev Immunol; Braunschweig et al. [2011]; Neurotoxicology 29:226-231). It has been proposed that brain injury by circulating brain-specific maternal autoantibodies might underlie multiple congenital, developmental disorders (Lee et al. [2009]: Nat Med 15:91-96). In this review, we will discuss the current state of research in the area of maternal autoantibodies and the development of autism. ? 2012 Wiley Periodicals, Inc. Develop Neurobiol, 2012.     

Non-stationary aging dynamics in ant societies

In recent experiments by Richardson et al. (2010) [Richardson, T.O., Robinson, E.J.H., Christensen, K., Jensen, H.J., Franks, N.R., Sendova-Franks, A.B., 2010. PLoS ONE 5, e9621.] ant motion out of the nest is shown to be a non-stationary process intriguingly similar to the dynamics encountered in physical aging of glassy systems. Specifically, exit events can be described as a Poisson process in logarithmic time, or, for short, a log-Poisson process. Nouvellet et al. (2010) [Nouvellet, P., Bacon, J.P.,Waxman, D., 2010. J. Theor. Biol. 266, 573.] criticized these conclusions and performed new experiments where the exit process could more simply be described by standard Poisson statistics. In their reply Richardson et al. (2011b) [Richardson, T.O., Robinson, E.J.H., Christensen, K., Jensen, J.H., Christensen, K., Jensen, H.J., Franks, N.R., Sendova-Franks, A.B., 2011b. J. Theor. Biol. 269, 356-358.] stressed that the two sets of experiments were performed under very different conditions and claimed that this was the likely source of the discrepancy. Ignoring any technical issues which are part of the above discussion, the focal point of this work is to ascertain whether or not both log-Poisson and Poisson statistics are possible in an ant society under different external conditions. To this end, a model is introduced where interacting ants move in a stochastic fashion from one site to a neighboring site on a finite 2D lattice. The probability of each move is determined by the ensuing changes of a utility function which is a sum of pairwise interactions between ants, weighted by distance. Depending on how the interactions are defined and on a control parameter dubbed ‘degree of stochasticity’ (DS), the dynamics either quickly converges to a stationary state, where movements are a standard Poisson process, or may enter a non-stationary regime, where exits can be described as suggested by Richardson et al. Other aspects of the model behavior are also discussed, i.e. the time dependence of the average value of the utility function, and the statistics of spatial re-arrangements happening anywhere in the system. Finally, we discuss the role of record events and their statistics in the context of ant societies and suggest the possibility that a transition from non-stationary to stationary dynamics can be triggered experimentally.     

Neuroinfections in developed versus developing countries

In recent supplement of neuroendocrinology letters, first time the authors from West and East, North and South of EU and the "Third World" present data on neuroinfections in high technology society - on nosocomial meningitis and vice versa in low technology and income countries of sub-Saharan Africa. 14 years survey of 171 cases of nosocomial paediatric meningitis is presented by Rudinsky et al. [1] and subpopulations of Acinetobacter baumannii and Pseudomonas aeruginosa [1,2] within last 20 years are briefly analyzed by Huttova et al. [2] and Ondrusova et al. [3]. All cases were complicating high technology procedures, such as neurosurgery, very low birth weight neonates after shunt implants etc. Current problems of management of nosocomial meningitis are reviewed by Bauer et al. [4] and consequence of inappropriate therapy by Huttova et al. [5]. Another high technology associated infection is septic embolisation followed by brain abscess and meningitis in patients with endocarditis after cardiac surgery (Kovac et al.) [6]. Experience from more than 600 cases is discussed in the article by Karvaj et al. [7] who outlines extremely high mortality in patients with endocarditis embolizing to central nervous system - up to 60%. The rest of papers are in contrary to problems of neuroinfections in EU and US focused on meningitis and cerebral malaria as commonest neuroinfections in the third world: 261 cases of cerebral malaria are discussed in a brief research note by Sudanese team of tropical programme in area of famine and civil war in southern Sudan (Bartkovjak and Ianetti et al.) [8]. Fungal neuroinfections complicating AIDS are of decreasing trend as reported by Njambi et al. from Kenya [9] and data from 497 cases from Uganda, Ethiopia and Burundi are presented by Benca et al. [10]. Finally an outbreak of meningococcal meningitis is reported by Benca et al. [11] from meningitis belt in Darfur and southern Sudan. We hope that the supplement may show difference in etiology, risk factors, therapy and outcome of neuroinfections (which is a burning public health and social problem in tropics) in other third world countries versus developed high-tech medical settings of US, EU and other high income countries, as presented by Benca et al. [12].     

Biomechanics and biomimetics in insect-inspired flight systems

Insect- and bird-size drones—micro air vehicles (MAV) that can perform autonomous flight in natural and man-made environments are now an active and well-integrated research area. MAVs normally operate at a low speed in a Reynolds number regime of 10⁴–10⁵ or lower, in which most flying animals of insects, birds and bats fly, and encounter unconventional challenges in generating sufficient aerodynamic forces to stay airborne and in controlling flight autonomy to achieve complex manoeuvres. Flying insects that power and control flight by flapping wings are capable of sophisticated aerodynamic force production and precise, agile manoeuvring, through an integrated system consisting of wings to generate aerodynamic force, muscles to move the wings and a control system to modulate power output from the muscles. In this article, we give a selective review on the state of the art of biomechanics in bioinspired flight systems in terms of flapping and flexible wing aerodynamics, flight dynamics and stability, passive and active mechanisms in stabilization and control, as well as flapping flight in unsteady environments. We further highlight recent advances in biomimetics of flapping-wing MAVs with a specific focus on insect-inspired wing design and fabrication, as well as sensing systems.This article is part of the themed issue ‘Moving in a moving medium: new perspectives on flight’.     

Passive bipedal walking with phasic muscle contraction

The existence of self-organizing walking patterns is often considered the result of a mechanical system interacting with the environment and a (neural) oscillating unit. The pattern generators might be thought of as an indispensable component for the existence of limit cycle behavior. This paper shows that this is not a necessity for the existence of a self-organizing bipedal walking pattern. Stable walking cycles emerge from a simple passive bipedal structure, with an energy source inevitably present to sustain the oscillation. In this work the energy source is chosen to be phasic muscle contraction. A two-dimensional model is composed of two legs and a hip mass, symbolizing the trunk. The stance leg stiffness is generated by two muscles. The hip stiffness is generated by four muscles. Muscle activation is caused by two reflex-like trigger signals, without feedback control. Human equivalent model parameters such as geometry and mass distribution were assumed. With return map analysis, the model is analyzed on periodic behavior. Stable walking cycles were found and could be manipulated during walking by varying the muscle or reflex parameters, forcing the oscillation to converge to a new attractor. Received: 5 November 1998 / Accepted in revised form: 26 March 1999     

Leg coordination and swimming in an ant, Camponotus americanus

ABSTRACT. Leg movements of Camponotus americanus workers during straight swimming and turning are described herein. Thrust is generated through the different speeds and drag control between power v. return strokes in the forelegs. During the power stroke, femur, tibia and tarsus are straightened and thereby increase resistance; they bend backward during the return stroke. These thrusting legs move in a vertical plane which is similar to their position during walking. The backward stretching mesothoracic and metathoracic legs act, in conjunction with the gaster, as a rudder. Swimming in ants can be derived from walking; the major transformation being a suppression of the rhythmic movements of the middle and hind legs.     

Sexing of mid‐incubation avian embryos as a management tool for zoological breeding programs

Skewed sex ratios in zoo breeding programs may require housing single birds of an overrepresented gender, increasing demands on limited resources that could otherwise be diverted to breeding pairs or other important species. The ability to selectively incubate and hatch eggs of a desired sex represents a significant improvement in the long‐term management of avian species. This study describes a successful method for in ovo sexing of embryos from stage 30 through 42 of incubation (Hamburger and Hamilton [1951] J Morphol 88:49–92). A 0.01–1 µl blood sample was collected from either the vitelline vessel (VV) or the blood vessels of the chorio–allantoic membrane (CAM) of embryos at stages 14–18 or 30–42, respectively. DNA was isolated from whole blood using the Chelex method (Walsh et al. [1991] Biotechniques 10:506–513; Jensen et al., [2003] Zoo Biol 22:561–571). Sex was determined by PCR amplification using the previously described P2/P8 (Griffiths et al. [1998] Mol Ecol 7:1071–1075) and 1237L/1272H (Kahn et al. [1998] Auk 115:1074–1078) primers or by commercial vendor. Success rate was calculated as the percent of sampled embryos surviving to hatch. Embryos of the undesired sex were not incubated, thus not included in the calculation. There was a considerable difference in success rate when blood was collected from the stage 14–18 VV (0–25%, average 12%) vs. stage 30–42 CAM (33–100%, average 76%). In conclusion, in ovo sexing of embryos between stages 30 and 42 yields acceptable embryo survival rates while providing enough blood for genetic testing. Zoo Biol 31:694‐704, 2012. © 2011 Wiley Periodicals, Inc.     

An analysis of swimming behavior in the portunid crab Callinectes sapidus

The swimming behavior of a portunid crab was analysed using high‐speed cinematography. The posture adopted for sideways swimming includes the rigid extension of trailing legs 1–4 and the cyclic beating of the modified 5th‐legs. There is also beating of leading legs 2–4. The 5th‐legs beat in near synchrony at approx. 4/sec while legs 2–4 beat in a normal walking gait at approx. 2/sec. There is no significant phase coupling between legs 2–4 and the 5th legs. Amputation of single walking‐legs (2–4) causes the remaining 2 legs to beat alternately and phase relationships now appear between remaining walking‐legs and the 5th‐legs. Amputation of single 5th‐legs cause no changes in walking‐legs and bilateral amputation effects are also absent. These results lead to the postulation of neural control systems to account for the observed behavior.     

The interaction of a kainate receptor from goldfish brain with a pertussis toxin-sensitive GTP-binding protein.

Kainate receptors are present in high concentrations in goldfish brain (Henley and Oswald, 1988a and b; Ziegra et al., 1990), possibly in neuronal and glial cells. In a number of systems, the kainate receptor has been assumed to be an integral ion channel (Watkins and Evans, 1981); but, for some kainate receptors, ion channel activity has not been demonstrated (Wada et al., 1989). This study presents evidence that a portion of the [3H]kainate-binding sites in goldfish brain is sensitive to guanine nucleotides, with a loss of high affinity binding in the presence of nonhydrolyzable GTP analogs. Pertussis toxin pretreatment of membranes causes a loss of high affinity [3H]kainate binding and of the guanine nucleotide-sensitive binding. Pertussis toxin catalyzes the specific [32P]ADP-ribosylation of a 40-kDa substrate in a kainate-sensitive manner. In addition, incorporation of [alpha-32P]GTP-gamma-azidoanilide by photoaffinity labeling was enhanced in the presence of kainate. These results indicate that a subpopulation of [3H]kainate-binding sites in goldfish brain may be coupled to G proteins.     

Leg stiffness increases with speed to modulate gait frequency and propulsion energy

Bipedal walking models with compliant legs have been employed to represent the ground reaction forces (GRFs) observed in human subjects. Quantification of the leg stiffness at varying gait speeds, therefore, would improve our understanding of the contributions of spring-like leg behavior to gait dynamics. In this study, we tuned a model of bipedal walking with damped compliant legs to match human GRFs at different gait speeds. Eight subjects walked at four different gait speeds, ranging from their self-selected speed to their maximum speed, in a random order. To examine the correlation between leg stiffness and the oscillatory behavior of the center of mass (CoM) during the single support phase, the damped natural frequency of the single compliant leg was compared with the duration of the single support phase. We observed that leg stiffness increased with speed and that the damping ratio was low and increased slightly with speed. The duration of the single support phase correlated well with the oscillation period of the damped complaint walking model, suggesting that CoM oscillations during single support may take advantage of resonance characteristics of the spring-like leg. The theoretical leg stiffness that maximizes the elastic energy stored in the compliant leg at the end of the single support phase is approximated by the empirical leg stiffness used to match model GRFs to human GRFs. This result implies that the CoM momentum change during the double support phase requires maximum forward propulsion and that an increase in leg stiffness with speed would beneficially increase the propulsion energy. Our results suggest that humans emulate, and may benefit from, spring-like leg mechanics.     

Killer systems in Saccharomyces cerevisiae: three distinct modes of exclusion of M2 double-stranded RNA by three species of double-stranded RNA, M1, L-A-E, and L-A-HN.

M1 and M2 double-stranded RNAs (dsRNAs) code for the K1R1 and K2R2 killer toxin and resistance functions, respectively. Natural variants of a larger dsRNA (L-A) carry various combinations of the [EXL], [HOK], and [NEX] genes, which affect the K1 and K2 killer systems. Other dsRNAs, the same size as L-A, called L-B and L-C, are often present with L-A. We show that K1 killer strains have [HOK] and [NEX] but not [EXL] on their L-A (in disagreement with Field et al., Cell 31:193-200, 1982). These strains also carry other L-size molecules detectable after heat-curing has eliminated L-A. The exclusion of M2 dsRNA observed on mating K2 strains with K1 strains is due to the M1 dsRNA (not the L-A dsRNA as claimed by Field et al.) in the K1 strains. Four independent mutants of a [KIL-k2] [NEX-o] [HOK-o] strain were selected for resistance to [EXL] exclusion of M2 ([EXLR] phenotype). The [EXLR] phenotype showed non-Mendelian inheritance in each case, and these mutants had simultaneously each acquired [HOK]. The mutations were located on L-A and not on M2, and did not confer resistance to M1 exclusion of M2.     

Isolation and sequence determination of peptide components of atrial natriuretic factor

The independent isolation and sequence determination in our laboratories of three closely related Atrial Natriuretic Factor peptides from rat atria confirm the sequences of ANF peptides reported by Seidah et al and synthesized by Nutt et al [Proc. Natl. Acad. Sci., (1984) in press] and contain the sequences reported by Flynn et al [Biochem. Biophys. Res. Commun. (1983) 117: 859-865] and by Currie et al [Science (1984) 223: 67-69]. In addition, we provide proof for a C-terminal tyrosine rather than tyrosine amide in our isolated peptides.     

Evaluation and re-evaluation of genetic radiation hazards in man. I. Interspecific comparison of estimates of mutation rates.

A detailed presentation is made of the experimental data from the various systems used by Abrahamson et al. [2] to conclude that the per locus per rad (low LET) radiation-induced forward mutation rates in organisms, whose DNA content varies by a factor of about 1000, is proportional to genome size. Additional information pertinent in this context is also reviewed. It is emphasized that the mutation rates cited by Abrahamson et al. [2], although considered as pertaining to mutations at specific loci, actually derive from a broad variety of genetic end-points. It is argued that an initial (if not sufficient) condition for sound inter-specific mutation rate comparisions, covering a wide range of organisms and detecting systems of various sensitivities, requires a reasonalbly consistent biological definition of a specific locus mutation, namely, a transmissible intra-locus change. Granting the differences between systems in their resolving power to detect intragenic change, the data cited in this paper do not support the existence of a simple proportionality between radiotion-induced intra-locus mutation rate and genome size for the different species reviewed here. Furthermore, in Drosophila melanogaster, where individual salivary gland chromosome bands (that can differ greatly in DNA content) are usually associated with individual loci or at least distinct complementation groups, radiation-induced intra-locus mutation rates are not correlated with apparent differences in the DNA content of bands. This result is incompatible with the notion that most of the DNA in a band represents a radiation-mutable target capable of eliciting the kind of mutation observed in mutation rate experiments. All these considerations argue against the validity of the hypothesis of Abrahamson et al. [2] and their generalization that, for the evaluation of genetic radiation hazards in man, we can now "extrapolate from mutation rates obtained in lower organisms to man with greater confidence" on the basis of DNA content (italics are ours).     

Testing the level of ant activity associated with quorum sensing: an empirical approach leading to the establishment and test of a null-model (response to the comment of Richardson et al.)

In a paper in this journal (Nouvellet et al., 2010), we presented results from experiments on the behaviour of the Pharaoh's ant, Monomorium pharaonis, along with a substantial statistical and theoretical analysis of the results. In a minor part of our paper, we compared our results with the related work of Richardson et al. (2010a). These authors have subsequently commented on our interpretation of their work (Richardson et al., 2011). In this Letter we respond to the comments of Richardson et al. (2011), and give detailed arguments why we stand by our original conclusions.     

Righting kinematics in beetles (Insecta: Coleoptera)

Twenty modes of stereotyped righting motions were observed in 116 representative species of coleoptera. Methods included cine and stereocine recording with further frame by frame analysis, stereogrammetry, inverse kinematic reconstruction of joint angles, stroboscopic photography, recording of electromyograms, 3D measurements of the articulations, etc. The basic mode consists of a search phase, ending up with grasping the substrate, and a righting, overturning phase. Leg coordination within the search cycle differs from the walking cycle with respect to phasing of certain muscle groups. Search movements of all legs appear chaotic, but the tendency to move in antiphase is still present in adjacent ipsilateral and contralateral leg pairs. The system of leg coordination might be split: legs of one side might search, while contralateral legs walk, or fore and middle legs walk while hind legs search. Elaborated types of righting include somersaults with the aid of contralateral or diagonal legs, pitch on elytra, jumps with previous energy storage with the aid of unbending between thoracic segments (well-known for Elateridae), or quick folding of elytra (originally described in Histeridae). Righting in beetles is compared with righting modes known in locusts and cockroaches. Search in a righting beetle is directed dorsad, while a walking insect searches for the ground downwards. Main righting modes were schematized for possible application to robotics.