Flexible locomotion in complex environments: the influence of species, speed and sensory feedback on panarthropod inter-leg coordination

Walking animals often vary the temporal and spatial coordination of their limb movements to move at different speeds or to navigate different terrains. During forward planar walking, for example, insects generally transition from a pentapodal coordination at slow speeds to a tripod stepping pattern during fast walking (Fig. 1). Recent studies have shown that transitions between inter-leg coordination patterns (ICPs) in insects occur in a probabalistic, continuous manner (Wosnitza et al., 2013; Szczecinski et al., 2018; DeAngelis et al., 2019). This is in contrast with observations in vertebrates (although, see Geyer et al., 2006), where switches between ICPs are often accompanied by a discontinuous transition in at least one kinematic parameter (e.g. duty factor or inter-leg phase relationship) and reliably occur at a characteristic speed (Alexander and Jayes, 1983; Alexander, 1989). This apparent lack of distinct gaits in insects implies that a single underlying controller may be able to generate their entire repertoire of ICPs (DeAngelis et al., 2019). Furthermore, commonalities in coordination patterns across a range of invertebrate species (Fig. 2) excitingly suggest the possibility of a shared control circuit that extends even beyond insects (Nirody, 2021).

The idea of a shared controller across panarthropods echoes an early observation of walking in Onychophora (velvet worms, which along with Tardigrada and Arthropoda, constitute Panarthropoda): onychophoran stepping patterns are ‘sufficiently wide to provide a common origin for all the more specialized types’ of arthropod walking patterns (Manton, 1952b). One proposed ‘universal’ circuit consists of mutual inhibition between contralateral leg pairs and a posterior-to-anterior inhibition on each ipsilateral side (DeAngelis et al., 2019; Nirody et al., 2021; Nirody, 2021). The broad framework of this model relies on the existence of distinct and largely autonomous central pattern generators (CPGs), each controlling the movement of a single limb; this idea has support from neurophysiological and biomechanical studies in several insects (Pearson and Franklin, 1984; Wosnitza et al., 2013; Ayali et al., 2015; Cruse, 1990; Cruse et al., 1995; Dürr et al., 2018). The nature of the connectivity between these CPGs, however, is far less obvious. While the above circuit can successfully generate the spectrum of panarthropod ICPs observed during forward planar walking, whether it can be extended to walking in more complex environments is unclear.

Here, I begin by detailing the structure of this phenomenological model and highlighting the commonalities in ICPs across panarthropods that form its basis (Fig. 3). I then extend this framework to accommodate movement beyond forward walking on flat terrain to situations in which variability in coordination (from the intra-individual to the inter-species level) becomes more apparent. Do the ‘universal’ patterns observed on flat ground persist when more complex environments are considered?

Inter-leg coordination patterns in panarthropods probably result from the interplay between CPG-driven output and sensory feedback from the environment. Many locomotive challenges faced by panarthropods [e.g. climbing over gaps (Blaesing and Cruse, 2004); walking over compliant or shifting substrates: (Humeau et al., 2019; Nirody et al., 2021); walking upside down (Ramdya et al., 2017); dealing with rough or three-dimensional terrain (Sponberg and Full, 2008)] necessitate that stepping patterns be constantly updated based on environmental and internal cues. There is evidence that even the ‘universal’ coordination patterns observed during walking on flat terrain also require both CPG activity and sensory feedback: electrophysiological studies of reduced insect preparations often show ICPs that deviate significantly from those observed in freely walking animals (Dürr et al., 2018).

Within the context of the above leg CPG model framework, I consider the contribution of two general types of sensory information: load sensing and proprioception. Broadly speaking, load sensing is relevant during the stance phase of walking (when the leg is in contact with the ground) and proprioceptive feedback is relevant during the swing phase (when the leg is lifted during a step). Sensory receptors responsive to both of these forms of information are prevalent in various panarthropods: campaniform sensilla in insects (Zill et al., 2011, 2012, 2015) and slit sensilla in spiders (French et al., 2002) monitor interaction forces with the substrate as strains in the exoskeleton, while hair fields near leg joints provide proprioceptive feedback in several insect species (Dürr et al., 2018; Mendes et al., 2013). Feedback from these receptors has been reported to impact leg movements and inter-leg coordination (Berg et al., 2013; Zill et al., 2009; Dallmann et al., 2017), as well as entrain CPG motor activity (Borgmann et al., 2009); this further emphasizes the importance of considering the effect of environmental feedback on panarthropod stepping patterns.

Throughout this review, I compile and present data from a range of studies on panarthropod coordination patterns during forward walking. In the first section, I begin with a discussion of the speed-dependent continuum of ICPs observed during walking on flat terrain in a wide range of panarthropod taxa. In the sections following, I explore deviations from this ICP spectrum, focusing on coordination patterns that arise in environments with challenging substrate material properties (which provide variable loading feedback) and with challenging substrate geometry (which compromise walking stability by disrupting swing-to-stance transitions).

Alongside data from biomechanical studies, I also report complementary results from neurophysiological analyses of various panarthropod species wherever appropriate. With this work, I hope to emphasize the value of: (1) performing experiments with an eye towards studying locomotion in naturalistic situations (e.g. walking over complex terrain, which often provides variable sensory feedback); (2) integrating results from neurophysiological studies with kinematic analyses; and (3) diversifying our repertoire of study systems across panarthropod taxa.

Within a lifetime (and often within a single hour), an animal must be able to walk at a wide range of speeds to achieve various behavioural goals: foraging for food requires relatively slow walking over long distances, while escaping a predator necessitates bursts of fast running. This can be done both by varying the dynamics of a single leg, as well as by modulating inter-leg coordination. With regard to single-leg dynamics, panarthropods vary both the length of their steps (stride length) and the time each step takes (stride frequency) to tune their walking speed. Increasing stride length beyond the limit imposed by leg morphology requires the insertion of an aerial phase, a strategy rarely used by panarthropod species (Full and Tu, 1991; Goldman et al., 2006; Wosnitza et al., 2013; Reinhardt and Blickhan, 2014; Pfeffer et al., 2019). Modulating stride frequency can be done by either shortening the time dedicated to swing (during which the leg is lifted) or stance (during which the leg is in contact with the ground). The majority of panarthropod species change walking speed by varying the duration of stance, with swing duration generally decreasing only slightly from low to medium speeds and remaining constant at higher walking speeds (Mendes et al., 2013;Wosnitza et al., 2013; Dürr et al., 2018).

The relative coordination between leg movements also varies with walking speed and has been reported to be optimized for stability in insects (Wosnitza et al., 2013; Szczecinski et al., 2018). Insects keep five feet on the ground in a ‘wave gait’ at slow speeds, walk using a tetrapod stepping pattern at intermediate speeds and prefer a tripod pattern during fast walking (Fig. 1). Wilson (1966) summarized the commonalities in walking patterns between slow and fast insects in a set of simple observations: (1) swing duration is independent of walking speed; (2) stride frequency increases with speed and is modulated by varying stance duration; (3) initiation of swing (lift-off of a leg) occurs in a posterior to anterior wave along each ipsilateral side; (4) contralateral leg pairs move in anti-phase.

Recent work on Drosophila more quantitatively characterized the structure of variability in observed coordination patterns on flat terrain across a wide range of walking speeds (Wosnitza et al., 2013; Szczecinski et al., 2018; DeAngelis et al., 2019). These studies show that flies transition smoothly between stepping patterns in a probabalistic manner, often making use of multiple ICPs at the same speed. Although these stepping patterns are often called ‘gaits’ in the literature (Nishii, 2000; Dürr et al., 2004; Bender et al., 2011), DeAngelis et al. (2019) show that flies actually progress through walking speeds along a speed-dependent continuum.

In agreement with Wilson's first and second observations, DeAngelis et al. (2019) showed that varying stance duration alone allows for the generation of the entire spectrum of Drosophila stepping patterns across walking speeds: from wave gait to tetrapod to tripod coordination. Varying stance duration also suffices to describe coordination patterns observed ‘beyond’ tripod in many fast-running hexapod species, such as the bipod and monopod stepping patterns observed in cockroaches, beetles and ants (Hughes, 1952; Full and Tu, 1991; Wahl et al., 2015).

These observations can also be easily generalized beyond hexapods. Coordination patterns in several non-insect panarthropods (Manton, 1950; 1952a; Spagna et al., 2011; Nirody et al., 2021) seem to follow the same patterns even though they do not show the exact progression of ICPs in insects (Fig. 1). For example, Wilson's third observation implies that swing phases of ipsilateral legs on adjacent segments do not overlap, with lift-offs occurring in a posterior-to-anterior wave. In a generalized panarthropod with leg number n_legs, this results in ipsilateral phase offset increasing from at low speeds, to a maximum offset of at the highest speeds (⁠ results in a retrograde wave of swing initiations that travels from anterior to posterior). Broadly, reducing stance duration increases the frequency of the traveling wave of swing initiations and a decrease in the number of leg pairs involved in each cycle n_cycle (‘the wavelength’) with walking speed; this corresponds to an increase in the phase offset between ipsilateral legs (Nirody, 2021).

In hexapods (n_legs=6), this corresponds to a continuum varying smoothly with speed from in wave coordination, to in tetrapods and in tripods (Fig. 1). In myriapods, the same fundamental control rules manifest in a metachronal wave coordination across all walking speeds (Manton, 1952a). In this manner, arthropods with many legs can reach very high speeds during grounded running with a relatively high number of feet on the ground at any given time (i.e. maintain a high duty factor at high speeds) (Manton, 1952a; Kuroda et al., 2018 preprint; Yasui et al., 2019). Finally, in agreement with Wilson's fourth observation, contralateral phase offset φ_C=0.5 remains constant across speeds in a wide range of panarthropod species (Fig. 2).

Wilson's observations can be quantified in the form of a simple model, composed of distinct central pattern generators (CPGs) in each leg (DeAngelis et al., 2019; Schilling and Cruse, 2020; Nirody, 2021). The existence of hemisegmental CPGs gains support from a long history of studies in insects, including experiments in the stick insect that showed that rhythmic leg movements are still generated in preparations transected along the midline of the thoracic ganglia (Büschges et al., 1995). This and other early work on deafferented animals determined that central neuronal networks in the thoracic ganglia are able to generate rhythmic activity in insect leg motor neurons without descending or sensory input when activated by applying the muscarinic agonist pilocarpine (Mantziaris et al., 2020). For example, work in locusts reported that coordinated activity akin to stepping could be observed in similar preparations (Ryckebusch and Laurent,1993, 1994; Knebel et al., 2017).

Within this simple model, each pair of contralateral legs displays mutual inhibitory coupling, while a posterior-to-anterior inhibitory coupling exists between ipsilateral legs on each side (Fig. 3). Much remains to be understood about the organization of these CPGs within the panarthropod nervous system, and whether these similarities in ICPs across panarthropod taxa suggest an underlying common neural mechanism is unclear.

Much of the neural circuitry for walking in panarthropods is contained within the ventral nerve cord (VNC), the topology of which is largely conserved across taxa: each ganglion (neuromere) is made up of a grouping of neurons that are responsible for dealing with the sensory inputs and motor outputs for the leg pair on the associated segment. Each thoracic neuromere is further subdivided into two halves (neuropil), each of which controls the motor neurons and muscles in a leg (Yang et al., 2016; Niven et al., 2008). Within this general framework, however, there exists significant morphological diversity; in particular, the position of each neuromere relative to adjacent ones, as well as to the segment they innervate, is highly variable among panarthropods (Niven et al., 2008).

It requires less time and metabolic energy to transmit signals between closely placed neurons, and several modelling studies have suggested that nervous systems in both vertebrates and invertebrates are organized to minimize total wiring cost (Laughlin, 2001). The distance between neighboring neuromeres and between a neuromere and the segment it innervates, then, may represent competing selective forces in shaping the structure of the nerve cord: as posterior neuromeres are drawn forward to ‘fuse’ with their anterior neighbor, they are drawn away from the leg pair that they are responsible for controlling (Niven et al., 2008). Comparative studies of extant and fossil morphology suggest that the ancestral VNC featured thoracic neuromeres that were ‘unfused’ (Yang et al., 2016) and the pattern of diversity of fusion patterns of the thoracic ganglia among extant taxa imply that multiple fusion and separation events have likely occurred (Niven et al., 2008). Whether the phylogenetic pattern of neuromere positioning suggests a functional trade-off between inter-neuromere and peripheral connectivity remains unclear: very little variation in coordination between ipsilateral limbs has been reported across panarthropod taxa, with tardigrades, fruit flies and centipedes showing the same general stepping pattern during forward walking on flat surfaces (Fig. 1).

Coupling between contralateral (intrasegmental) limb CPGs is generally far more variable than coupling between ipsilateral legs, both intraspecifically and among different panarthropod species (Dürr, 2005; Nirody, 2021). Studies in onychophorans may hint at a possible structure–function relationship here: kinematic analyses report that velvet worms display little coordination between contralateral limb pairs, even on flat terrain (Oliveira et al., 2019), while structural studies show a lateralized VNC architecture with completely unfused and distantly located intrasegmental neuropil across Onychophora (Yang et al., 2016). However, neural coupling between contralateral leg pairs is generally quite weak across panarthropod species and whether the observed variability in coordination actually corresponds to VNC morphology is far from clear. The variability in panarthropod coordination patterns observed during walking on flat terrain is very likely the tip of the iceberg. Apparent ‘universal’ features observed in planar stepping patterns may be misleading and phenomenological models rooted in these commonalities probably fall short of providing the full picture of panarthropod walking.

There is mounting evidence that inter-leg coordination arises from a complex – and possibly species-specific – combination of central and peripheral influences. For instance, the pattern of central interactions between leg CPGs in pharmacologically stimulated insect preparations varies between species. Pilocarpine application in cockroach (David et al., 2016) and hawk moth (Johnston and Levine, 2002) preparations resulted in a tripod-like walking pattern with anti-phase contralateral coordination as in intact animals; CGPs in the stick insect (Mantziaris et al., 2017) and locust (Knebel et al., 2017), however, tended towards in-phase coordination. This deviation from observations in freely behaving animals may be due to the influence of sensory input, which has been hypothesized to affect coordination more strongly in slow-walking insects (such as stick insects and locusts) than in fast-walking animals (such as cockroaches and hawk moths) (Mantziaris et al., 2020).

The neural underpinning of these influences remains largely unknown. Even more elusive is how analogous combinations of descending control and sensory feedback generate locomotive strategies in more complex environments, as well as in other behaviors such as grooming or searching. In particular, uncovering whether similarly convergent coordination strategies across species arise in more complex maneuvers will require deeper and more comprehensive investigation of walking in a wider range of environments and in a wider range of panarthropod species.

Legged locomotion encompasses a variety of terrain, which can pose a range of locomotive challenges. One such challenge relevant to a number of natural environments is walking over substrates that are slippery, compliant (tendency to flow) or otherwise unsteady. For example, arthropods such as mites and ladybirds must move along deformable – and often wet and slippery – plant leaves (Eigenbrode et al., 2009). Many tropical ecosystems (which are of course packed with a huge number of panarthropods) oscillate between being primarily terrestrial to semi-aquatic owing to seasonal monsoons. Finally, granular media such as soil and sand are present in a huge range of environments like deserts, seashores and underwater substrates – all of which are densely inhabited by diverse panarthropod species. Many predators have also evolved strategies to exploit these locomotive challenges to catch insect prey: for example, the slippery peristome of carnivorous plants (Bohn and Federle, 2004) and sandy antlion pits (Fertin and Casas, 2006).

Still, a range of panarthropod species can move adeptly across these terrains. Neurophysiological and biomechanical studies have illustrated the importance of sensory feedback from the leg in organising ICPs for walking (Zill et al., 2004; Dallmann et al., 2017; Harris et al., 2022). What happens when feedback signals are disrupted by shifting or unsteady substrates?

The model shown in Fig. 3A proposes a connectivity scheme between leg CPGs on coordination patterns that emerge during walking on flat terrain. In order to accommodate a broader range of naturalistic situations, I shift from a phenomenological framework to a more mechanistic one. Even within the context of planar walking, it has been well documented that the observed continuum of stepping patterns is probabilistic and shows large intra- and inter-individual variability (Wosnitza et al., 2013; Mendes et al., 2013; DeAngelis et al., 2019). This variability becomes even more significant when movement over more complex terrain is considered.

To this end, rather than constructing a set of observations starting with these idealized stepping patterns, Cruse (1990) used data from behavioral studies of the stick insect Carausius morosus to put forward a set of locally distributed coordination rules from which these patterns might naturally arise. These are often called ‘Cruse's rules’, and they describe how the movement of a limb effects the stance-to-swing transition (that is, the lifting of a leg off the ground) of its ipsilateral and contralateral neighbors (Fig. 4). Rule 1 states that the initiation of swing of a leg is suppressed when its neighbor is in swing and rule 2 states that the likelihood lift-off increases once its neighbor is set down. These rules emphasize the idea that panarthropod walking patterns do not constitute distinct ‘gaits’ with distinct underlying controllers, but rather a spectrum of continuously varying emergent patterns (DeAngelis et al., 2019). For forward walking, these rules result in the model shown in Fig. 3A and produce the spectrum of patterns shown in Fig. 1. Importantly, however, these rules (unlike Wilson's observations) can be adapted to a wide range of locomotive patterns, as the coupling strength between legs can be made context dependent (Cruse et al., 2004; Dürr et al., 2018; Schilling and Cruse, 2020).

Indeed, the relative importance of sensory feedback in coordinating inter-leg coupling likely depends on speed, species and substrate. For instance, when faced with changes in load due to slipping or shifting substrate, several panarthropods vary the coupling between contralateral leg pairs. This often results in a coordination akin to ‘galloping’, in which contralateral limb pairs move in synchrony (Nirody, 2021). Although long recorded in aquatic (Zhang et al., 2014; Mulloney and Smarandache-Wellmann, 2012) and fossorial (Manton, 1954; Faulkes and Paul, 1997) species, synchronous contralateral stepping is rarely seen as a primary locomotive strategy in terrestrial panarthropods. However, this coordination pattern seems to be adopted as a response to abrupt changes in load by a wide range of species in a variety of challenging environments (Fig. 5). The tardigrade Hypsibius exemplaris, when walking on compliant substrates, switches to galloping coordination often for several strides at a time (Nirody et al., 2021). The pseudoscorpion Chelifer cancroides transitions from an alternating tetrapod (Fig. 1) to a slow, variable stepping pattern containing several in-phase contralateral steps during inverted walking (Tross et al., 2022). Semi-aquatic spiders often switch to a ‘rowing’ or ‘galloping’ coordination on the water's surface (Suter et al., 2003); the faster-running mainly terrestrial spider Cupiennius salei resists rowing until it becomes absolutely necessary (Barnes and Barth, 1991; Barth, 2021). This parallel convergence onto a similar inter-leg coordination strategy by such a diverse group of organisms may reflect an energetic or stability benefit on unstable or shifting terrain.

Although this stepping pattern is observed across a wide range of species, there are also many panarthropods that show little to no change in inter-leg coordination when traversing unsteady substrates. For example, the fast-running desert ant Aphaenogaster subterranea adopts a wave gait but maintains anti-phase contralateral coordination (and sometimes even maintains tripod coordination) when showing signs of leg slipping (Humeau et al., 2019); this is in contrast to results showing that tardigrades switch to in-phase contralateral coordination after similar leg-slipping events (Nirody et al., 2021). The cockroach Nauphoeta cinerea also transitions between equivalent high-speed stepping patterns on slippery and stable substrates (all of which retain anti-phase contralateral coupling), albeit at different characteristic speeds (Weihmann et al., 2017). Drosophila prefer tripod gaits during vertical climbs, aided by leg adhesion structures that prevent slipping; however, when adhesion is disrupted, flies abandon a tripod gait in favour of a ‘bipod’ stepping pattern characterized by the synchronization of contralateral leg pairs (Ramdya et al., 2017). As it has been shown that several agile animals like ants and cockroaches make use of leg adaptations such as claws to traverse challenging terrain (Dai et al., 2002; Reinhardt and Blickhan, 2014; Federle and Labonte, 2019; Merienne et al., 2021), it would be interesting to more broadly investigate how other panarthropod species cope when such specializations are blocked.

These changes in contralateral coordination may be a specialization to deal with substrates that provide variable feedback to loading sensors (Ramdya et al., 2017). Several species, such as Lycosa tarentula (Ward and Humphreys, 1981), Dolomedes aquaticus (Pullar and Paulin, 2018 preprint) and Carausius morosus (Cruse, 1976), show contralateral uncoupling mainly in the front leg pair, which may be used for sensing or searching. This coordination pattern is hypothesized to have become fixed in some species: several panarthropods adapted for living in environments with unstable terrain exhibit exclusively in-phase coupling between contralateral legs (rather than the broadly observed anti-phase pattern). Pachysoma dung beetles gallop when moving through their sand dune habitat (Smolka et al., 2013) and water striders row with synchronous contralateral leg pairs on the water's surface (Hu et al., 2003). This coupling pattern is also prevalent in behaviors other than straight walking. Honeybees use synchronous stepping to steer and turn along a wall (Zhao et al., 2018) and Albuneid sand crabs move their hind limbs in synchrony when faced with abrupt changes in loading signals during backwards digging (Faulkes and Paul, 1997). Fossorial myriapods such as millipedes show exclusively in-phase contralateral coordination when burrowing or walking on soil (Manton, 1954). In-phase contralateral coupling of thoracic legs is also observed during swimming in several panarthropods (Spirito, 1972; Paul, 1981;Faulkes and Paul, 1997).

A possible reason for the observed species-specific discrepancies in response to changes in loading may be that coordination in slow-walking animals is driven more strongly by sensory input than in fast-walking animals (Fig. 5); although note that experiments have demonstrated examples of fast sensory feedback processes (Höltje and Hustert, 2003). As discussed previously, fictive locomotive patterns in cockroaches and hawk moths (David et al., 2016; Johnston and Levine, 2002) mirror those seen during free walking, while experiments in slower moving insects (stick insects and locusts) show pharmacologically induced coordination patterns that deviate significantly from observations in intact animals (Mantziaris et al., 2017; Knebel et al., 2017). Because of its tendency to freely walk at a wide range of speeds, Drosophila is once again useful in bridging these two regimes. Leg ablation experiments in fruit flies provide support for this speed-dependent hypothesis: amputated legs twitch in coordination with intact legs only during fast walking (Berendes et al., 2016). Similarly, sensory deprived Drosophila retain tripod coordination with high fidelity only at high forward walking speed (Mendes et al., 2013).

These results may point to distinct neural programs that are more or less dependent on sensory feedback, depending on the speed of locomotion (Mendes et al., 2013). In contrast to observations that effectiveness of sensory feedback is speed dependent in Drosophila, walking in cockroaches maintains a constant level of centralization across all speeds (Neveln et al., 2019); this is consistent with experiments in deafferented animals that show fictive locomotion patterns akin to those observed during walking (David et al., 2016). Many studies have highlighted that the role of a limb, and consequently the contribution of sensory feedback, are context specific and hinge crucially on the behavioural goal of the animal (Dürr et al., 2018). In addition, taken together with neurophysiological and biomechanical analyses across several species, recent results suggest that centralization might not just be context specific but also species specific. Studies in generalist walkers like Drosophila (for which genetic tools to manipulate and probe sensory pathways are conveniently available) can be very informative, but understanding how neural programs underlying limb control have diversified across panarthropods will require similarly integrative investigations of walking through naturalistic environments in a wider range of species (in particular, both fast and slow walkers across taxa).

In addition to material properties, the geometry of the substrate can also compromise walking stability. Natural terrain is rarely flat, and panarthropods must contend with obstacles and roughness across a range of length scales. The natural habitats of many cockroach and stick insect species constitute a three-dimensional maze of twigs and leaf litter (Dürr, 2001; Sponberg and Full, 2008). Limnoterrestrial tardigrades stroll over three-dimensional moss landscapes to find food and mates (Nirody et al., 2021). Foraging ants must carry food over long stretches of coarse sand and gravel (Bernadou et al., 2011). Efficient locomotion through spatially complex surroundings necessitates the constant update of walking coordination in response to environmental variability; this likely results in deviation from stereotypic stepping patterns observed on flat terrain. What mechanisms facilitate such adaptivity when faced with loss of ground contact during stepping?

The generation of short steps during climbing or walking has been well characterized in stick insects. If all steps taken by an animal arose from a single underlying mechanism, the relevant kinematic parameters (e.g. stride length, frequency of stepping) would be expected to show a unimodal distribution. Since short stepping is a relatively rare event, it can be challenging to test whether short steps – which were primarily observed when facing three-dimensional obstacles – represent the tail of a unimodal distribution or are in fact distinct from normal strides. Bläsing and Cruse (2004) showed that step length distribution during climbing in Aretaon asperrimus was indeed bimodal, with short steps occurring right before gap traversal; in comparison, short steps occurred very rarely during walking and the step length distribution could not be definitively distinguished from unimodal. Later experiments that analyzed a larger dataset in C. morosus were able to capture a more accurate picture of these statistics, showing that steps were similarly distributed during walking and climbing (Theunissen and Dürr, 2013). The step lengths of Drosophila (Mendes et al., 2013) and several species of stick insects (Theunissen et al., 2015) are distributed similarly (Fig. 6). Interestingly – in a similar pattern as observed in stick insects – the step length distribution for Argentine ant workers (Linepithema humile) appears unimodal on flat ground, whereas an increase in short steps is observed on challenging, rough terrain (Clifton et al., 2020).

These short steps have been hypothesized to be searching movements, which is supported by results showing that the proportion of short steps increases as a function of climbing effort in stick insects (Theunissen and Dürr, 2013). Hindering gripping ability via ablation of the tarsal claws results in a shift towards a higher number of short steps, as would be expected for corrective movements in response to sensory cues relaying an inappropriate interaction with the substrate (Theunissen and Dürr, 2013; Dürr et al., 2018). In accordance with this idea, sensory deprivation in Drosophila results in a drastic reduction of the number of short steps (Mendes et al., 2013).

Several species also use alternative strategies to cope with gap-filled or rough terrain. Grasshoppers (Niven et al., 2012) and locusts (Niven et al., 2010) use visual input to cross gaps and do not display stereotyped searching movements. Cockroaches gain information about their environment using their antennae (Camhi and Johnson, 1999; Okada and Toh, 2006; Watson et al., 2002; Harley et al., 2009) and do not alter their stepping patterns over complex three-dimensional terrain (Sponberg and Full, 2008). Information transfer among legs themselves also allows hind legs to exploit their ipsilateral predecessor's successful footholds (Song and Choi, 1989). This spatial coordination of limb positioning makes up Cruse's third rule and is widely observed across arthropod species (Cruse, 1990; Dürr et al., 2018).

The question of whether searching movements represent an extreme of a sensory feedback-driven neural program or whether they constitute a distinct type of movement separate from locomotive stepping remains open. Both hypotheses find support across different species and methods of investigation. The former is supported by observations in stick insects that the coordination among the joints of a single leg differ significantly between searching and swing movements (Berg et al., 2015). Furthermore, searching movements could be initiated and halted by injecting depolarizing and hyperpolarizing currents, respectively, into a local interneuron of the mesothoracic ganglion (Berg et al., 2015).

In support of the latter, experiments ablating the trochanteral hair field or otherwise restricting proprioreceptive input in stick insects suggest that swing and searching movements are informed by the same afferent information and thus may be subject to a single feedback controller (Dürr, 2001; Schumm and Cruse, 2006; Theunissen et al., 2014); this is similar to sensory deprivation experiments in Drosophila (Mendes et al., 2013). Experiments in Drosophila also show that short steps do not occur at fast speeds, when walking is hypothesized to be less influenced by sensory feedback (Mendes et al., 2013). In accordance, specialized fast-walking insects such as cockroaches generally do not show changes in leg coordination patterns when traversing challenging terrain. As such, swing and searching may be differentiated only by the fact that swing is interrupted by a touch down event, allowing the leg to become mechanically coupled to the other limbs and responsive to sensory feedback from load receptors (Dürr et al., 2018). These discrepancies once again emphasize the importance of synthesizing information from a wider range of species using a wider range of experimental approaches – for instance, neurophysiological experiments on reduced preparations together with biomechanical analyses on freely-behaving animals in naturalistic situations (Tytell et al., 2011).

Panarthropods can adeptly move across a wide range of challenging terrain and their ability to do so with relatively simple nervous systems makes them compelling study organisms. This diversity is in part what makes recent studies that suggest a broadly shared coordination strategy across taxa particularly exciting (Wosnitza et al., 2013; DeAngelis et al., 2019; Nirody, 2021). However, variability (from intra-individual to inter-species) observed during forward walking on flat terrain becomes even more salient when considering movement over more complex terrain (Dürr et al., 2018). Panarthropod locomotion through complex environments is the result of interplay between central pattern generators and sensory feedback, a relationship that is likely tuned to species, speed and situation. In this Review, I emphasize the value of integrative and comparative perspectives towards properly characterizing this variability, both in the range of species studied and the diversity of techniques used.

Early behavioral studies of walking in stick insects and cockroaches resulted in a set of observations able to explain ICPs across speeds (Wilson, 1966). These observations can be put in the context of a ‘universal’ model comprising distinct leg CPGs, with mutual inhibition between contralateral limbs and posterior-to-anterior inhibition on each ipsilateral side (DeAngelis et al., 2019; Nirody et al., 2021; Nirody, 2021). Here, I compile kinematic data from studies of planar walking in a range of panarthropod species that highlight the key features of this model (Figs 1, 2 and 3A). When discussing movement over more complex terrain, observed coordination deviates from the original observations. Accordingly, shifting our perspective from phenomenological models to a mechanistic framework based on locally distributed coordination ‘rules’ between neighboring leg CPGs, from which the previously discussed spectrum of coordination patterns naturally emerges (Cruse, 1990; Schilling and Cruse, 2020). An important feature of this framework is that the nature of connections between individual leg controllers are not fixed but can be adapted to include context-dependent influences, including various forms of sensory feedback.

In an earlier review, Dürr et al. (2018) synthesized a range of experimental and computational results from stick insects to argue for the consideration of behavioral goals in experimental design. It is important to note that panarthropod limbs are used for a wide range of tasks, across which the relative contribution of sensory feedback can vary widely. Indeed, panarthropod limbs are adapted to many behaviors, including grooming (Seeds et al., 2014), communication (Riley et al., 2005) and long-distance navigation (Wehner, 2003; Wittlinger et al., 2006). Although I have focused my discussion here on locomotion (and more specifically, on the pattern of coordination between legs during walking), this variability is clear, even within this limited context.

A step cycle is made up of two phases, one in which the leg is in contact with the ground and mechanically coupled to the other legs (stance) and one in which the leg is lifted in the air (swing). I have structured this Review to consider two broad categories of mechanical challenges posed in natural environments: those that correspond to substrate material properties (which generally affect sensing of load and the forces between body and environment and are primarily relevant during stance phase) and those that correspond to substrate geometry (which generally affect proprioception and are primarily relevant during swing phase). These challenges are presented by environments densely occupied by a range of panarthropod species: unsteady substrates that provide variable sensory feedback about load, such as slippery terrain or sand, and rough three-dimensional landscapes that result in a higher number of searching movements (which might be regarded as ‘swings that fail to transition into stance’). As in the discussion on the speed-dependent spectrum of ICPs, I also present kinematic data from studies in which panarthropods are subjected to various mechanical cues from the environment.

Any synthesis attempted in this Review is of course limited by the availability of data in the literature. I have limited the discussion to ICPs rather than discussing true gaits, which cannot be defined simply by leg kinematics but also must take the animal's inertia into account. Although there is mounting evidence that distinct gaits do not exist in panarthropods as they do in vertebrates (DeAngelis et al., 2019), several studies suggest that transitions between invertebrate ICPs may be driven by an optimization against physical constraints (Nishii, 2000; Szczecinski et al., 2018). However, data concerning changes in center of mass dynamics are available in the literature for a very limited number of arthropod species (e.g. Full and Tu, 1990, 1991; Ting et al., 1994; Dallmann et al., 2017). As such, I constrain analysis to stepping patterns, for which datasets are far more accessible (Mendes et al., 2013; Wosnitza et al., 2013; DeAngelis et al., 2019; Nirody et al., 2021).

The breadth of this discussion across species is similarly limited by data availability in the literature: note that the majority of the examples focus on walking in insects. This reflects the distribution of past research in the field and I attempt to include data from a range of non-insect panarthropods whenever possible. As such, a final important point I hope to emphasize is that both depth (e.g. integrating results from different experimental techniques) and breadth (e.g. across taxa and naturalistic behaviours) are needed to more comprehensively examine flexible locomotion in complex environments.

Such comprehensive analyses require not only the implementation of new techniques, but also the careful consolidation of possible discrepancies in the results across these techniques – for example, between fictive locomotive patterns from reduced preparations and coordination patterns observed in behavioral and biomechanical analyses on freely walking animals (Johnston and Levine, 2002; David et al., 2016; Mantziaris et al., 2017; Knebel et al., 2017). This intrinsically calls for a deeper consideration of how both species and behavioral goal shape the relationship between sensory feedback and CPG-driven control. These steps towards a more comprehensive and integrative understanding of flexible and naturalistic panarthropod locomotion necessitate that: (1) more experiments are designed and performed with naturalistic behaviors in mind, whether in the field (Yanoviak et al., 2005; Bohn et al., 2012; Stark et al., 2018) or in the lab (Smolka et al., 2013; Dallmann et al., 2019; Humeau et al., 2019; Othayoth et al., 2022; Wang et al., 2022) and (2) that data across a wide range of species is both collected and made freely available for future comparative analyses (Couzin-Fuchs et al., 2015; Russell et al., 2017; Muñoz and Price, 2019).

I am thankful to Volker Dürr and Sheila Patek for their constructive comments on an earlier version of this review, as well as to two anonymous reviewers; all of these suggestions have greatly improved this manuscript.