The Biomechanics of Multi-articular Muscle-Tendon Systems in Snakes

ArborSim: Articulated, branching, OpenSim routing for constructing models of multi-jointed appendages with complex muscle-tendon architecture

Computational models of musculoskeletal systems are essential tools for understanding how muscles, tendons, bones, and actuation signals generate motion. In particular, the OpenSim family of models has facilitated a wide range of studies on diverse human motions, clinical studies of gait, and even non-human locomotion. However, biological structures with many joints, such as fingers, necks, tails, and spines, have been a longstanding challenge to the OpenSim modeling community, especially because these structures comprise numerous bones and are frequently actuated by extrinsic muscles that span multiple joints-often more than three-and act through a complex network of branching tendons. Existing model building software, typically optimized for limb structures, makes it difficult to build OpenSim models that accurately reflect these intricacies. Here, we introduce ArborSim, customized software that efficiently creates musculoskeletal models of highly jointed structures and can build branched muscle-tendon architectures. We used ArborSim to construct toy models of articulated structures to determine which morphological features make a structure most sensitive to branching. By comparing the joint kinematics of models constructed with branched and parallel muscle-tendon units, we found that among various parameters-the number of tendon branches, the number of joints between branches, and the ratio of muscle fiber length to muscle tendon unit length-the number of tendon branches and the number of joints between branches are most sensitive to branching modeling method. Notably, the differences between these models showed no predictable pattern with increased complexity. As the proportion of muscle increased, the kinematic differences between branched and parallel models units also increased. Our findings suggest that stress and strain interactions between distal tendon branches and proximal tendon and muscle greatly affect the overall kinematics of a musculoskeletal system. By incorporating complex muscle-tendon branching into OpenSim models using ArborSim, we can gain deeper insight into the interactions between the axial and appendicular skeleton, model the evolution and function of diverse animal tails, and understand the mechanics of more complex motions and tasks.

Functional diversity of snake locomotor behaviors: A review of the biological literature for bioinspiration

Organismal solutions to natural challenges can spark creative engineering applications. However, most engineers are not experts in organismal biology, creating a potential barrier to maximally effective bioinspired design. In this review, we aim to reduce that barrier with respect to a group of organisms that hold particular promise for a variety of applications: snakes. Representing >10% of tetrapod vertebrates, snakes inhabit nearly every imaginable terrestrial environment, moving with ease under many conditions that would thwart other animals. To do so, they employ over a dozen different types of locomotion (perhaps well over). Lacking limbs, they have evolved axial musculoskeletal features that enable their vast functional diversity, which can vary across species. Different species also have various skin features that provide numerous functional benefits, including frictional anisotropy or isotropy (as their locomotor habits demand), waterproofing, dirt shedding, antimicrobial properties, structural colors, and wear resistance. Snakes clearly have much to offer to the fields of robotics and materials science. We aim for this review to increase knowledge of snake functional diversity by facilitating access to the relevant literature.

The relative contributions of multiarticular snake muscles to movement in different planes

Muscles spanning multiple joints play important functional roles in a wide range of systems across tetrapods; however, their fundamental mechanics are poorly understood, particularly the consequences of anatomical position on mechanical advantage. Snakes provide an excellent study system for advancing this topic. They rely on the axial muscles for many activities, including striking, constriction, defensive displays, and locomotion. Moreover, those muscles span from one or a few vertebrae to over 30, and anatomy varies among muscles and among species. We characterized the anatomy of major epaxial muscles in a size series of corn snakes (Pantherophis guttatus) using diceCT scans, and then took several approaches to calculating contributions of each muscle to force and motion generated during body bending, starting from a highly simplistic model and moving to increasingly complex and realistic models. Only the most realistic model yielded equations that included the consequence of muscle span on torque-displacement trade-offs, as well as resolving ambiguities that arose from simpler models. We also tested whether muscle cross-sectional areas or lever arms (total magnitude or pitch/yaw/roll components) were related to snake mass, longitudinal body region (anterior, middle, posterior), and/or muscle group (semispinalis-spinalis, multifidus, longissimus dorsi, iliocostalis, and levator costae). Muscle cross-sectional areas generally scaled with positive allometry, and most lever arms did not depart significantly from geometric similarity (isometry). The levator costae had lower cross-sectional area than the four epaxial muscles, which did not differ significantly from each other in cross-sectional area. Lever arm total magnitudes and components differed among muscles. We found some evidence for regional variation, indicating that functional regionalization merits further investigation. Our results contribute to knowledge of snake muscles specifically and multiarticular muscle systems generally, providing a foundation for future comparisons across species and bioinspired multiarticular systems.

Snakes combine vertical and lateral bending to traverse uneven terrain

Terrestrial locomotion requires generating appropriate ground reaction forces which depend on substrate geometry and physical properties. The richness of positions and orientations of terrain features in the 3D world gives limbless animals like snakes that can bend their body versatility to generate forces from different contact areas for propulsion. Despite many previous studies of how snakes use lateral body bending for propulsion on relatively flat surfaces with lateral contact points, little is known about whether and how much snakes use vertical body bending in combination with lateral bending in 3D terrain. This lack had contributed to snake robots being inferior to animals in stability, efficiency, and versatility when traversing complex 3D environments. Here, to begin to elucidate this, we studied how the generalist corn snake traversed an uneven arena of blocks of random height variation five times its body height. The animal traversed the uneven terrain with perfect stability by propagating 3D bending down its body with little transverse motion (11° slip angle). Although the animal preferred moving through valleys with higher neighboring blocks, it did not prefer lateral bending. Among body-terrain contact regions that potentially provide propulsion, 52% were formed by vertical body bending and 48% by lateral bending. The combination of vertical and lateral bending may dramatically expand the sources of propulsive forces available to limbless locomotors by utilizing various asperities available in 3D terrain. Direct measurements of contact forces are necessary to further understand how snakes coordinate 3D bending along the entire body via sensory feedback to propel through 3D terrain. These studies will open a path to new propulsive mechanisms for snake robots, potentially increasing the performance and versatility in 3D terrain.

Dynamic movements facilitate extreme gap crossing in flying snakes

In arboreal habitats, direct routes between two locations can be impeded by gaps in the vegetation. Arboreal animals typically use dynamic movements, such as jumping, to navigate these gaps if the distance between supports exceeds their reaching ability. In contrast, most snakes only use the cantilever crawl to cross gaps. This behavior imposes large torques on the animal, inhibiting their gap-crossing capabilities. Flying snakes (Chrysopelea), however, are known to use dynamic behaviors in a different arboreal context: they use a high-acceleration jump to initiate glides. We hypothesized that flying snakes also use jumping take-off behaviors to cross gaps, allowing them to cross larger distances. To test this hypothesis, we used a six-camera motion-capture system to investigate the effect of gap size on crossing behavior in Chrysopelea paradisi, and analyzed the associated kinematics and torque requirements. We found that C. paradisi typically uses cantilevering for small gaps (<47.5% snout-vent length, SVL). Above this distance, C. paradisi were more likely to use dynamic movements than cantilevers, either arching upward or employing a below-branch loop of the body. These dynamic movements extended the range of horizontal crossing to ∼120% SVL. The behaviors used for the largest gaps were kinematically similar to the J-loop jumps used in gliding, and involved smaller torques than the cantilevers. These data suggest that the ability to jump allows flying snakes to access greater resources in the arboreal environment, and supports the broader hypothesis that arboreal animals jump across gaps only when reaching is not mechanically possible.

Motion Planning and Iterative Learning Control of a Modular Soft Robotic Snake

Snake robotics is an important research topic with a wide range of applications, including inspection in confined spaces, search-and-rescue, and disaster response. Snake robots are well-suited to these applications because of their versatility and adaptability to unstructured and constrained environments. In this paper, we introduce a soft pneumatic robotic snake that can imitate the capabilities of biological snakes, its soft body can provide flexibility and adaptability to the environment. This paper combines soft mobile robot modeling, proprioceptive feedback control, and motion planning to pave the way for functional soft robotic snake autonomy. We propose a pressure-operated soft robotic snake with a high degree of modularity that makes use of customized embedded flexible curvature sensing. On this platform, we introduce the use of iterative learning control using feedback from the on-board curvature sensors to enable the snake to automatically correct its gait for superior locomotion. We also present a motion planning and trajectory tracking algorithm using an adaptive bounding box, which allows for efficient motion planning that still takes into account the kinematic state of the soft robotic snake. We test this algorithm experimentally, and demonstrate its performance in obstacle avoidance scenarios.