Redundant contacts and force redistribution stabilize limbless vertical climbing

Abstract: Animals navigating complex vertical environments must secure stable footholds, a challenge for species without feet. While arboreal climbing has evolved repeatedly in snakes, the physical mechanisms they use to scale broad, nearly flat surfaces remain poorly understood. By measuring three-dimensional body kinematics and per-contact forces on a smooth vertical wall with protruding posts, we show that cornsnakes climb by dynamically balancing forces across a highly redundant network of 5 to 16 simultaneous contacts--far exceeding the three contacts minimally required for physical stability. Using a computational model and a robotic climber, we demonstrate that while simple body undulations and passive friction are mechanically sufficient to climb this terrain, snakes systematically deviate from this passive baseline. While downward climbing relies primarily on friction, ascending snakes actively generate positive mechanical work at their contacts to propel themselves. Furthermore, we found that whenever a snake engages a new contact, it triggers a stereotyped, system-wide redistribution of force that seamlessly integrates the new foothold without disrupting whole-body balance. These results reveal how a continuous, flexible body can transform sparse environmental features into a robust, fault-tolerant network. This mechanism provides a biomechanical framework for understanding the repeated evolution of limbless climbing and offers physical principles for designing agile robots for unstructured terrain.

• The paper demonstrates that cornsnakes maintain 8–16 simultaneous contacts on dense posts and 5–7 on widely spaced posts, exceeding the three contacts theoretically required for planar balance.
• The paper combines force-sensing experiments, a quasi-static model, and an open-loop robot to show that passive friction and a traveling body wave can support climbing, but ascending snakes add active force generation, with over 40% of dynamic contacts performing positive mechanical work.
• The paper finds that each new contact triggers balance-preserving force redistribution over 1–3 seconds, with reliable dense substrates supporting smaller, faster adjustments and sparse or short posts requiring broader, larger rearrangements.

Cornsnakes (Pantherophis guttatus) climb smooth vertical surfaces by maintaining a highly redundant network of simultaneous contacts and actively redistributing forces across that network as contacts are gained and lost. This study combines per-contact force measurements on an instrumented climbing wall, a quasi-static computational model, and an open-loop robotic climber to separate what is mechanically sufficient for limbless vertical locomotion from what the animals actually do (2607.06239). The central finding is a clear dissociation: passive friction and a propagating body wave suffice to climb in principle, yet ascending snakes systematically exceed this baseline through active force generation and stereotyped, balance-preserving force rearrangements.

Experimental approach

The authors built a vertical acrylic wall instrumented with a single column of 22 force-sensing posts (8 mm diameter sleeves), each coupled to two load cells resolving horizontal and vertical forces at approximately 10 Hz, synchronized with 60 Hz infrared marker tracking of 30–40 reflective markers along the snake's dorsum. Five juvenile cornsnakes completed 227 trials across three post configurations: 25 mm posts spaced 50 mm apart, 3 mm posts spaced 50 mm apart, and 25 mm posts spaced 100 mm apart. Without posts, snakes slid on the acrylic above inclines of only $16 \pm 2^\circ$, confirming that post contacts were essential for vertical progress.

Quasi-static balance and contact redundancy

Across all conditions, climbing was quasi-static: net horizontal force summed to zero, net vertical force matched body weight within a few percent, and torque about the center of mass remained centered near zero. Formally, the animals satisfied three constraints at all times—zero net horizontal force, net vertical force equal to $Mg$, and zero net torque about the center of mass. Because three non-collinear contacts can satisfy these constraints, planar stability requires a minimum of three footholds; the snakes instead maintained 8–16 simultaneous contacts on closely spaced posts and 5–7 even when spacing was doubled to 100 mm. This redundancy implies that whole-body equilibrium does not uniquely determine individual contact loads, leaving the animal a large space of internally valid force configurations—a point the authors exploit quantitatively later in the analysis.

Kinematics varied with substrate but performance was robust. Long, closely spaced posts elicited lateral undulation and faster climbing; short posts induced a mixed lateral-undulation/concertina gait with slower speeds. Contact location on the post shifted adaptively—toward the sides of short posts (producing lateral bracing forces totaling roughly one additional body weight) and toward the tops of widely spaced posts (aligning remaining forces more vertically).

A minimal mechanical baseline

A quasi-static computational model represented the body as 220 rigid segments following a prescribed traveling serpenoid wave, with one-sided penalty spring contacts and kinetic Coulomb friction at posts. Despite containing no sensing, feedback, or active actuation, this model climbed both up and down while satisfying the balance constraints at every instant. An open-loop servo-motor robot confirmed physical viability, climbing a PVC post array with only 3–4 simultaneous contacts and dissipative tangential forces at its single instrumented post after a brief adjustment period. Together these models establish that open-loop wave propagation with passive frictional contacts is sufficient for quasi-static limbless climbing—neither redundant contacts nor feedback is strictly required.

Active force generation during ascent

The energetic contrast between directions is the paper's most striking result. Decomposing each dynamic contact into tangential power $P_t = F_t v_t$, descents were dominated by dissipative contacts ($P_t < 0$), consistent with the models, yielding an effective kinetic friction coefficient $\mu \approx 0.22$. Ascents reversed this pattern: the measured tangential force differed from the passive-friction prediction by roughly $2\mu F_n$, and more than 40% of dynamic contacts performed positive mechanical work on the body in every condition. The authors emphasize that positive $P_t$ is not a generic consequence of propagating a body wave—their robot produces dissipative contacts on average—and they carefully scope "active" as an energetic statement rather than a claim about neural control, since their measurements cannot distinguish sensory feedback, feed-forward muscular programs, or passive mechanics of the deformable body cross-section. Notably, the directional asymmetry arose primarily from reversal of sliding direction rather than from changed tangential-force distributions, meaning similar forces oppose sliding during descent but align with it during ascent.

Contact-triggered force redistribution

Each new contact triggered a repeatable, system-wide redistribution of force. Representing contact forces as a vector $\vec{f}$ subject to linear balance constraints $\mathbf{B}\vec{f} = \vec{c}$, the authors decomposed rearrangements into a nullspace component that preserves whole-body balance and a residual component that violates it. The nullspace magnitude rose rapidly after contact formation and then drifted, well described by a saturating exponential plus linear ramp with timescale $\tau \sim 1$–3 s across all conditions. Residual out-of-balance force stayed below 1% of body weight on long posts, rising modestly on short ones.

The fitted parameters revealed a trade-off tied to substrate reliability: on dense, reliable contacts, each new contact required only a small redistribution amplitude $Mg$0 but forces propagated down the body at roughly twice the rate $Mg$1 compared to sparse or short-post conditions, where large per-contact rearrangements occurred slowly. Spatially, redistribution concentrated just behind the new contact on long closely spaced posts, spread broadly across body segments on short posts (where mid-body segments sometimes flipped over posts to engage them from the opposite side), and was dominated by the new contact itself at wide spacing.

Limitations and open questions

The paper concedes several constraints explicitly. Force sensing is limited to two dimensions in the wall plane; supplementary six-axis measurements at a single post showed outward pulling forces up to ~5% of body weight on short posts, indicating unmeasured friction against the wall itself. Environmental conditions could not be randomized because the apparatus required manual reconfiguration between conditions. The exponential-plus-ramp fit is presented as descriptive rather than mechanistic, and fit uncertainties for $Mg$2 and $Mg$3 overlapped across conditions. Most fundamentally, the mechanism producing active contacts remains unresolved: whether force redirection is neurally controlled or a passive consequence of body deformation falls outside the data, though the authors posit localized rib-to-skin musculature as a candidate. Species generality is also bounded—kingsnakes failed on the same wall—so redundancy alone does not guarantee climbing competence.

Conclusion

By separating mechanically sufficient conditions from observed behavior, this work identifies management of a redundant, balance-preserving contact network—not friction at isolated footholds—as the defining feature of limbless climbing on surfaces that cannot be wrapped or braced. Descents match a passive-friction baseline; ascents deploy active, positive-work contacts integrated through stereotyped nullspace redistributions whose amplitude and spatial spread track substrate density. The framework connects snake arboreality to broader principles of motor redundancy and fault tolerance, and provides concrete design targets—redundant sensing-rich contacts with coordinated load sharing—for limbless robots on sparse, vertical terrain.