Locomotion Tunneling in Confinement

• Locomotion tunneling is a family of movement strategies that enables controlled progression through narrow, confined, and tunnel-like environments while meeting strict clearance constraints.
• Recent studies employ reinforcement learning, tendon-driven continuum robots, and bio-inspired methods to optimize stability, energy efficiency, and collision avoidance in varied tunnel geometries.
• Key research shows that strategic contact, adaptive posture, and environmental force redirection can transform geometric confinement from a barrier into a resource for effective locomotion.

Locomotion tunneling denotes a family of locomotor problems in which motion is organized around enclosing boundaries, severe clearance limits, or structured passage through tunnel-like geometry. In current research usage, the term spans several distinct but related settings: quadrupedal traversal of narrow, confined 3D tunnels (Raj et al., 13 May 2026), occupancy transfer through a meta-module path in the joint-movement amoebot model (Padalkin et al., 2023), burrowing and subsurface locomotion in granular or saturated sediments (Li et al., 2019, Kudrolli et al., 2020), helical rolling in narrow tubes by tendon-driven continuum robots (Shentu et al., 2024), manipulation-based cave traversal with force closure on surrounding walls (Chen et al., 2024), whole-body crawling under low-clearance obstacles by humanoids (Yang et al., 7 Jan 2026), and wave-mediated cavity-to-cavity crossing in walking-droplet systems (Sankaran et al., 23 Dec 2025). Across these literatures, the unifying issue is not merely forward progression, but controlled progression under geometric confinement, contact constraints, and environment-dependent transmission of force.

1. Scope and defining conditions

In the robotics literature, tunneling is not restricted to subsurface excavation. It also includes traversal of narrow rigid tunnels, low-clearance passages, tubes, caves, and collapsed structures. The central geometric problem is that the locomotor must satisfy clearance constraints against floor, walls, and ceiling simultaneously while maintaining stability, negotiating turns or slopes, and adapting posture to asymmetric openings. One formal expression of this requirement is the clearance constraint

$$\min_t \operatorname{dist}(\text{robot\_hull}(t), \partial \Omega_{\text{tunnel}}) \ge c_{\min},$$

which is used for collision checks and success criteria in quadrupedal tunnel traversal. Related geometric constraints appear in tubular rolling, where a helical centerline must satisfy

$R \le r_{\text{tube}} - r_{\text{robot}}/2,$

and in confined biological climbing, where fall arrest depends on tunnel diameter relative to deployable lateral span rather than on nominal gait alone [(Raj et al., 13 May 2026); (Shentu et al., 2024); (Gravish et al., 2013)].

A recurring result across scales is that confinement can be either an obstacle or a resource. Fire ants construct tunnels with effective diameter $D = 1.06 \pm 0.23 L$, a posture transition occurs at $D_c = 1.03 \pm 0.01 L$, and the fall-arrest transition is governed by $D_s = 1.31 \pm 0.02 L$, so that $D < D_s$ makes jam-arrest likely. ReachBot, by contrast, exploits enclosure by establishing force closure across walls, ceiling, and floor using long booms in tension. These cases indicate that locomotion tunneling is often governed by morphology-to-geometry ratios, contact reach, and the ability to redirect loads into surrounding boundaries rather than by open-terrain stride optimization [(Gravish et al., 2013); (Chen et al., 2024)].

2. Reinforcement-learned traversal of rigid tunnels

A recent formulation of locomotion tunneling for quadrupeds models the task as an MDP $M=(S,A,P,R,\gamma)$ in Isaac Gym, with a 12D joint-position action sent to a PD controller,

$$\tau_j = k_p (q_j^d - q_j) + k_d (\dot q_j^d - \dot q_j),$$

and rewards that encourage forward progress with stability while strongly penalizing wall and ceiling collisions. The method uses four expert teacher policies, each specialized to a procedurally generated tunnel class—triangle, circle, half-circle, and gap-with-shelves—and distills them into one student policy using DAgger and class-conditioned action matching,

$$L_{\text{distill}}(\theta)=\mathbb{E}\big[\|a_T^{(c_t)}(s_t,\xi)-a_S(s_t,z_t)\|_2^2\big].$$

Teachers receive proprioception plus a privileged 108D terrain grid; the student receives forward-facing depth images at $64\times 48$, IMU orientation, joint encoders, and past actions. Procedural generation varies cross-section, rotation, slope, and support geometry, including triangular tunnels with rotated segments, circular and half-circular tunnels with shrinking radii, and gap tunnels with widening central voids and tilted shelves. The student architecture combines a LeNet-style CNN vision encoder, proprioceptive fusion, and a GRU for temporal context. Training proceeds in two stages: PPO teacher training for $R \le r_{\text{tube}} - r_{\text{robot}}/2,$0 iterations per class, approximately 8 hours per class on an RTX 3090 with 2,048 parallel environments, followed by tunnel-conditioned DAgger with class-balanced replay and depth corruption by noise and dropout (Raj et al., 13 May 2026).

The learned behaviors are explicitly posture-adaptive. Circular and half-circular tunnels induce crouching for ceiling clearance; triangular tunnels induce lateral body shift, shoulder roll, and stance-width modulation; asymmetric openings induce yaw offsets; gap tunnels induce shelf-aware stepping with precise lateral placement and shorter swing arcs. Evaluation uses success rate, completion time, collision frequency, and energy

$R \le r_{\text{tube}} - r_{\text{robot}}/2,$1

averaged over 50 trials per class and difficulty. Against Vanilla RL and a Hierarchical Planner using elevation mapping, the distilled policy achieves the highest success rates across all tunnel classes, the lowest collision frequency, shorter completion times than the overly cautious planner, and lower energy per meter. Representative ablations report 70% success for the full multi-teacher procedural-distillation pipeline, 35% for a single teacher, 39% without procedural generation, and 19% for two-layer elevation-map teachers that did not converge. On a Unitree Go2 in modular 1 m tunnel segments, success over 10 trials each was 70% in a circular tunnel of radius 0.20 m, 80% in a gap tunnel with 0.50 m central gap and side shelves, and 60% in a triangular tunnel with side $R \le r_{\text{tube}} - r_{\text{robot}}/2,$2 m and base inclined at $R \le r_{\text{tube}} - r_{\text{robot}}/2,$3. The reported failure modes were depth dropout in high-tilt segments, late crouch or insufficient roll, and rare shelf-foot slip on steep supports (Raj et al., 13 May 2026).

3. Morphology, contact planning, and whole-body confined locomotion

Biological confined locomotion provides a compact geometric benchmark. Fire ants can move in excavated or artificial tunnels at routine ascent and descent speeds of $R \le r_{\text{tube}} - r_{\text{robot}}/2,$4 and $R \le r_{\text{tube}} - r_{\text{robot}}/2,$5 body lengths per second, and under alarm in ant-built tunnels they reach $R \le r_{\text{tube}} - r_{\text{robot}}/2,$6 and $R \le r_{\text{tube}} - r_{\text{robot}}/2,$7 body lengths per second, with peak speed $R \le r_{\text{tube}} - r_{\text{robot}}/2,$8 body lengths per second. During slips, antennae-wall contact precedes arrest in 92% of cases, and slips are arrested within $R \le r_{\text{tube}} - r_{\text{robot}}/2,$9 ms. The arrest mechanism is a multipoint jam involving limbs, antennae, and body pitch into the wall. This makes tunnel diameter a control variable in its own right: the excavated geometry supports sprawled bracing above $D = 1.06 \pm 0.23 L$0, while remaining below $D = 1.06 \pm 0.23 L$1 so that falls are almost always arrested by reach-limited jamming (Gravish et al., 2013).

A mechanized analogue appears in the universal-jointed tendon-driven continuum robot for narrow tubes. Its backbone is discretized into a chain of universal joints and rigid spacer links with general tendon routing defined by relative waypoints $D = 1.06 \pm 0.23 L$2. Configuration is $D = 1.06 \pm 0.23 L$3, with segment transform

$D = 1.06 \pm 0.23 L$4

and tendon lengths constrained by commanded displacements $D = 1.06 \pm 0.23 L$5. A friction-aware optimizer incorporates Capstan tension propagation,

$D = 1.06 \pm 0.23 L$6

and plans helical shapes for rolling in confinement. Axial advance per full helical revolution is

$D = 1.06 \pm 0.23 L$7

The reported prototype for locomotion had outer diameter 15 mm inside a 21 mm tube, operated at 0.33 Hz, and the shape-estimation model achieved average tip error $D = 1.06 \pm 0.23 L$8 mm, or $D = 1.06 \pm 0.23 L$9 of length, for dual helical actuation (Shentu et al., 2024).

ReachBot addresses lava tubes and caves through “locomotion via manipulation.” With eight extendable booms, microspine grippers, and internal force control, it treats body motion as in-grasp manipulation under quasi-static equilibrium,

$D_c = 1.03 \pm 0.01 L$0

where the null-space term is chosen so that all prismatic boom forces remain nonnegative, keeping the booms in tension. Contact feasibility is governed by Coulomb friction $D_c = 1.03 \pm 0.01 L$1, with field-measured $D_c = 1.03 \pm 0.01 L$2, and grasp quality is ranked through Monte Carlo limit surfaces on convex features. In a Mojave Desert lava tube, the two-stage perception pipeline found many suitable targets, and pull-off forces of at least 34.2 N were measured on spherical and cylindrical rock features, consistent with predicted directional anisotropy of grasp strength (Chen et al., 2024).

Whole-body humanoid tunneling uses a different contact strategy: not wall bracing, but support polygons enlarged by hands, knees, forearms, elbows, and torso. In “Locomotion Beyond Feet,” passing under chairs with vertical space shorter than the robot’s standing height of 53 cm is handled by physics-grounded keyframes, DeepMimic-style RL motion tracking, and a hierarchical vision-to-skill framework. The low-level policy outputs joint position references for PD control, the high-level skill planner runs at 3.1 Hz from stereo depth on a Jetson Orin NX 16GB, and low-level control runs at 50 Hz. The real-world skill classifier was trained on 27,987 depth-label pairs and achieved 93.9% accuracy on a 3,394-sample held-out test set. The system demonstrated zero-shot sim-to-real crawling under chairs and obstacle sequences including two chairs in a row (Yang et al., 7 Jan 2026).

4. Tunneling as a modular motion primitive

In the joint-movement amoebot model, tunneling is not traversal through an external conduit but a primitive for transferring a meta-module through a path of adjacent modules. The environment is the infinite triangular grid graph $D_c = 1.03 \pm 0.01 L$3, amoebots are contracted or expanded occupancies of grid nodes, and joint movement augments classical expansions and contractions by allowing push and pull operations, selective bond release, and handovers. A round has a bond-release step followed by continuous-time motion under two constraints: the released-bond graph $D_c = 1.03 \pm 0.01 L$4 must remain connected, and there must be neither collision of non-adjacent bonds nor structural conflict that prevents re-embedding on the triangular grid. Handover, which swaps occupancy locally between a contracted and an expanded amoebot while preserving adjacency, is explicitly identified as necessary for narrow tunnels (Padalkin et al., 2023).

The central primitive is the $D_c = 1.03 \pm 0.01 L$5-tunnel. Given a simple path of meta-modules with $D_c = 1.03 \pm 0.01 L$6 corners, a designated rhombical meta-module is transferred from one end to the other by coordinated pull and push operations rather than by carrying it node by node. Straight-segment transfer uses synchronized contraction at the source and expansion at the destination; corner crossing uses a pull followed by a push, scheduled so that each corner consumes one round. The resulting complexity is $D_c = 1.03 \pm 0.01 L$7 rounds, or $D_c = 1.03 \pm 0.01 L$8 rounds for a higher-connectivity variant that partitions each module into submodules. Rotation is the special case $D_c = 1.03 \pm 0.01 L$9. Because tunneling, slide, contraction, and reorientation are all constant-round meta-module operations, the construction breaks the canonical $D_s = 1.31 \pm 0.02 L$0 lower bound that applies when information and mass move one node per step. On top of tunneling, the paper constructs rolling, crawling, and walking locomotors. Their idealized velocities are given explicitly as

$D_s = 1.31 \pm 0.02 L$1

showing that tunneling functions both as a reconfiguration primitive and as a throughput mechanism for locomotion (Padalkin et al., 2023).

5. Granular terramechanics and biological burrowing

In granular media, locomotion tunneling is governed by yielding, dilatancy, and depth-dependent resistance. Granular media remain solid below a yield stress and flow when local stresses exceed yield; above the dilatancy onset $D_s = 1.31 \pm 0.02 L$2, shear concentrates in bands and drag oscillations appear. Controlled fluidized-bed preparation makes it possible to vary packing fraction from $D_s = 1.31 \pm 0.02 L$3 to $D_s = 1.31 \pm 0.02 L$4, and the quasi-static force laws relevant to burrowing take simple empirical forms. Vertical penetration of a horizontal plate obeys

$D_s = 1.31 \pm 0.02 L$5

with $D_s = 1.31 \pm 0.02 L$6 in slow quasi-static intrusion, while horizontal drag of a vertical plate obeys

$D_s = 1.31 \pm 0.02 L$7

At the local level, granular resistive force theory decomposes a body into differential surface elements with orientation $D_s = 1.31 \pm 0.02 L$8, depth $D_s = 1.31 \pm 0.02 L$9, and area $D < D_s$0,

$D < D_s$1

with $D < D_s$2 and $D < D_s$3. This formulation predicts drag and lift on cylinders, half-cylinders, and wedges, and it emphasizes that tunneling performance depends on depth, packing, and shape-induced anisotropy rather than on speed alone in the quasi-static regime (Li et al., 2019).

Aquatic worms in water-saturated sediments show a complementary principle: locomotion tunneling can be produced by combining drag-anisotropy-based undulation with anchoring-based peristalsis. For a slender body with transverse undulations of amplitude $D < D_s$4, wavelength $D < D_s$5, and frequency $D < D_s$6, the low-amplitude RFT estimate used in the paper is

$D < D_s$7

where $D < D_s$8. In water, $D < D_s$9; in the sediment used in the study, rod measurements gave $M=(S,A,P,R,\gamma)$0. Peristaltic advance is modeled by a dynamic anchor mechanism with net advance $M=(S,A,P,R,\gamma)$1, giving mean speed

$M=(S,A,P,R,\gamma)$2

The data show that in consolidated, non-cohesive sediments, peristalsis contributes at least half of forward speed, with $M=(S,A,P,R,\gamma)$3, while the total speed is captured by

$M=(S,A,P,R,\gamma)$4

Anchoring fails near the surface, where overburden and yield stress vanish, and the worms switch to undulatory swimming only. The same dual-stroke interpretation is extended to Eisenia fetida, for which the reported components are $M=(S,A,P,R,\gamma)$5 mm s$M=(S,A,P,R,\gamma)$6 and $M=(S,A,P,R,\gamma)$7 mm s$M=(S,A,P,R,\gamma)$8 against a measured $M=(S,A,P,R,\gamma)$9 mm s$$\tau_j = k_p (q_j^d - q_j) + k_d (\dot q_j^d - \dot q_j),$$0 (Kudrolli et al., 2020).

6. Robotic self-burrowing and bore propagation

A distinct robotic line of work studies tunneling by deliberately adding rotation to reduce penetration resistance. In sand, the force ratio is fit by an approximately hyperbolic decay,

$$\tau_j = k_p (q_j^d - q_j) + k_d (\dot q_j^d - \dot q_j),$$1

where $$\tau_j = k_p (q_j^d - q_j) + k_d (\dot q_j^d - \dot q_j),$$2 is the tangential-to-axial velocity ratio. For conical tips, representative asymptotes are $$\tau_j = k_p (q_j^d - q_j) + k_d (\dot q_j^d - \dot q_j),$$3–0.12, whereas flat tips can have much higher $$\tau_j = k_p (q_j^d - q_j) + k_d (\dot q_j^d - \dot q_j),$$4, up to 0.48 in deep tests with a steel flat penetrator. The study reports that force-energy decreases with $$\tau_j = k_p (q_j^d - q_j) + k_d (\dot q_j^d - \dot q_j),$$5, but total energy increases because of rotational torque, and therefore recommends low velocity ratios, approximately $$\tau_j = k_p (q_j^d - q_j) + k_d (\dot q_j^d - \dot q_j),$$6–3, as the balance point between force reduction and energy efficiency. Representative shallow-test coefficients include circular-loose $$\tau_j = k_p (q_j^d - q_j) + k_d (\dot q_j^d - \dot q_j),$$7, decagon-loose $$\tau_j = k_p (q_j^d - q_j) + k_d (\dot q_j^d - \dot q_j),$$8, and square $$\tau_j = k_p (q_j^d - q_j) + k_d (\dot q_j^d - \dot q_j),$$9, indicating that reduced roundness accelerates force reduction at low $$L_{\text{distill}}(\theta)=\mathbb{E}\big[\|a_T^{(c_t)}(s_t,\xi)-a_S(s_t,z_t)\|_2^2\big].$$0 without changing the asymptote much (Tang et al., 10 Mar 2025).

The dual-auger self-burrowing robot translates similar principles to horizontal motion in dry granular media. Its principal dimensionless quantity is the relative slip velocity

$$L_{\text{distill}}(\theta)=\mathbb{E}\big[\|a_T^{(c_t)}(s_t,\xi)-a_S(s_t,z_t)\|_2^2\big].$$1

and the measured drag collapses well against the normalized force $$L_{\text{distill}}(\theta)=\mathbb{E}\big[\|a_T^{(c_t)}(s_t,\xi)-a_S(s_t,z_t)\|_2^2\big].$$2. For right-handed augers rotating clockwise, the reported horizontal glass-bead data are $$L_{\text{distill}}(\theta)=\mathbb{E}\big[\|a_T^{(c_t)}(s_t,\xi)-a_S(s_t,z_t)\|_2^2\big].$$3 at $$L_{\text{distill}}(\theta)=\mathbb{E}\big[\|a_T^{(c_t)}(s_t,\xi)-a_S(s_t,z_t)\|_2^2\big].$$4, $$L_{\text{distill}}(\theta)=\mathbb{E}\big[\|a_T^{(c_t)}(s_t,\xi)-a_S(s_t,z_t)\|_2^2\big].$$5 at $$L_{\text{distill}}(\theta)=\mathbb{E}\big[\|a_T^{(c_t)}(s_t,\xi)-a_S(s_t,z_t)\|_2^2\big].$$6, $$L_{\text{distill}}(\theta)=\mathbb{E}\big[\|a_T^{(c_t)}(s_t,\xi)-a_S(s_t,z_t)\|_2^2\big].$$7 at $$L_{\text{distill}}(\theta)=\mathbb{E}\big[\|a_T^{(c_t)}(s_t,\xi)-a_S(s_t,z_t)\|_2^2\big].$$8, and $$L_{\text{distill}}(\theta)=\mathbb{E}\big[\|a_T^{(c_t)}(s_t,\xi)-a_S(s_t,z_t)\|_2^2\big].$$9 at $64\times 48$0. At 210 rpm and 5 mm s$64\times 48$1, both augers rotating clockwise gave the lowest drag, approximately 9 N, compared with approximately 12 N for front-CW/back-STOP or front-CW/back-CCW and approximately 20 N for front-STOP/back-CW. Thrust tests on the stationary robot yielded approximately 1.6 N at 105 rpm, 3.4 N at 160 rpm, and 3.8 N at 210 rpm. In horizontal burrowing trials the robot showed an initial horizontal speed of approximately 0.08 mm s$64\times 48$2 for about 30 s, total horizontal travel of approximately 20 cm, and upward drift of approximately 5 cm (Shaharear, 2023).

At a larger scale, the subsurface bore propagator combines earthworm-like anchoring with TBM-like excavation. The reported mechanism has five modules: one drill head, two anchoring modules, and two propagation modules. Reported system values are drill diameter $64\times 48$3 mm, module outer diameter approximately 160 mm, total length approximately 0.7 m, mass approximately 6 kg, anchoring-pad stroke up to 25 mm per side, and propagation stroke up to 20 mm. The drilling force target is $64\times 48$4 N, and the anchoring-force setpoint used in simulation is 250 N per anchoring module. Dynamics are formulated with Euler–Lagrange equations,

$64\times 48$5

while the gait is managed by a centralized state machine that alternates drilling, front release, front propagation, front lock, rear release, rear propagation, and rear lock. In the Unity-plus-ROS validation using the real CAD geometry, the robot completed three gait cycles and advanced 30 mm into the soil. The paper attributes the shortfall from the nominal 20 mm per cycle stroke to slip during body-propagation contraction, likely because the 250 N anchoring setpoint was insufficient under the larger lever arm loading at the front anchor (Brügge et al., 1 Jul 2026).

7. Pilot-wave tunneling and analogue dynamics

Walking-droplet research extends locomotion tunneling into a non-robotic but mechanically explicit setting. Here a tunneling event is operationally defined when a walking droplet crosses from one cavity to another over a thin-film barrier and remains in the neighboring cavity for at least one Faraday period $64\times 48$6, with continuous wave-field evolution and no coalescence. The reported experiments use square cavities of depth 6 mm separated by a thin oil film of thickness $64\times 48$7 mm, with optimal single-droplet crossing at cavity width $64\times 48$8 mm, driving acceleration amplitude $64\times 48$9 m s$R \le r_{\text{tube}} - r_{\text{robot}}/2,$00, and forcing frequency $R \le r_{\text{tube}} - r_{\text{robot}}/2,$01 Hz. The paper is explicit that the analogy to quantum-mechanical tunneling is qualitative: the dynamics are deterministic and governed by classical fluid mechanics with dissipation and periodic forcing (Sankaran et al., 23 Dec 2025).

The theoretical core is a three-dimensional generalized Dirichlet-to-Neumann operator that maps free-surface potential $R \le r_{\text{tube}} - r_{\text{robot}}/2,$02 to vertical velocity $R \le r_{\text{tube}} - r_{\text{robot}}/2,$03 over variable topography. In the flat-bottom periodic case,

$R \le r_{\text{tube}} - r_{\text{robot}}/2,$04

and the droplet obeys the horizontal equation of motion

$R \le r_{\text{tube}} - r_{\text{robot}}/2,$05

Tunneling probability is computed by event counting, $R \le r_{\text{tube}} - r_{\text{robot}}/2,$06, rather than by an energy-barrier law. In three one-hour runs, the average crossing rate was 9.3 per minute. The paper also reports cooperative tunneling by two droplets, with higher crossing probability than in the single-droplet case and occasional post-crossing coalescence into a single bouncing droplet. Within the broader concept of locomotion tunneling, this work shows that barrier crossing can be mediated not by appendage contact or excavation, but by memory-bearing wave-field evolution over structured topography (Sankaran et al., 23 Dec 2025).