Sleeve Routing: Corridor-Based Control Strategies

• Sleeve routing is a family of corridor-based techniques that constrain paths, forces, or sensor layouts using physical or abstract sleeve structures across diverse applications.
• In large-graph visualization, sleeve routing computes edge paths by selecting a triangle corridor via dual graph search and then applying the funnel algorithm for the shortest path.
• Other applications, including elastic rod dynamics, myoelectric prosthetic control, exosuit anchoring, and haptic feedback, demonstrate how sleeve designs ensure repeatable sensor placement and controlled force transmission.

Searching arXiv for the cited papers to ground the article and verify topical scope. Searching arXiv for “Sleeve Routing” and related papers. Sleeve routing denotes several distinct technical ideas that are linked by a common structural motif: a route, force path, sensing pattern, or motion is constrained by a sleeve-like corridor, sleeve-like device, or sleeve-indexed representation. In the most explicit usage, sleeve routing is an edge-routing method for large graph visualization in which a sequence of triangles is selected in the dual graph of a Constrained Delaunay Triangulation and the geometric shortest path is then computed inside that triangle strip by the funnel algorithm (Nachmanson et al., 17 May 2026). In other literatures, the term or closely related sleeve-based procedures refer to a frictionless sliding sleeve that generates configurational forces in an elastic rod (Koutsogiannakis et al., 2023), a surface electromyography sleeve whose grommets align electrodes with natural skin markings to stabilize myoelectric decoding over time (George et al., 2020), a stretchable pneumatic sleeve that routes exosuit load into the arm with low displacement (Schaffer et al., 2024), and a haptic forearm sleeve that maps depth data to vibration patterns for obstacle avoidance (Zahn et al., 2022). This distribution of meanings suggests that sleeve routing is not a single standardized term; its interpretation depends on whether the sleeve is geometric, mechanical, sensing-related, or wearable.

1. Terminological scope and recurrent structure

Across the cited literature, the “sleeve” may be a geometric corridor, a mechanical constraint, or a wearable interface. In the browser-based graph-visualization paper, the sleeve is a sequence of triangles through free space (Nachmanson et al., 17 May 2026). In the elastica paper, the sleeve is a frictionless sliding constraint through which a rod can be injected or ejected (Koutsogiannakis et al., 2023). In the prosthetics, exosuit, and haptic papers, the sleeve is a physical textile or pneumatic device wrapped around the forearm or arm (George et al., 2020, Schaffer et al., 2024, Zahn et al., 2022).

Domain	Sleeve entity	Routing or guidance function
Large-graph visualization	Triangle sequence in a CDT	Obstacle-avoiding edge path
Elastic rod dynamics	Frictionless sliding sleeve	Configurational-force-mediated motion
Prosthetic control	sEMG forearm sleeve	Repeatable electrode placement
Exosuit anchoring	Pneumatic arm sleeve	Low-displacement load transfer
Obstacle avoidance	Vibrotactile forearm sleeve	Spatial depth-to-haptic mapping
Source-controlled networking	Packet-carried DAG or segment list	Local detour under constraints

A recurring pattern is that the sleeve constrains admissible evolution. In geometry, it constrains a path to a corridor. In mechanics, it constrains deformation and produces a configurational force at the sleeve entrance. In wearables, it constrains sensor placement, actuator attachment, or the spatial layout of feedback. A plausible implication is that “sleeve routing” is best treated as a family of corridor-based or sleeve-indexed control strategies rather than as a unitary technique.

2. Geometric sleeve routing in large-graph visualization

In "Browsing Large Graphs with Tile Pyramids and Sleeve Routing in the Browser," sleeve routing is the edge-routing method used to make large graphs browsable “in the style of online geographic maps” (Nachmanson et al., 17 May 2026). The free space around nodes is represented by padded obstacle polygons, and a Constrained Delaunay Triangulation $T$ is computed on those polygons. The dual graph $D$ has one vertex per triangle of $T$, one edge for each shared triangle side, and a dual-edge weight equal to the Euclidean distance between triangle centroids. For an edge $(s,t)$, routing finds a triangle path in $D$ from a triangle adjacent to $s$ to a triangle adjacent to $t$, excluding triangles inside obstacles other than those of $s$ and $t$. The resulting triangle strip is the sleeve, and the funnel algorithm then computes the shortest polyline inside that corridor.

The two-stage decomposition is central. The dual-graph search chooses the homotopy class, while the funnel algorithm computes the shortest path within that class. The paper describes the natural per-edge method as A* on $D$ with straight-line distance to $D$0 as heuristic, but the implementation is primarily batched per source: edges are grouped by source, a single Dijkstra computation is run from that source on the dual graph, search continues until all targets are reached, and each triangle sequence is recovered through parent pointers. This is augmented by a root-reduction heuristic based on the demand graph $D$1: a feasible root set $D$2 is exactly a vertex cover of $D$3, and a greedy maximum-degree approximation is used because minimum vertex cover is NP-hard.

The implementation includes several additional speedups. It tries the straight segment first; if that segment traverses the CDT without obstacle conflict, full sleeve search is skipped. Near endpoints, it collapses corner-hugging vertices on the source and target chains to the corresponding endpoints, which widens the funnel opening and removes spurious corner detours. Optional Bezier smoothing exists but is disabled by default because polyline rendering is fast and visually acceptable.

Sleeve routing is integrated with a tile-pyramid pipeline for semantic zoom. The finest level uses all nodes and all edges. At each coarser level, the method chooses a PageRank-ranked prefix of nodes, scales nodes adaptively so they remain pairwise disjoint, reroutes edges around the resulting obstacles using sleeve routing, and rebuilds tile contents. Runtime rendering is delegated to deck.gl’s TileLayer: the browser fetches precomputed tiles containing nodes, edge clips, labels, and arrowheads, while panning changes the visible tiles and zooming switches between adjacent precomputed levels with TileLayer cross-fade. The entire pipeline runs client-side in the WebGL renderer of MSAGLJS, and the benchmark suite comprises nine graphs with up to 32,768 nodes and 236,978 edges, measuring browser-side parsing, layout, routing, and tile-pyramid construction. The paper’s rationale is that per-level routing is more visually stable across zoom changes than reusing one global routing and clipping it per tile.

3. Sliding-sleeve dynamics and configurational-force routing

In "Stabilization against gravity and self-tuning of an elastic variable-length rod through an oscillating sliding sleeve," the sleeve is a frictionless constraint that partially contains an elastic, inextensible, variable-length rod carrying a lumped mass $D$4 at one end (Koutsogiannakis et al., 2023). The sleeve’s sliding direction is vertical and parallel to gravity. Without sleeve motion, the mass falls and the rod is completely injected into the sleeve. When the sleeve entrance is forced to oscillate transversely according to

$D$5

the rod can exhibit a stable sustained oscillation around a finite external length $D$6. The crucial mechanism is a configurational force at the sleeve entrance. The tangential force balance includes

$D$7

where $D$8 is the entrance bending moment. Because the force depends on the square of the bending moment, bending generated by transverse sleeve motion can oppose gravity.

The paper formulates the bent external portion of the rod by the planar elastica equation

$D$9

with $T$0 at the free end. Exact spatial integration yields expressions for $T$1, $T$2, $T$3, and $T$4 in terms of elliptic integrals, and the configurational-force balance becomes a nonlinear algebraic condition involving $T$5, $T$6, and $T$7. The sleeve force is therefore not externally prescribed; it depends on the instantaneous bending state of the rod.

A small-rotation asymptotic treatment, neglecting dissipation, clarifies the suspended-motion mechanism. The transverse and vertical dynamics reduce to

$T$8

$T$9

with $(s,t)$0. The analysis leads to a self-tuning mean external length that tends toward the resonant clamped length

$(s,t)$1

as the relevant parameter $(s,t)$2. This is the paper’s main analytical result: the rod spontaneously adjusts its mean external length to remain near the clamped-free resonance length corresponding to the imposed frequency.

Three global outcomes are identified: complete injection $(s,t)$3, complete ejection $(s,t)$4, and suspended motion, meaning a stable periodic or quasi-periodic oscillation around a finite $(s,t)$5. The analogy with the Kapitza inverted pendulum is explicit but qualified: the comparison is qualitative, not literal, because stabilization occurs through a geometry-dependent configurational force under transverse excitation, and the suspended configuration is not a classical equilibrium. Numerical integration of the full nonlinear differential-algebraic system reveals periodic sustained motion, quasi-periodic sustained motion, and divergence leading to injection or ejection. Experiments with carbon-fiber rods, rollers forming a frictionless sleeve, and an electromagnetic actuator validate the asymptotic prediction, especially the stable branch $(s,t)$6.

4. Sleeve routing as repeatable sensor placement in myoelectric prosthetic control

In "Inexpensive surface electromyography sleeve with consistent electrode placement enables dexterous and stable prosthetic control through deep learning," the paper’s sleeve-routing strategy is the use of grommets positioned near embedded electrodes so that the sleeve can be aligned with natural skin markings such as freckles, moles, and scars (George et al., 2020). The sleeve is built from neoprene fabric as a hollow cylindrical sleeve and contains 32 monopolar recording electrodes distributed across the forearm, with 2 additional electrodes proximally positioned on the ulna as reference and ground. The electrodes are brass-coated marine snap fasteners, each soldered to flexible wire, reinforced with high-strength heat shrink, stitched into the sleeve, and terminated at a 38-pin SAMTEC connector. A loose Lycra cover electrically isolates the wires and reduces movement/contact noise. Manufacturing requires a few hours, and the reported total cost is $58.47.

The purpose of the grommet alignment scheme is to make electrode placement reproducible across donning sessions. Seven intact participants each donned the sleeve five times while aligning grommets with colored forearm markings. The reported donning time was 10.30 ± 3.35 s, and placement precision was 7.32 ± 0.26 mm, explicitly described as sub-centimeter precision. Acquisition used 32 single-ended (monopolar) sEMG channels sampled at 1 kHz with Micro2+Stim Front-Ends and a Grapevine Neural Interface Processor. Signals were processed as 300-ms smoothed Mean Absolute Value (MAV) features computed at 30 Hz. Signal quality was quantified by the ratio of mean 300-ms smoothed MAV during movements to mean 300-ms smoothed MAV during rest, yielding SNR = 14.03 ± 4.43 across participants.

The paper’s central argument is that consistent sleeve routing makes it possible to accumulate large spatially aligned datasets over time, which is particularly important for deep learning. Two neural network controllers were evaluated for six-DOF myoelectric control. The shallow controller was a 10-layer neural network with 50% dropout layers after each ReLU. The deep controller was a 74-layer residual neural network whose input was a 32 × 32 “image” formed from 32 electrodes over the last 32 time samples, covering about 1.07 s of history. Its structure included nine residual convolutional units, each with two repetitions of 3×3 convolution, batch normalization, and ReLU. Output was a 6-DOF kinematic prediction for a virtual prosthetic hand, and an optional Kalman filter was used for smoothing. Training used Stochastic Gradient Descent with Momentum, an initial learning rate of 0.001, a 97% training / 3% validation split, and automatic stopping when validation RMSE increased.

Longitudinally, one intact participant contributed 20 datasets, with sleeve removal and re-donning between collections and variation in movement speed, movement hold time, and forearm posture. A shallow network trained on only the first dataset and tested over 263 days showed statistically significant variation across days by one-way ANOVA (p < 0.05), but performance on day 1 was not significantly different from any later day, including day 263 (p > 0.05 in pairwise comparisons). Accumulated consistent data materially improved dexterity. A shallow network trained on 10 prior datasets doubled hold-time duration relative to one trained on a single dataset collected immediately before testing (p < 0.05, paired t-test). A 74-layer deep residual network trained on 20 datasets improved further, and DNN + KF achieved up to a 152% improvement relative to a modified Kalman filter baseline from prior work, namely 4.42 s vs. 1.75 s. The participant also used DNN+KF to operate a physical LUKE Arm, grasping objects while simultaneously rotating and flexing the wrist. In this usage, “routing” refers not to edge routing but to a repeatable indexing of sleeve placement that stabilizes the sensor geometry on which decoding depends.

5. Pneumatic sleeve routing of exosuit forces

In "Stretchable Pneumatic Sleeve for Adaptable, Low-Displacement Anchoring in Exosuits," the sleeve is an anchoring device that can adjust its compression to the arm while keeping the actuator mounting-point displacement small during operation (Schaffer et al., 2024). Three sleeve types are compared: a hook-and-loop sleeve, an SPM sleeve based on a series pouch motor, and an fPAM sleeve built from fabric pneumatic artificial muscle bands. The fPAM is made from silicone-coated ripstop nylon fabric, cut with 45° fiber orientation, sewn/glued into a simple tube, and when inflated it contracts in length and expands radially. Nine fPAM band prototypes were tested with widths 3 cm, 4 cm, 5 cm and lengths 27 cm, 28 cm, 30 cm. The paper defines geometric variables $(s,t)$7, $(s,t)$8, $(s,t)$9, $D$0, and inflated dimensions $D$1, $D$2.

Performance was evaluated through compressing force $D$3, holding force $D$4, and sleeve force-displacement behavior. Holding force was defined as the pulling force at the mounting point required to achieve 2 cm displacement in the $D$5 direction. Tests used a rigid test cylinder representing the arm, with diameter 8 cm and a 0.5 cm silicone layer. Pressures of 0 kPa, 13.8 kPa, 27.6 kPa, and 41.1 kPa were used for compressive and holding force tests; sleeve stiffness tests used all four pressures for the fPAM sleeve but only three for the SPM sleeve because the SPM sleeve failed above 27.6 kPa.

The geometric design rules are explicit. Increasing width increased both compressive and holding force, while decreasing length also increased both forces. The paper attributes these trends to increased force-generating area and to operation closer to the fully stretched, high-force state. The shortest 27 cm bands had nonzero compressive force even at 0 kPa because the test-cylinder circumference was 28.3 cm, which stretched the bands and created passive compression. Comparing 3 cm and 5 cm widths, holding force increased by 28% for the longest bands, 56% for the mid-length bands, and 78% for the short bands.

At sleeve level, the fPAM sleeve closely matched the SPM sleeve in compression when geometrically equivalent, but the fPAM sleeve tolerated higher pressure and therefore had a larger possible force range. Both pneumatic sleeves decreased mounting-point displacement relative to the hook-and-loop sleeve. In the wrist-exosuit demonstration with the wrist constrained by a 2 kg weight, actuator-end displacement was 8.0 mm for the fPAM sleeve, 8.4 mm for the SPM sleeve, and 12.0 mm for the hook-and-loop sleeve. When the wrist was allowed to move and the sleeves were then deflated, the SPM sleeve caused a 14.0° decrease in wrist angle, whereas the fPAM sleeve caused only a 4.7° decrease. The paper therefore treats the sleeve not merely as a strap but as part of the force path, helping to route actuator load into the body with less slip and deformation.

6. Haptic sleeve routing of depth information for obstacle avoidance

In "Obstacle avoidance for blind people using a 3D camera and a haptic feedback sleeve," the sleeve is a vibrotactile display that maps depth-camera data to the forearm (Zahn et al., 2022). The system combines an Intel RealSense D415 depth camera mounted on glasses, an AAEON Up Board running Linux, and a wearable forearm sleeve containing a 2D array of 25 vibration motors sewn onto stretchable fabric. The motors are independently controlled through PNP transistors, an Adafruit 24-Channel TLC5947 driver, and an Adafruit Feather 32u4 microprocessor. The RealSense depth stream, although capable of up to 1280×720 and 90 fps, was run in the prototype at 480p and 6 fps to reduce computation. A 5V, 5A battery pack supplied power.

The mapping algorithm downsamples the depth image to a 5×5 grid, with one grid cell per vibration motor. Depth values in each cell modulate vibration intensity through PWM voltage. The core encoding rule is simple: closer obstacle → stronger vibration and farther obstacle → weaker vibration or no vibration, depending on mode. Position in the depth image is mapped to position on the forearm array, so the sleeve conveys both direction and proximity. In a hallway, vibrations are stronger at the edges of the sleeve when walls are near, producing a tactile corridor pattern. The paper defines two display modes: indoor mode, with feedback restricted to about 3 m, and outdoor mode, in which only distances greater than 2 m are mapped so that the system supplements cane-based sensing.

A pattern-recognition experiment tested whether users could interpret the haptic codes independently of navigation. 8 users were presented with 11 vibration patterns over 3 test iterations separated by 1 week. Patterns included single-motor, multi-motor, single-axis, and multi-axis stimuli; one example moved from the top-left corner (motor 1) to the bottom-right corner (motor 25), with each motor vibrating for 500 ms. Responses were scored for correctness of movement direction and the number of simultaneously vibrating motors. Users achieved 98.6% correct recognition/localization for single-motor patterns and about 70% for multi-motor patterns. The paper attributes the drop for more complex patterns to motor interference, perceptual blending, and sensitivity differences across the forearm.

A second experiment evaluated the full obstacle-avoidance system on an indoor testing route with walkways, doors, and obstacles in complete darkness. 5 volunteers completed the route using only haptic guidance, with 3 runs separated by 1 week. All participants completed the route. Mean completion time improved from 320 s in run 1 to 179 s in run 2 and 148 s in run 3, which the paper summarizes as a 53% improvement from first to third run. The paper interprets the result as evidence that the sleeve is effective for simple directional cues, proximity warnings, and corridor-like routing information, while complex multi-motor encodings are less robust.

7. Relation to source-controlled and segment routing in networking

The networking papers in the data set do not define sleeve routing in the geometric or wearable sense, but they illuminate related corridor-based and instruction-carrying routing ideas. "Slick Packets" is a source-controlled routing scheme in which the packet header carries a forwarding subgraph (FS) represented as a DAG containing a primary route and alternate branches, allowing the packet to “slip around failures” without waiting for end-to-end reconvergence (Nguyen et al., 2012). The paper states that its behavior is closely related to what is often called sleeve routing or tunneling-style source-controlled routing, but it differs from a fixed tunnel because the packet carries multiple locally valid forwarding options. The packet can locally switch to an alternate edge if the preferred next hop is unavailable, while acyclicity of the FS avoids loops. The paper gives two header encodings, Direct and Default, and reports moderate header sizes on real topologies: for the AS-level Internet map, 90% of source-destination pairs were under 21 bytes, 99% under 26 bytes, and the maximum was 50 bytes. Failure response is comparable to the best network-controlled alternate-path scheme, with worst-case stretch for non-dropping schemes bounded by about 3, while Fast-VSR reached 27 in the Sprint topology.

"La ROUTOURNE va tourner" addresses a different but adjacent problem: rather than encoding a physical path first and translating it into a segment list afterward, ROUTOURNE makes the routing algorithm compute optimal deployable segment lists directly under the hardware-imposed Maximum Segment Depth or PMS (Bramas et al., 2024). The key obstacle is that Segment Routing induces a loss of isotonicity in the segment-count dimension. ROUTOURNE therefore combines on-the-fly encoding of explored distances into minimal segment lists with a modified dominance rule. A dominated state is kept only if it is at most one segment worse than the dominating states and has a different last detour/source than the dominating segment lists. The framework proves correctness and optimality, incurs at worst a linear overhead, and in practice the additional number of maintained states is usually less than a factor of 3 on realistic graphs.

Taken together, these networking works show that sleeve-like routing concepts also arise when a packet or routing algorithm must carry a compact deployable corridor of admissible next hops. This suggests a broader conceptual family: routing methods that avoid unconstrained global recomputation by embedding a restricted but actionable path structure directly into the object being routed, whether that object is a graph edge, an elastic rod, an sEMG sleeve, an exosuit load path, a haptic map, or a network packet.