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Peristaltic locomotion without digital controllers: Exploiting the origami multi-stability to coordinate robotic motions
Priyanka Bhovad, Joshua Kaufmann, Suyi Li
TL;DR
Many peristaltic robots need numerous actuators and complicated controllers to coordinate segment motion, limiting their mechatronic simplicity. This paper uses a two-segment bistable Kresling module and foldable anchors, controlling only total length. Its deterministic actuation cycle supports peristaltic-like crawling with one actuator and no digital controllers.
Problem
Peristaltic robots often require many actuators and complicated controllers, which can constrain applications, especially for soft, untethered robots.
Source: §1 · p. 2Method
A two-segment bistable Kresling module with foldable anchors uses changes in total length to generate a deterministic actuation cycle for peristaltic-like gait phases.
Source: §1 · p. 3Results
The demonstrated peristaltic-like crawling uses one actuator and no digital controllers, with multi-stability generating the coordinated deformation sequence.
Source: §1 · p. 3, §5 · p. 13Takeaways & Limitations
The module’s multi-stable mechanics coordinate locomotion phases without individually actuating each segment or digitally coordinating multiple actuators.
Source: §1 · p. 3, §5 · p. 13
Abstract
from arXiv · showhide
This study proposes and examines a novel approach to generate peristaltic-like locomotion in a segmented origami robot. Specifically, we demonstrate the use of multi-stability embedded in origami skeleton to eliminate the need for multiple actuators or digital controllers to coordinate the complex robotic movements in peristaltic crawling. The crawling robot in this study consists of two serially connected bistable origami segments, each featuring a generalized Kresling design and a foldable anchoring mechanism. Mechanics analysis and experimental testing of this dual-segment module reveal a deterministic deformation sequence or actuation cycle, which is then used to generate the different phases in a peristaltic-like locomotion gait. Instead of individually controlling the segment deformation like in earthworm and other crawling robots, we only control the total length of this robot. Therefore, this approach can significantly reduce the total number of actuators needed for locomotion and simplify the control requirements. Moreover, the richness in Kresling origami design offers us substantial freedom to tailor the locomotion performance. Results of this study will contribute to a paradigm shift in how we can use the mechanics of multi-stability for robotic actuation and control.
1. Introduction
Peristaltic crawling coordinates segment deformation and anchoring, but robotic implementations can require many actuators and complicated controllers. This study uses Kresling origami multi-stability to generate peristaltic-like locomotion with one actuator and no digital controller.
1. Introduction
- Earthworm locomotion coordinates contracting, anchoring, and extending segments so a wave travels toward the tail while the body moves forward.Contraction and extension involve opposite length changes; anchoring occurs when a segment is fully contracted.Source: §1 · p. 1
- Conventional worm-inspired robots individually actuate segments and require complicated control, creating a cumbersome setup that can constrain applications, especially for soft, untethered robots.The paper identifies pneumatic chambers, SMA springs, electric motors, and permanent magnets as actuation approaches used in prior robots.Source: §1 · pp. 2–3
- Prior work has used multi-stability for controller-free swimming, crawling, gripping, and walking, motivating its use to coordinate peristaltic locomotion.The paper defines multi-stability as a structure having multiple stable states that it can switch between through external or internal actuation.Source: §1 · p. 3
- A two-segment Kresling driving module uses multi-stability to produce a deterministic deformation sequence, coordinating peristaltic-like crawling with one actuator and no digital controller.Changing the module’s total length generates the actuation cycle, whose phases define the locomotion gait.Source: §1 · p. 3
2. Generalized Kresling Origami
The generalized Kresling segment provides a bistable origami skeleton whose geometry can be tailored to retain nonzero length when contracted. Analysis and experiments characterize how its design parameters shape bistability and folding behavior.
2. Generalized Kresling Origami
- Kresling origami forms a tubular prism with rigid end polygons and two stable states; facet deformation between those states underlies its bistability.The design is characterized by polygon side count N, side length P, and angle ratio λ.Source: §2 · p. 4
- Unlike traditional Kresling, whose fully contracted length is always zero, generalized Kresling adds a nonzero contracted-state length that broadens the design space for peristaltic kinematics.The generalized design permits nonzero lengths at both fully contracted and fully extended states.Source: §2 · p. 4
- The equivalent truss-frame analysis represents mountain and valley creases as pin-jointed trusses, assumes valley-crease lengths remain fixed, and describes folding with α, l, and b.Mountain-crease trusses are undeformed at the stable states and compressed during folding between them.Source: §2 · pp. 4–5
- Increasing the angle ratio raises the energy barrier between stable states; bistability is weakest at λ = 0.5, strongest at λ = 1, and absent for λ < 0.5.The analytical comparison holds L(0) constant.Source: §2 · p. 6
- Higher angle ratios require greater actuation force to switch states, while measured extension and contraction curves show hysteresis that fabrication adjustments can minimize.The authors attribute hysteresis probably to crease-line delamination and contact between triangular facets; it is not expected to significantly affect actuation-cycle generation.Source: §2 · p. 6
3. Actuation Cycle from the Multi-stable Driving Module
The two Kresling segments are driven only by changing the module’s total length, which produces a deterministic deformation sequence. The sequence combines two jumps into a four-phase actuation cycle, and experiments broadly agree with its analytical prediction.
3. Actuation Cycle from the Multi-stable Driving Module
- The module uses two generalized Kresling segments with different angle ratios and bistability strengths, while only its total length is controlled.The segments are not manipulated individually.Source: §3 · p. 7
- For a prescribed total length, the analysis locally minimizes total strain energy over segment lengths subject to their sum and individual bounds.The resulting equilibrium paths are used to identify the deformation sequence.Source: §3 · p. 8
- The actuation cycle combines two jumps into four phases that redistribute the segments’ lengths as the module is stretched and compressed.The phases are g→b→c, c→d, d→d*→f, and f→g.Source: Figure 3 · p. 7, §3 · p. 8
- Experimental measurements broadly agree with the predicted cycle, although jump lengths differ slightly and measured jumps are slower.These discrepancies do not hinder the creation of peristaltic-like locomotion.Source: §3 · pp. 8–9
4. Locomotion Gait Generation
Foldable anchors couple the two-segment bistable module’s four-phase actuation cycle to peristaltic-like crawling, while Kresling design choices govern gait length and whether a usable cycle occurs.
4. Locomotion Gait Generation
- Because Kresling segments do not change diameter as their length changes, foldable anchors mimic the radial deformation needed for anchorage.The anchors are designed to deploy when a segment contracts longitudinally below its cut-off length.Source: §4 · p. 9, §4.1 · p. 9
4.1. Anchor Design
- Facet-mounted anchors deploy as Kresling segments contract, with cut-off lengths set so they engage the pipe and switch anchoring between segments.Foam tips provide friction; the tail anchor is attached to Segment I and the head anchor to Segment II.Source: §4.1 · p. 9, Figure 4 · p. 10
4.2. Peristaltic-like Locomotion Gait
- The four-phase cycle alternates forward movement with anchor transfers between the tail and head, using total-length changes to move the robot.In Phase I the tail is anchored as the body lengthens; in Phase III the head is anchored as contraction moves the tail forward.Source: §4.1 · p. 9, §4.2 · pp. 10–11
- The prototype’s repetitive gait and phase sequence agreed well with analytical predictions, validating one-actuator crawling coordinated by multi-stability.The authors attribute the measured gait-length discrepancy to idealization in the analytical model and temporary anchor slippage during switching.Source: Figure 5 · p. 11, §4.2 · p. 12
- Changing motor speed adjusts locomotion-cycle frequency and average crawling speed, but not gait length, which depends on Kresling design and multi-stability.The actuation cycle is independent of the rate of total-length stretching or compression.Source: §4.2 · p. 12
4.3. Parametric Study: Gait Length
- For fixed λI, gait length increases with λII, while for fixed λII it is insensitive to λI; some angle-ratio combinations prevent a four-phase gait.Locomotion is unavailable when both ratios are below 0.65, when they are very close, or when they are equal.Source: Figure 5 · p. 11, §4.3 · p. 13
5. Summary and Conclusion
The study uses origami multi-stability to coordinate peristaltic-like crawling with a two-segment module and total-length actuation. Its applicability depends on the segment’s deformation and bistability properties.
5. Summary and Conclusion
- Multi-stability in a robotic origami skeleton generated peristaltic-like locomotion without multiple actuators or complicated controllers.The demonstrated module combines two bistable Kresling segments and generates a deterministic deformation sequence by changing total length.Source: §5 · p. 13
- Two folding-induced jumps divide the actuation cycle into four phases, two for forward motion and two for switching anchoring locations.The jumps change the lengths of the constituent segments without changing the module’s total length.Source: §5 · p. 13
- The locomotion principle may extend beyond Kresling designs when segments couple longitudinal and radial deformation and have tunable bistability.The authors also note that other actuators may be used if they work across the required deformation range.Source: §5 · p. 13
Appendix A. Equilibrium Paths Search
The equilibrium path is found by minimizing the module’s total strain energy over segment lengths at each prescribed total length. The search advances incrementally from the minimum length, and compression may follow a different path than stretching.
Appendix A. Equilibrium Paths Search
- At each prescribed total length, the module’s equilibrium path is found by minimizing total strain energy over individual segment lengths subject to the total-length constraint.The last segment length is determined by the prescribed module length and the other segment lengths; segment lengths are bounded by their minimum and maximum values.Source: Appendix A · pp. 15–16
- The search increments total length from its minimum to maximum, solving the optimization problem at each increment.The increment size is ∆lt, and m is the total number of increments.Source: Appendix A · pp. 15–16
- The first increment starts from segments’ fully contracted stable-state lengths, which already form an energy minimum and require no optimization.The fully contracted stable-state length can differ from the segment’s minimum allowable length.Source: Appendix A · p. 16
- For each later increment, the previous increment’s optimized segment lengths initialize the next optimization, whose result records the segment lengths and energy along the path.The final segment length and the module’s corresponding total energy are then calculated.Source: Appendix A · pp. 16–17
- Compression can follow an equilibrium path different from stretching, so the search procedure is also applied from the module’s maximum length.Together, the two searches provide paths for stretching and compression.Source: Appendix A · p. 17