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The capability of effectively moving on complex terrains such as sand and gravel can empower our robots to robustly operate in outdoor environments, and assist with critical tasks such as environment monitoring, search-and-rescue, and supply delivery. Inspired by the Mount Lyell salamander’s ability to curl its body into a loop and effectively roll across sand and gravel, in this study we develop a sand-rolling robot and investigate how its locomotion performance is governed by the shape of its body. We experimentally tested three different body shapes: Hexagon, Quadrilateral, and Triangle. We found that Hexagon and Triangle can achieve a faster rolling speed on sand, but also exhibited more frequent failures of getting stuck in sand. Analysis of the interaction between robot and sand revealed the failure mechanism: the deformation of the sand produced a local “sand incline” underneath robot contact segments, increasing the effective region of supporting polygon (ERSP) and preventing the robot from shifting its center of mass (CoM) outside the ERSP to produce sustainable rolling. Based on this mechanism, a highly-simplified model successfully captured the critical body pitch for each rolling shape to produce sustained rolling on sand, and informed design adaptations that mitigated the locomotion failures and improved robot speed by more than 200%. Our results provide insights into how locomotors can utilize different morphological features to achieve robust rolling motion across deformable substrates.
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Geometrically modulated contact forces enable hula hoop levitation
Mechanical systems with moving points of contact—including rolling, sliding, and impacts—are common in engineering applications and everyday experiences. The challenges in analyzing such systems are compounded when an object dynamically explores the complex surface shape of a moving structure, as arises in familiar but poorly understood contexts such as hula hooping. We study this activity as a unique form of mechanical levitation against gravity and identify the conditions required for the stable suspension of an object rolling around a gyrating body. We combine robotic experiments involving hoops twirling on surfaces of various geometries and a model that links the motions and shape to the contact forces generated. The in-plane motions of the hoop involve synchronization to the body gyration that is shown to require damping and sufficiently high launching speed. Further, vertical equilibrium is achieved only for bodies with “hips” or a critical slope of the surface, while stability requires an hourglass shape with a “waist” and whose curvature exceeds a critical value. Analysis of the model reveals dimensionless factors that successfully organize and unify observations across a wide range of geometries and kinematics. By revealing and explaining the mechanics of hula hoop levitation, these results motivate strategies for motion control via geometry-dependent contact forces and for accurately predicting the resulting equilibria and their stability.
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- Award ID(s):
- 1847955
- PAR ID:
- 10651259
- Publisher / Repository:
- PNAS
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 122
- Issue:
- 1
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.2411588121
