Source-linked AI summary
Omnidirectional Amphibious Locomotion via Internal Mass Actuation
Niko Weaver, Boxi Xia, Li-Yu Lo, Yuhao Huang, Boyuan Chen
TL;DR
Field robots must traverse varied terrain and aquatic regions while tolerating environmental exposure and contact. MARBLE uses three internal mass sliders and an enclosed spherical shell for omnidirectional land rolling and water-surface propulsion. Experiments demonstrate locomotion across land, water, transitions, and obstacle contact, while the current platform remains limited to surface locomotion and lacks autonomous navigation.
Problem
Field robots must traverse heterogeneous terrain and aquatic regions, where exposed moving components can be obstructed, contaminated, or entangled by vegetation, debris, and water.
Source: §I · p. 1Method
MARBLE uses three orthogonal internal mass sliders to rotate an enclosed spherical shell for terrestrial rolling and passive-fin water-surface propulsion without mechanical reconfiguration.
Source: §I · pp. 1–2Results
Experiments demonstrated omnidirectional locomotion, terrestrial rolling, water-surface propulsion, land-water transitions, and continued pushing during obstacle contact.
Source: §VI · p. 7Takeaways & Limitations
A shared enclosed actuation design supports cross-medium mobility while keeping active locomotion mechanisms inside the robot body.
Source: §VI · p. 7The current platform is limited to water-surface locomotion, and autonomous navigation is not supported.
Source: §VI · p. 7
Abstract
from arXiv · showhide
Field robots must traverse varied terrain and obstacles while remaining robust to water, debris, vegetation, and physical contact. We present MARBLE, a fully enclosed omnidirectional amphibious rolling robot driven entirely by internal mass redistribution. Three mutually orthogonal linear sliders shift internal masses to generate body rotation, while an orientation-aware controller maps planar velocity commands into slider positions. A rigid spherical shell encloses all active mechanisms and simultaneously serves as the terrestrial contact surface, buoyant enclosure, and mounting structure for passive fins that enable water-surface propulsion. Rotation of the same shell architecture hence produces rolling on land and surface propulsion in water without mechanical reconfiguration or separate locomotion actuators. The spherical morphology further allows the robot to accommodate changes in body orientation and contact location during direct interactions with terrain and obstacles. We evaluate MARBLE through omnidirectional locomotion characterization, traversal across heterogeneous terrestrial environments, aquatic surface locomotion, land-water transitions, and deliberate obstacle interactions. These experiments demonstrate how a single enclosed mechanical architecture can combine omnidirectional mobility, cross-medium locomotion, and tolerance to environmental contact. MARBLE provides a compact design for field mobility across heterogeneous terrain, obstacles, and land-water transitions. We will open-source all software and hardware design. Our website is https://generalroboticslab.com/MARBLE
I. INTRODUCTION
Field robots must cross heterogeneous terrain and water while tolerating environmental exposure and contact. MARBLE uses one enclosed, internally mass-actuated spherical body for omnidirectional rolling and water-surface propulsion, and experiments evaluate locomotion across land, water, transitions, and obstacles.
I. INTRODUCTION
- Field missions can span uneven ground, vegetation, debris, and aquatic regions, while exposed moving components can be obstructed, contaminated, or entangled.Mobility must also tolerate physical contact and environmental exposure during traversal.Source: §I · p. 1
- Spherical morphology permits continuously changing contact locations without a fixed upright orientation, while internal actuation keeps motors and transmissions away from direct environmental contact.These properties motivate using a common body and actuation system across environments.Source: §I · p. 1
- MARBLE combines three orthogonal mass sliders, an orientation-aware controller, and a rigid spherical shell to produce omnidirectional land and water locomotion without mechanical reconfiguration.The shell also provides buoyancy and supports passive fins; the same body rotation produces rolling on land and surface propulsion in water.Source: §I · pp. 1–2
- Experiments characterize directional response, heterogeneous-terrain traversal, water-surface propulsion, land-water transitions, and deliberate obstacle interactions.The evaluation examines whether shared enclosed actuation supports mobility across environments and during environmental contact.Source: §I · p. 2
II. RELATED WORK
Prior multimodal robots share structures or reconfigure mechanisms, while spherical and internally actuated designs address changing contacts and enclosed motion. MARBLE combines these ideas in a rigid shell that serves as its land interface, buoyant enclosure, and support for passive aquatic propulsion.
II. RELATED WORK
- Air-ground and land-water robots reuse structures or reconfigure mechanisms, whereas MARBLE uses one enclosed mass-actuation mechanism without reconfiguration.The shell serves as the terrestrial contact surface, buoyant enclosure, and support for passive aquatic propulsion.Source: §II · p. 2
- Spherical and symmetric robots use changing body orientations, distributed contacts, or compliance for locomotion across irregular terrain; MARBLE instead uses a rigid shell as its continuous external interface.That interface serves terrain, water, and obstacle contact while active mechanisms remain enclosed.Source: §II · p. 2
- Prior internally actuated spherical robots use rotors, mass redistribution, pendulums, dedicated steering, or inner-shell wheels; MARBLE uses three orthogonal linear sliders for omnidirectional locomotion and both land and water propulsion.Its shared actuation avoids separate steering and propulsion mechanisms.Source: §II · p. 2
A. Shell Design
- The 387 mm diameter shell encloses the robot, provides the rolling surface, and carries passive fins that generate hydrodynamic forces as the body rotates.The same exterior structure also provides buoyancy, and its sealing performance is characterized experimentally.Source: A. Shell Design · pp. 2–3
B. Structural Frame
The structural frame supports three orthogonal linear mass sliders, whose coordinated motion shifts the center of mass to rotate the shell. The resulting body rotation produces terrestrial rolling or water-surface propulsion through the shell’s interaction with each medium.
B. Structural Frame
- The snap-fit frame uses 48 beams and 14 hubs, eliminating 96 fasteners relative to an assembly using two fasteners per beam.Secondary members fill gaps to create a more continuous rolling external profile, and the complete sealed shell is used in field experiments.Source: B. Structural Frame · p. 3
C. Mass-Slider Actuation
- Three identical sliders translate 700 g masses over 220 mm strokes along mutually orthogonal body axes, shifting the center of mass in arbitrary reachable directions.The sliders use belt drives and carbon-fiber guide rods; coordinated positions redistribute mass to generate motion.Source: C. Mass-Slider Actuation · p. 3
D. Locomotion Principle
- On land, mass redistribution creates a horizontal center-of-mass offset whose gravitational moment rotates the shell when tangential traction is sufficient for rolling without slip.The simplified model neglects transient inertial effects, slip, and discrete contacts from the fins.Source: D. Locomotion Principle · pp. 3–4
- At the water surface, the same mass redistribution rotates the shell, and submerged fins generate net propulsion through asymmetric hydrodynamic interaction.Thrust depends on immersion depth, fin geometry, and body rotation rate.Source: D. Locomotion Principle · p. 4
E. Sensors and Computing
The onboard IMU supplies body orientation for transforming motion commands into the rotating body frame. Geometric and learned controllers share the same joint-level slider position-control interface.
E. Sensors and Computing
- An onboard IMU estimates body orientation, while experimental position and velocity measurements come from external video.The onboard computer communicates with the motor drives through a microcontroller and CAN interface.Source: E. Sensors and Computing · p. 4
IV. CONTROL
- The geometric controller maps planar commands to slider positions using measured orientation, while the learned controller predicts the same targets from onboard observations.Both controllers use the shared joint-level position-control interface.Source: §IV · p. 4
A. Coordinate Frames and Command Mapping
The controller separates world, body, IMU, and operator-command frames, then uses measured orientation and a fixed heading to interpret planar velocity commands as a direction in the rotating body frame.
A. Coordinate Frames and Command Mapping
- The body frame is centered on the robot with axes aligned to its three sliders, while the IMU and operator-command frames provide sensing and input references.The rotation matrix maps vectors from the body frame into another specified frame.Source: A. Coordinate Frames and Command Mapping · p. 4
- The IMU’s magnetic north–east–down frame is converted to the world convention by diag(1, −1, −1), and measured IMU orientation combines with the fixed mounting transform to compute body orientation.The command frame differs from the world frame by a constant heading ψ0, which the operator sets once per run.Source: A. Coordinate Frames and Command Mapping · p. 4
- A planar velocity command specifies the desired travel direction; a nonzero input defines a virtual target at fixed distance δ from the robot center.Normalization removes command magnitude, yielding binary stop-or-move input with continuous planar direction.Source: A. Coordinate Frames and Command Mapping · p. 4
B. Geometric Controller
The geometric controller projects a virtual target onto each slider rail to set mass displacements, updating for body rotation and enforcing calibrated travel limits before sending motor commands.
B. Geometric Controller
- The controller projects the virtual target onto each slider axis, selecting the point on each rail closest to the shared target as the desired mass displacement.As the robot rotates, the target position in body coordinates changes continuously to maintain the commanded world-relative direction.Source: B. Geometric Controller · p. 4
- The commanded displacement is clipped to calibrated limits; a 220 mm stroke gives nominal limits of +114 mm and −106 mm before a ±10 mm safety margin.A zero-motion command returns the masses to their centered configuration.Source: B. Geometric Controller · p. 4
- Slider displacement is converted to a motor-angle setpoint through the belt transmission, using a center-calibrated encoder angle and a polarity factor for transmission and encoder direction.The final angle setpoints are sent to the three motor drives over CAN.Source: B. Geometric Controller · pp. 4–5
- At each update, measured body orientation transforms the target into body coordinates, and projected rail displacements are clipped to slider limits before conversion to motor commands.This redistributes the internal masses to create rolling motion.Source: B. Geometric Controller · pp. 4–5
C. Learned Controller
The paper describes learned policies sharing the geometric controller’s slider-target interface, alongside simulation methods for training terrestrial and aquatic locomotion. The water model supplies buoyancy, drag, and fin thrust, while training randomizes unmodeled aquatic thrust effects.
C. Learned Controller
- Terrestrial and aquatic learned policies output three slider position targets through the geometric controller’s common hardware interface, allowing runtime exchange without low-level motor-control changes.The terrestrial and aquatic configurations share the robot model, actuation, observations, and action space; aquatic training adds water-surface forces and thrust randomization.Source: C. Learned Controller · p. 5
- Aquatic simulation models buoyancy, the offset-induced moment, submerged-shell drag, and fin thrust at a flat water surface with no waves or current.The fin thrust model discretizes fins into segments across 13 rings; 24 segments per ring resolve the waterline to 15° of arc, and summed segment forces yield thrust and torque.Source: C. Learned Controller · p. 5
- The model omits added mass, wave-making drag, and interactions between fin wakes, so the combined effects are handled with per-episode ring-force scaling.Deployment runs the simulation-trained policy onboard at 50 Hz without hardware fine-tuning or an additional adaptation phase.Source: C. Learned Controller · pp. 5–6
- The policy maps a 23-dimensional onboard observation to three slider targets, with actions scaled by 0.104 m about the centered rest pose and tracked by the shared joint-level position controller.Three consecutive observation frames are stacked; the training critic additionally receives uncorrupted observations and ground-truth linear velocity unavailable to the deployed policy.Source: C. Learned Controller · pp. 5–6
- Training samples per-axis velocity commands within ±0.7 m/s, resamples them every 2–8 s, and includes zero commands in 10% of samples while rewarding velocity tracking and regularizing slider motion.Episodes last 20 s without failure termination, and each policy is trained for 15,000 iterations with randomized contact, actuation, mass, and latency parameters.Source: C. Learned Controller · p. 6
A. Terrestrial, Aquatic, and Transitional Locomotion
MARBLE sustained locomotion on land and water and traversed directly between them using its shared internal actuation. Shoreline entry was slower amid changing contact and buoyancy conditions.
A. Terrestrial, Aquatic, and Transitional Locomotion
- 10.60 m over 14.00 s on land yielded 0.745 ± 0.163 m/s mean speed and 1.025 m/s maximum; 5.24 m over 14.00 s on water yielded 0.375 ± 0.059 m/s mean and 0.488 m/s maximum.The terrestrial trajectory was approximately closed; both modes used no separate aquatic propulsion mechanism.Source: A. Terrestrial, Aquatic, and… · p. 6
- 5.21 m over 23.93 s during land-to-water transition yielded 0.215 ± 0.146 m/s mean speed and 0.840 m/s maximum speed.The robot progressed from terrestrial rolling to sustained aquatic locomotion using the same internal mass actuation, without mechanical reconfiguration or propulsion-hardware switching.Source: A. Terrestrial, Aquatic, and… · p. 6
- Changing contact and buoyancy conditions during shoreline entry coincided with the reduced transition mean speed.The reported mean speed was 0.215 ± 0.146 m/s during the 5.21 m, 23.93 s transition.Source: A. Terrestrial, Aquatic, and… · p. 6
B. Omnidirectional Velocity Characterization
MARBLE produced planar motion across arbitrary directions, and the learned controller reached higher translational speeds than the geometric controller during water-surface locomotion.
B. Omnidirectional Velocity Characterization
- Commands in the operator frame were transformed into the rotating body frame using measured orientation.This procedure was used to characterize planar mobility across travel directions and compare the geometric and learned controllers.Source: B. Omnidirectional Velocity… · p. 6
- Velocity responses across the full 360° range showed planar motion in arbitrary directions without a preferred fixed heading.The capability arose from coordinated mass redistribution along three mutually orthogonal body axes.Source: B. Omnidirectional Velocity… · p. 6
- 0.348 ± 0.114 m/s mean and 0.592 m/s maximum for the learned controller exceeded the geometric controller’s 0.252 ± 0.088 m/s mean and 0.461 m/s maximum during water-surface locomotion.Both controllers produced omnidirectional aquatic locomotion; Fig. 5 plots 7,568 samples per controller using identical axis and color scales.Source: B. Omnidirectional Velocity… · p. 6, Figure 5 · p. 7
C. Object Interaction with Direct Shell Contact
MARBLE maintained internal actuation during direct buoy contact, then disengaged and resumed locomotion; the paper concludes that enclosed actuation supports cross-medium mobility.
C. Object Interaction with Direct Shell Contact
- During buoy contact, MARBLE continued actuating its internal masses, then disengaged and resumed locomotion while active components remained enclosed.The buoy perturbed the robot’s orientation and motion; the shell and passive fins served as the contact interface.Source: C. Object Interaction with Direct… · p. 7
VI. CONCLUSIONS, LIMITATIONS, AND FUTURE WORK
- The conclusion identifies shared internal mass actuation as supporting terrestrial rolling and water-surface propulsion while keeping active mechanisms enclosed.The three orthogonal sliders drive the same body rotation for land locomotion and passive-fin propulsion in water, without separate active aquatic propulsion.Source: §VI · p. 7
- The current platform is limited to water-surface locomotion, and its learned aquatic controller relies on an approximate hydrodynamic model.Autonomous navigation is not supported by the current platform.Source: §VI · p. 7