Source-linked AI summary
Adaptive and Resilient Soft Tensegrity Robots
John Rieffel, Jean-Baptiste Mouret
TL;DR
Soft robots’ complex dynamics make control difficult, and manually developed gaits limit adaptation to changing contexts or physical damage. This paper uses vibration-driven tensegrity and data-efficient learning to find and relearn locomotion gaits. The prototype exceeds 10 cm/s and learns new gaits in fewer than 30 trials, but is not fully autonomous.
Problem
Soft robots’ high-dimensional dynamics make conventional control difficult, while hand-designed gaits are time-consuming and cannot adapt when terrain or damage changes.
Source: Introduction · pp. 1–2Method
A vibration-driven tensegrity robot uses Bayesian optimization with system intuitions as a non-constant reward prior to find effective gaits with few trials.
Source: Introduction · p. 2, Results · p. 3, Discussion · p. 7Results
More than 10 cm/s and more than 1 body length per second, with new gaits learned in fewer than 30 trials.
Source: Discussion · p. 4Takeaways & Limitations
Tuned structural resonance can support fast locomotion, while learning enables the prototype to adapt its behavior to damage or new situations.
Source: Discussion · pp. 4–5The prototype is not fully autonomous: it relies on a power tether, external motion capture, and an offboard computer for learning.
Source: Discussion · p. 7
Abstract
from arXiv · showhide
Living organisms intertwine soft (e.g., muscle) and hard (e.g., bones) materials, giving them an intrinsic flexibility and resiliency often lacking in conventional rigid robots. The emerging field of soft robotics seeks to harness these same properties in order to create resilient machines. The nature of soft materials, however, presents considerable challenges to aspects of design, construction, and control -- and up until now, the vast majority of gaits for soft robots have been hand-designed through empirical trial-and-error. This manuscript describes an easy-to-assemble tensegrity-based soft robot capable of highly dynamic locomotive gaits and demonstrating structural and behavioral resilience in the face of physical damage. Enabling this is the use of a machine learning algorithm able to discover effective gaits with a minimal number of physical trials. These results lend further credence to soft-robotic approaches that seek to harness the interaction of complex material dynamics in order to generate a wealth of dynamical behaviors.
Introduction
Soft robots’ flexibility and elasticity make them difficult to control, and their gaits have generally been hand-designed, limiting adaptation when conditions change. This work introduces a vibration-driven soft tensegrity robot whose resonance is tuned by a data-efficient learning algorithm to discover locomotion gaits.
Introduction
- Soft materials create high-dimensional, dynamically coupled systems whose resonances complicate conventional robotic control.Their many degrees of freedom limit the use of traditional kinematic and inverse-dynamics approaches.Source: Introduction · pp. 1–2
- Hand-designed empirical gait tuning is time-consuming and prevents control adaptation to new terrain or physical damage.Source: Introduction · p. 2
- The robot combines a modular, deformable tensegrity structure with vibration actuation and data-efficient learning to discover gaits and adapt after damage.Tensegrity structures use rigid struts and tensile springs or cables, and are described as robust to deformation and relatively easy to construct.Source: Introduction · p. 2
- Conventional tensegrity control uses quasi-static strut or cable length changes, making it unsuitable for compliant robots and slow in locomotion.Source: Introduction · p. 2
- Prior dynamic tensegrity control produced simulated behaviors, but substrate dependence created a reality gap that hindered transfer to real robots.A vibrating tensegrity-inspired robot had previously changed between forward and backward locomotion by changing oscillator frequency.Source: Introduction · p. 2
- The authors test whether properly exciting real-world tensegrity resonance can produce step-like locomotion, using trial-and-error learning to tune vibration frequencies.The robot’s stated goal is to locomote as fast as possible across flat terrain.Source: Introduction · p. 2
Results
Prior-based Bayesian optimization found the fastest gaits in 30 trials, while the robot also retained locomotion after spring removal and outperformed a rigid replica. Performance profiles showed that the best intact-robot gaits did not transfer to the damaged robot, making adaptation relevant.
Robot design
- The pocket-sized robot uses six composite struts, 24 elastic springs, and three vibration motors; its spring constants were chosen to produce low natural frequencies and large displacements.The structure holds its shape in normal operation but can be compressed flat by hand.Source: Results · p. 2
Learning algorithm
- The prior favors high motor speeds, but learning remains necessary because some full-speed combinations cause tumbling and small speed changes can alter gait performance.The algorithm balances exploitation and exploration using a probabilistic model of motor speeds and locomotion speed.Source: Results · p. 3
- 11.5 cm/s was the best median locomotion speed with prior-based Bayesian optimization, versus 6.3 cm/s without the prior and 5.4 cm/s with random search.Each algorithm was run independently 20 times, with 30 trials per run; the absolute best speed was 15 cm/s.Source: Results · pp. 3–4, Figure 2 · p. 3
Flexible versus rigid structure
- The flexible tensegrity robot moved at 11.5 cm/s versus 7.1 cm/s for the rigid replica, and its measured strut-end movement was more than twice as large.Movement amplitudes were 2.3 cm for the flexible robot and 0.99 cm for the rigid replica, measured across 50 random gaits.Source: Results · p. 4
Damage resilience
- 6.5 cm/s was achieved after spring removal, below the intact robot’s 11.5 cm/s, but successful straight gaits were found within 30 trials.The damaged robot was relearned after its shape changed; both conditions were tested over 20 independent runs.Source: Figure 3 · p. 3, Results · p. 4
Performance profiles
- Performance profiles showed that the intact robot’s best gaits did not work best on the damaged robot, supporting the need to adapt gaits after damage.The profiles also showed prior knowledge consistent with the intact, rigid, and damaged robots; the authors suggest it might help under other damage conditions.Source: Results · p. 4
Discussion
The authors argue that vibratory tensegrity robots can exploit flexibility and resonance for fast locomotion, with Bayesian optimization finding effective gaits in few physical trials. The discussion highlights step-like foot motions and adaptation, while noting limits in substrate coverage, autonomy, and understanding optimal suppleness.
Discussion
- The prototype reaches locomotion speeds above 10 cm/s and learns new gaits in fewer than 30 trials, adapting to damage or new situations.The authors attribute its speed to harnessing tensegrity flexibility and resonance.Source: Discussion · p. 4
- Tuned vibration produces large structural deformations and step-like foot patterns that may help the robot step over small ground irregularities.The authors identify the mix of soft and rigid elements as making these patterns possible and potentially harder to induce and control in fully soft or fully rigid robots.Source: Discussion · p. 5
- Bayesian optimization reduces physical trials and robot wear compared with earlier hill-climbing experiments that needed hundreds of trials and hours to find effective gaits.The discussion links this data efficiency to faster, more autonomous adaptation.Source: Discussion · pp. 5, 7
- The method trades computation for data efficiency, and its acquisition-function optimization may be costly on low-power embedded computers.The authors use Bayesian optimization because it can incorporate prior knowledge and handle noisy evaluations when only a few dozen samples are possible.Source: Discussion · p. 7
- The algorithm found effective gaits across the tested levels of suppleness, although the mechanism behind damage-related speed changes and the optimal suppleness remain unresolved.The authors suggest damage may loosen the structure or alter the transmission of oscillations or resonance modes.Source: Discussion · p. 7
- Evaluation covered only one substrate, and the prototype remains tethered and dependent on external motion capture and an offboard learning computer.The authors also identify robustness to perturbations and changes in substrate as an open question.Source: Discussion · p. 7
Material and Methods
The robot uses a six-bar tensegrity frame with elastic springs selected for low natural frequencies and large displacements, while its control policy sets the three vibrating motors’ input voltages.
Robot
- Six equal-length composite struts connect through 24 identical helical springs, with four springs attached at each strut end.The geometry follows the TR-6 form and requires few machining operations.Source: Robot · p. 8
- Three 12 mm vibrational motors are mounted on the struts and connected through motor controllers to a USB serial adapter.The springs attach to holes in nylon washers fixed at the strut ends.Source: Robot · p. 8
- A spring constant of 0.209 N/cm limits estimated static deflection to 5% of strut length while targeting low natural frequencies and large structural displacements.The spring choice was based on modeling individual struts and the full six-bar structure.Source: Robot · p. 8
Control policy
- Each control policy is a three-value PWM vector that sets the input voltage of the three vibrating motors.Values range from 0 for full-speed backward to 1 for full-speed forward; 0.5 means no movement.Source: Control policy · p. 8
Performance function
The performance function estimates locomotion speed from the robot’s displacement during a three-second controller test, with evaluation stopped if yaw exceeds one radian.
Performance function
- Each controller runs for 3 seconds, and performance is the Euclidean start-to-end distance divided by 3, reported in cm/s.The distance is recorded when the test ends, including when the yaw threshold is exceeded early.Source: Performance function · p. 8
- If yaw exceeds 1 radian during the test, evaluation stops and distance is measured at the threshold crossing.Source: Performance function · p. 8
- An external Optitrack motion-tracking system evaluates policies, though an embedded camera with visual odometry can obtain the same measurements.Source: Performance function · p. 8
Profile plots
The profile plots visualize the three-motor search space by showing pairwise motor-speed profiles, each maximized over the third motor’s speed.
Profile plots
- Motor speeds are discretized into 25 bins for each pair of dimensions.Source: Profile plots · p. 8
- Each profile reports the maximum robot performance over the third motor speed for a fixed pair of motor speeds.Source: Profile plots · p. 8
- Three plots cover the pairs v1-v2, v1-v3, and v2-v3.Source: Profile plots · p. 8
Learning algorithm
The learning algorithm uses Bayesian optimization to select motor-speed trials for the robot’s locomotion objective. A Gaussian-process model and an acquisition function balance predicted performance with uncertainty while incorporating a prior.
Learning algorithm
- The algorithm discovers effective rotation speeds for the robot’s three motors using Bayesian optimization to maximize an expensive performance function with few evaluations.Bayesian optimization models the objective, selects a point to evaluate, and updates its model as trials proceed.Source: Learning algorithm · pp. 8–9
- A Gaussian process models the objective function by assigning a probability distribution to possible function values, represented by a mean and variance.The mean and variance can vary across input points, defining a probability distribution over functions.Source: Learning algorithm · p. 9
- The Gaussian-process estimates are fitted from the performance values and tested points collected up to each iteration.The covariance matrix uses a kernel to define how samples influence one another; the implementation uses an exponential kernel with β fixed to 0.15.Source: Learning algorithm · p. 9
- A prior mean function guides optimization toward promising regions, and the next trial is selected by an acquisition function balancing exploration and exploitation.The prior is implemented as a second Gaussian process defined by hand-picked points; the chosen acquisition function is UCB with κ = 0.2.Source: Learning algorithm · p. 9
Prior for the learning algorithm
The gait-learning prior favors combinations of motors at full forward or reverse speed. It is implemented as a Gaussian process using nine hand-picked points, ignoring variance and using an exponential kernel with β = 0.15.
Prior for the learning algorithm
- The prior encodes the assumption that the highest-performing gaits are likely combinations of motors at full forward or reverse speed.This was based on common sense, preliminary modeling, and preliminary experiments, as described in the passage.Source: Prior for the learning algorithm · p. 9
- The prior uses a Gaussian process defined by nine hand-picked points, with variance ignored and an exponential kernel with β = 0.15.The points are shown in Fig. 5D.Source: Prior for the learning algorithm · p. 9
- Eight listed motor-command points have prior probability 0.3 each, while the zero-command point has probability 0.The listed commands are combinations of −100%, +100%, and 0% motor settings.Source: Prior for the learning algorithm · p. 9
Statistics
Experiments report the 5th and 95th percentiles and use two-tailed Mann-Whitney U tests. Box plots show medians and interquartile ranges, with whiskers and significance stars defined by stated conventions.
Statistics
- All experiments report the 5th and 95th percentiles.The passage specifies these percentiles as the reported spread.Source: Statistics · p. 9
- Statistical tests use the two-tailed Mann-Whitney U test, with stars marking thresholds from p ≤ 0.05 to p ≤ 0.0001.One through four stars correspond respectively to p ≤ 0.05, 0.01, 0.001, and 0.0001.Source: Statistics · p. 9
- Box plots mark the median, span the 25th–75th percentiles, and use whiskers extending 1.5 IQR beyond the quartiles; points outside are outliers.The passage identifies this outlier convention as the interquartile rule.Source: Statistics · p. 9
Computer code
A code archive is provided, and the code is planned for open-source release on GitHub with the final publication.
Computer code
- The code archive is available at the listed limbo-tensegrity.tar.gz address.The authors state that the code will be released with an open-source license on GitHub for the final publication.Source: Computer code · p. 9
Data availability
A data archive is provided, and the data are planned for release on Dryad with the final publication.
Data availability
- The data archive is available at the listed tensegrity.tar.gz address.The authors state that the data will be released on Dryad for the final publication.Source: Data availability · p. 9
Supplementary information
Video S1 presents the soft tensegrity robot locomoting and learning to compensate when damaged.
Video S1
- The video shows the soft tensegrity robot locomoting.Source: Video S1 · p. 12
- The video shows the robot learning to compensate when damaged.Source: Video S1 · p. 12
- The video is available online.Source: Video S1 · p. 12