Data-Driven Precision Control of Soft Helicoid Robots
TL;DR A 5D reduced-order model of a tendon-driven soft trunk robot is learned from two hours of motion-capture data and used in 50 Hz model predictive control. On hardware it keeps the maximum tracking error to 5 cm across 2D and 3D tracks, against 10-38 cm for linear, Koopman and RL baselines, and also avoids virtual obstacles.
What they do
Soft robots are nonlinear and hard to model from first principles. This paper learns a low-dimensional model of a soft trunk robot purely from hardware data, using the theory of adiabatic spectral submanifolds (aSSMs), and uses it in model predictive control. The robot is a 42 cm trunk of three trimmed-helicoid modules printed in an elastomer, driven by 12 tendons on 6 motors, with the midpoint and end-effector tracked by motion capture.
How it works
- Idea. Soft robots are heavily damped, so their internal vibrations decay much faster than the task motion. The dynamics then settle onto a low-dimensional attracting manifold attached to the set of static shapes the robot takes under constant inputs.
- Data. 30 minutes of random step inputs give static states and decays (992 static states); 90 minutes of slow, smooth random inputs calibrate a higher-order correction.
- Model. The static shapes are fit with radial basis functions, and the dynamics around them with polynomials in a delay-embedded observable space, giving a 5D nonlinear ODE. The test error on unseen decays is 9.6%.
- Control. The ODE is the dynamics constraint in an MPC solved as a sequence of convex problems at 50 Hz, with no inverse-kinematics initial guess.
Results
- Tracks: a planar figure-8 0.2 m wide, a 3D random track and a 3D “Pacman” track, at several speeds. Only the aSSM controller stays mostly within the 3 cm repeatability tolerance of the hardware.
- Maximum error across the tracking tasks: 5 cm for aSSM, against 18 cm for DMDc, 38 cm for Koopman-pregain, 17 cm for MZ-Koopman and 10 cm for PPO.
- Training takes 5 minutes on 2 hours of data; the PPO baseline used 6 hours of on-robot data and training.
- With added constraints, the controller steers around static spheres on the track and keeps the trunk body clear of a moving cylinder.
Limitations
The obstacles are virtual constraints, not physical objects. The largest sphere is avoided but the end-effector stays inside its buffer zone. The theory assumes targets that vary slowly relative to the robot’s own dynamics, and the model does not account for external forces such as payloads or contact.
Figures
Abstract
A purely data-driven method grounded in the theory of adiabatic spectral submanifolds (aSSMs) was recently used to model and control nonlinear soft robotic simulators. Here, we extend the methodology to learn aSSM-reduced models from data collected from hardware soft robotic platforms. Specifically, we learn a five dimensional (5D) aSSM-reduced nonlinear ordinary differential equation (ODE) that accurately models the dynamics of a soft-helicoid trunk robot. We then use this ODE in a model predictive control scheme to demonstrate real-time precision control across various challenging closed-loop trajectory-tracking tasks, ranging from 2D to 3D trajectories with static and dynamic constraints. We find that our methodology enhances accuracy and precision across all control tasks compared to available data-driven linear methods and model-free reinforcement learning. While we focus here on a soft-helicoid trunk robot, our methodology relies solely on hardware data and is therefore applicable to a broader class of soft robotic systems.
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