Researchers report a control system that tracked prescribed paths with a single soft pneumatic actuator, also tested user-guided motion and changed a reference path when a dynamic obstacle approached. The same work examined whether a learned model’s local stability classifications matched representative stable, oscillatory and divergent responses. The evidence comes from one spatial actuator with three parallel bellows.
A control model split into two parts
The framework decomposed actuator behavior into a nonlinear static equilibrium model and a linear residual dynamics model identified with EDMDc. For control, it combined feedforward pressure compensation with task-space proportional-integral feedback. Static-model identification used 500 seconds of staircase pressure excitation and yielded 161 equilibrium pressure-position pairs.
With a degree-2 polynomial, the static map had a total fitting RMSE of 12.89 mm. Reference-tracking RMSE was averaged over three trials, and the same controller gains were used for precomputed and user-guided tracking.
Reported errors varied across path conditions
In the listed tests, the higher-speed conditions were associated with higher reported RMSE for both the helix and lemniscate paths. The helix’s average RMSE was 1.09 mm at 10 mm/s and 9.47 mm at 100 mm/s. For the lemniscate, a figure-eight-like path, the corresponding values were 1.36 mm and 6.60 mm. The staircase path recorded 1.79 mm at 6.5 mm/s. All reference-tracking values were averaged over three trials, and no confidence intervals were reported.
User-guided tests differed between the two representative command styles reported. Smooth motion had an overall RMSE of 10.1 mm and a peak reference acceleration of 9.18 m/s2. Step-like motion had 16.8 mm RMSE and a peak reference acceleration of 25.92 m/s2. The study presents these as representative smooth and step-like cases, so they describe those examples rather than a broad distribution of user behavior.
A path around a moving obstacle
The obstacle trial used an outer safety distance of 100 mm and an inner safety distance of 25 mm. As the dynamic obstacle approached, the reference-modification layer maintained the minimum separation described by the test. Once the obstacle was beyond the 100 mm outer threshold, the reference returned smoothly to nominal tracking. This was one described experiment, with no broader robustness statistics reported.
A local check of closed-loop behavior
To assess local closed-loop stability, the analysis used spectral radius, a measure used here to judge whether the modeled response settles or grows. The reported rule predicted stability when the spectral radius of the augmented closed-loop model, written ρ(Aaug), was below 1. The nominal residual model had ρ(A) of 0.9540. This was a local check and did not establish global nonlinear stability.
Randomly sampled, perturbed gain tests were associated with three representative regimes. With proportional gain magnitude around KP=2 and integral gain magnitude around KI=10, the response was associated with stable tracking and ρ(Aaug)<1. Around KP=5 and KI=5, the response was oscillatory as the spectral radius approached 1. Around KP=10 and KI=1, the response rapidly diverged when ρ(Aaug)>1. The gain cases were examples rather than an aggregate validation statistic.
The combined controller had the lowest reported error
An internal comparison tested feedforward-only control, residual feedback-only control and their combination. The combined FF+FB controller had the lowest RMSE in each listed trajectory: 2.14 mm for the helix, 2.37 mm for the lemniscate and 1.94 mm for the staircase. The corresponding feedforward-only values were 18.43, 19.81 and 20.67 mm; feedback-only values were 7.14, 6.57 and 5.14 mm. No external controller baseline was reported.
What remains untested
The models were identified from free-space motion and do not explicitly represent external loading or contact interactions. The evidence is expected to be strongest within the workspace, pressure limits and motion bandwidth represented in the training data. The hardware evaluation involved one spatial soft pneumatic actuator with three parallel bellows, so transfer to other continuum-robot architectures remains untested.
The stability analysis has its own boundary: it is local and may not accurately predict behavior after large operating-point changes or long-term material drift. The document states that the work was submitted to IEEE for possible publication. No funding source was reported in the supplied text or metadata.
Paper data and sources
Original title: Control-Oriented Learning for Dynamic Tracking and Stability Analysis of Soft Pneumatic Actuators
Authors: Nithin S. Kumar, Eric J. Barth
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text