Task-space model-based control of pneumatic soft actuators

Summary

Abstract Summary

Soft actuators enable dexterous and compliant interaction, but closed-loop task-space control remains challenging due to strong nonlinearities, distributed deformation, and uncertainty in their dynamics. This paper presents a real-time dynamic-model-based task-space feedback and estimation framework based on a non-minimal coordinate discrete elastic rod model formulated in absolute coordinates with holonomic constraints. The resulting structure preserves distributed mechanics while maintaining computational efficiency through sparse system matrices, enabling real-time control with up to 10 discretized rods. A quasi-static feedforward inverse model is combined with a task-space PI controller and a dynamic observer that fuses measurement residuals as virtual forces, enabling full-state estimation from sparse sensing. The approach is experimentally validated on three planar pneumatic soft actuators with varying geometries. Across five tasks, including drawing the digits 0-9 across the workspace (3-18 mm/s tip speed), tracking periodic motion (up to 37 cm/s), cross-platform generalization, reduced sensing conditions, and real-time user-defined references, our method achieves 1.5-2.3 mm root mean square error (RMSE) for precision motions and 5.5-12.4 mm RMSE at 1-2 Hz. Results demonstrate that structured, non-minimal dynamic models can enable real-time, high-precision, moderate-bandwidth task-space control of planar soft pneumatic actuators in free space.

Key Points

Soft actuators enable dexterous and compliant interaction, but closed-loop task-space control remains challenging due to strong nonlinearities, distributed deformation, and uncertainty in their dynamics.
This paper presents a real-time dynamic-model-based task-space feedback and estimation framework based on a non-minimal coordinate discrete elastic rod model formulated in absolute coordinates with holonomic constraints.
The resulting structure preserves distributed mechanics while maintaining computational efficiency through sparse system matrices, enabling real-time control with up to 10 discretized rods.
A quasi-static feedforward inverse model is combined with a task-space PI controller and a dynamic observer that fuses measurement residuals as virtual forces, enabling full-state estimation from sparse sensing.
The approach is experimentally validated on three planar pneumatic soft actuators with varying geometries.

Methods

The backbone of the soft continuum actuator is discretized as a chain of $N$ rigid rods with rotational elasticity and damping as shown in Fig. 2 . A non-minimal (maximal) set of generalized coordinates is used to describe the configuration: where ($x_{i},y_{i}$) and $\theta_{i}$ denote the absolute center-of-mass position and orientation of rod $i$, respectively.

Adjacent rods are connected through holonomic constraints enforcing geometric continuity, and the base of rod 1 is pinned to the origin.

Methods — Task-space model-based control of pneumatic soft actuators — Fig. 2: The planar discretized soft actuator model is overlaid with the physical actuator (P2). The actuator backbone is represented by $N$ rigid rods with rotational spring–damper elements generating elastic ($\tau_{k}$) and damping ($\tau_{b}$) torques. Adjacent rods are connected through holonomic constraint forces ($F_{x,hc},F_{y,hc}$). Pneumatic actuation is modeled as generalized torques ($\tau_{ext}$) applied at selected rod indices.

Experimental Results

We begin by characterizing the step response of the soft actuator P1 under four control strategies: feedforward only (FF), FF with proportional (FF+P), FF with integral (FF+I), and FF+PI feedback. This was performed to demonstrate the relative importance of each component of the controller architecture.

The actuator tip was commanded to a sequence of four task-space step inputs at 3 s intervals, forming a diamond-shaped trajectory (Fig. 4 ).

Experimental Results — Task-space model-based control of pneumatic soft actuators — Fig. 3: The system block diagram is shown here. The reference trajectory is processed by a quasi-static inverse (feedforward) module to generate $u_{FF}$. A dynamic observer integrates the constrained rod model and incorporates measurement residuals as virtual generalized forces to estimate the system state. The estimated state is used within the task-space PI control block to compute a feedback correction $u_{FB}$ via the local sensitivity mapping. The total input $u=u_{FF}+u_{FB}$ is applied through proportional valves with low-level pressure regulation.

Sources and Demonstrations

Figures are reproduced from Kumar et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.