Soft Synergies: Model Order Reduction of Hybrid Soft-Rigid Robots via Optimal Strain Parameterization

TL;DR

The paper tackles the challenge of high-dimensional soft-robot dynamics by marrying the Geometric Variable Strain (GVS) model with Proper Orthogonal Decomposition (POD) to produce a compact, interpretable ROM based on coupled strain synergies. By constructing optimal strain bases from data, the method achieves substantial dimensionality reduction while preserving accuracy for soft, rigid, and hybrid configurations, including closed-chain systems. The ROM demonstrates strong interpolation and extrapolation capabilities, enables shape estimation from limited sensors, and delivers real-time performance with speed-ups up to and beyond an order of magnitude in many cases. Experimental validations on soft, hybrid, and rigid-like prototypes confirm the approach’s practical utility for real-time simulation, control, and estimation in complex robotic systems. The work lays a foundation for real-time soft robotics applications and suggests future directions in modal derivatives and data-driven extensions to further enhance accuracy and scalability.

Abstract

Soft robots offer remarkable adaptability and safety advantages over rigid robots, but modeling their complex, nonlinear dynamics remains challenging. Strain-based models have recently emerged as a promising candidate to describe such systems, however, they tend to be high-dimensional and time-consuming. This paper presents a novel model order reduction approach for soft and hybrid robots by combining strain-based modeling with Proper Orthogonal Decomposition (POD). The method identifies optimal coupled strain basis functions -- or mechanical synergies -- from simulation data, enabling the description of soft robot configurations with a minimal number of generalized coordinates. The reduced order model (ROM) achieves substantial dimensionality reduction in the configuration space while preserving accuracy. Rigorous testing demonstrates the interpolation and extrapolation capabilities of the ROM for soft manipulators under static and dynamic conditions. The approach is further validated on a snake-like hyper-redundant rigid manipulator and a closed-chain system with soft and rigid components, illustrating its broad applicability. Moreover, the approach is leveraged for shape estimation of a real six-actuator soft manipulator using only two position markers, showcasing its practical utility. Finally, the ROM's dynamic and static behavior is validated experimentally against a parallel hybrid soft-rigid system, highlighting its effectiveness in representing the High-Order Model (HOM) and the real system. This POD-based ROM offers significant computational speed-ups, paving the way for real-time simulation and control of complex soft and hybrid robots.

Figures (20)

• Figure 1: An overview of our order reduction method. The last element of each row in the snapshots, which is the strain field solution, is the sum of the preceding elements, each governed by separate coordinates. This example shows the reduction of a single soft, slender manipulator with multiple actuators.
• Figure 2: Schematics of the GVS model: (A) Soft manipulator with a representative strain and velocity field. The recursive computation from $X_{j-1}$ to $X_j$ using two Zannah points, $Z1$ and $Z2$, is highlighted. (B) A generic hybrid multibody system with branched and close-loop joints.
• Figure 3: The resulting $1^{st}$ mode of the decomposition for the scenario in Section \ref{['sec:Single cable planar- no gravity']}. As inset, the corresponding family of shapes produced from different scaling of the mode.
• Figure 4: The resulting first four modes of the decomposition for the scenario in Section \ref{['sec:Single cable planar- no gravity']} with dynamics and gravitational load. As inset, the corresponding family of shapes produced from different scalings of each mode. The relative energy is indicated above each mode. The colors follow the same scheme of Figs. \ref{['fig::SingleCabNoGrav_mode']},\ref{['fig::MultiCabNoGrav_Modes']} and \ref{['fig::6Cables_Mode']}. However, only the red (y-bending) is apparent due to the planar actuator path in the $x-z$ local plane, while the other strains are almost zero.
• Figure 5: The first three modes of Section \ref{['sec::Multi cable']} scenario decomposition, with their respective family of shapes below. The relative energy is indicated above each mode. The blue, red, yellow, purple, green and light blue curves are the modes of the torsional, y-bending, z-bending, elongation, y-shearing and z-shearing strains respectively.