  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 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. Finally, the approach is
leveraged for shape estimation of a real six-actuator soft manipulator using
only two position markers, showcasing its practical utility. This POD-based ROM
offers significant computational speed-ups, paving the way for real-time
simulation and control of complex soft and hybrid robots.
