Control of soft robots with inertial dynamics

Abstract

Soft robots promise improved safety and capability over rigid robots when deployed near humans or in complex, delicate, and dynamic environments. However, infinite degrees of freedom and the potential for highly nonlinear dynamics severely complicate their modeling and control. Analytical and machine learning methodologies have been applied to model soft robots but with constraints: quasi-static motions, quasi-linear deflections, or both. Here, we advance the modeling and control of soft robots into the inertial, nonlinear regime. We controlled motions of a soft, continuum arm with velocities 10 times larger and accelerations 40 times larger than those of previous work and did so for high-deflection shapes with more than 110° of curvature. We leveraged a data-driven learning approach for modeling, based on Koopman operator theory, and we introduce the concept of the static Koopman operator as a pregain term in optimal control. Our approach is rapid, requiring less than 5 min of training; is computationally low cost, requiring as little as 0.5 s to build the model; and is design agnostic, learning and accurately controlling two morphologically different soft robots. This work advances rapid modeling and control for soft robots from the realm of quasi-static to inertial, laying the groundwork for the next generation of compliant and highly dynamic robots.

Model-based linear control of nonlinear pneumatic soft bending actuators

“…For the PSBA system, the input u is the command pressure, and the output is the bending angle θ. Referring to previous studies [21,22], we employed random step and sinusoidal signals as inputs to adequately stimulate the fast and periodic dynamics of the system across its entire operational range. Given the open-loop bandwidth of the PSBA typically less than 1 Hz, we gathered 63 min of input and output data sampled at 20 Hz.…”

“…Fortunately, Koopman operator theory proves that high-fidelity global linearization can be realized by mapping the nonlinear dynamics to a high-dimensional Koopman space via proper lifting functions [17,18]. Recent work has attempted to use the Koopman operator to model and control robotic fish [19], soft arms [20][21][22], and wheeled mobile robots [23]. Unlike the analysis modeling, the Koopman modeling is data-driven and generic for PSBAs with customized materials and structures.…”

Visuo-dynamic self-modelling of soft robotic systems

“…Several static controllers that directly learn mappings from the task space coordinates to the actuator space have been proposed, with different strategies for learning the ill-defined inverse mapping ( Rolf, 2012 ; Giorelli et al, 2013 ; Giorelli et al, 2015 ; George et al, 2017 ). Similarly, task-space dynamic models can also be directly learned for open-loop control ( Thuruthel et al, 2017 ; Satheeshbabu et al, 2019 ) or closed-loop dynamic control ( George Thuruthel et al, 2018b ; Gillespie et al, 2018 ; Haggerty et al, 2023 ). Regardless of whether the approach is analytical or learning-based, and whether it focuses on static or dynamic modeling, all these techniques significantly reduce the complexity of the state-space to make modeling feasible.…”

Discrete-Time Impedance Control for Dynamic Response Regulation of Parallel Soft Robots

“…Soft robots, i.e., robots made from soft materials, have attained tremendous research attention in recent years [ 1 , 2 , 3 , 4 , 5 ]. They have shown great potential as a research platform as well as practical applications in industry [ 6 , 7 ] and healthcare [ 8 , 9 , 10 , 11 ].…”