TY - GEN
T1 - Nonlinear Modes as a Tool for Comparing the Mathematical Structure of Dynamic Models of Soft Robots
AU - Pustina, Pietro
AU - Calzolari, Davide
AU - Albu-Schaffer, Alin
AU - De Luca, Alessandro
AU - Santina, Cosimo Della
N1 - Publisher Copyright:
© 2024 IEEE.
PY - 2024
Y1 - 2024
N2 - Continuum soft robots are nonlinear mechanical systems with theoretically infinite degrees of freedom (DoFs) that exhibit complex behaviors. Achieving motor intelligence under dynamic conditions necessitates the development of control-oriented reduced-order models (ROMs), which employ as few DoFs as possible while still accurately capturing the core characteristics of the theoretically infinite-dimensional dynamics. However, there is no quantitative way to measure if the ROM of a soft robot has succeeded in this task. In other fields, like structural dynamics or flexible link robotics, linear normal modes are routinely used to this end. Yet, this theory is not applicable to soft robots due to their nonlinearities. In this work, we propose to use the recent nonlinear extension in modal theory -called eigenmanifolds- as a means to evaluate control-oriented models for soft robots and compare them. To achieve this, we propose three similarity metrics relying on the projection of the nonlinear modes of the system into a task space of interest. We use this approach to compare quantitatively, for the first time, ROMs of increasing order generated under the piecewise constant curvature (PCC) hypothesis with a high-dimensional finite element (FE)-like model of a soft arm. Results show that by increasing the order of the discretization, the eigenmanifolds of the PCC model converge to those of the FE model.
AB - Continuum soft robots are nonlinear mechanical systems with theoretically infinite degrees of freedom (DoFs) that exhibit complex behaviors. Achieving motor intelligence under dynamic conditions necessitates the development of control-oriented reduced-order models (ROMs), which employ as few DoFs as possible while still accurately capturing the core characteristics of the theoretically infinite-dimensional dynamics. However, there is no quantitative way to measure if the ROM of a soft robot has succeeded in this task. In other fields, like structural dynamics or flexible link robotics, linear normal modes are routinely used to this end. Yet, this theory is not applicable to soft robots due to their nonlinearities. In this work, we propose to use the recent nonlinear extension in modal theory -called eigenmanifolds- as a means to evaluate control-oriented models for soft robots and compare them. To achieve this, we propose three similarity metrics relying on the projection of the nonlinear modes of the system into a task space of interest. We use this approach to compare quantitatively, for the first time, ROMs of increasing order generated under the piecewise constant curvature (PCC) hypothesis with a high-dimensional finite element (FE)-like model of a soft arm. Results show that by increasing the order of the discretization, the eigenmanifolds of the PCC model converge to those of the FE model.
UR - http://www.scopus.com/inward/record.url?scp=85193809885&partnerID=8YFLogxK
U2 - 10.1109/RoboSoft60065.2024.10521987
DO - 10.1109/RoboSoft60065.2024.10521987
M3 - Conference contribution
AN - SCOPUS:85193809885
T3 - 2024 IEEE 7th International Conference on Soft Robotics, RoboSoft 2024
SP - 779
EP - 785
BT - 2024 IEEE 7th International Conference on Soft Robotics, RoboSoft 2024
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 7th IEEE International Conference on Soft Robotics, RoboSoft 2024
Y2 - 14 April 2024 through 17 April 2024
ER -