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Compared with traditional rigid-body robots, soft robots not only exhibitunprecedented adaptation and flexibility but also present novel challenges intheir modeling and control because of their infinite degrees of freedom. Mostof the existing approaches have mainly relied on approximated models so thatthe well-developed finite-dimensional control theory can be exploited. However,this may bring in modeling uncertainty and performance degradation. Hence, wepropose to exploit infinite-dimensional analysis for soft robotic systems. Ourcontrol design is based on the increasingly adopted Cosserat rod model, whichdescribes the kinematics and dynamics of soft robotic arms using nonlinearpartial differential equations (PDE). We design infinite-dimensional statefeedback control laws for the Cosserat PDE model to achieve trajectory tracking(consisting of position, rotation, linear and angular velocities) and provetheir uniform tracking convergence. We also design an infinite-dimensionalextended Kalman filter on Lie groups for the PDE system to estimate all thestate variables (including position, rotation, strains, curvature, linear andangular velocities) using only position measurements. The proposed algorithmsare evaluated using simulations.

PDE-based Dynamic Control and Estimation of Soft Robotic Arms