An Experimental Validation of the Polynomial Curvature Model: Identification and Optimal Control of a Soft Underwater Tentacle

Abstract

The control possibilities for soft robots have long been hindered by the lack of accurate yet computationally treatable dynamic models of soft structures. Polynomial curvature models propose a solution to this quest for continuum slender structures. Nevertheless, the results produced with this class of models have been so far essentially theoretical. With the present work, we aim to provide a much-needed experimental validation to these recent theories. To this end, we focus on soft tentacles immersed in water. First, we propose an extension of the affine curvature model to underwater structures, considering the drag forces arising from the fluid-solid interaction. Then, we extensively test the model's capability to describe the system behavior across several shapes and working conditions. Finally, we validate model-based control policies, proposing and solving an optimal control problem for directional underwater swimming. Using the model we show an average increase of more than 3.5 times the swimming speed of a sinusoidal baseline controller, with some tentacles showing an improvement in excess of 5.5 times the baseline.

The science of soft robot design: A review of motivations, methods and enabling technologies

“…Finally, in simulation the structure morphology and control strategy is optimized, and brought back to reality. Thanks to the generality of the learnt model, the simulation can be used to optimize both the morphology and the control policy of the system ( Stella et al, 2022 ). In the middle row, the robot is automatically manufactured, thanks to multi-material 3D printing, 4D printing or other automatic manufacturing technologies.…”

“…To leverage the advantages of simulation ( Milana et al, 2021 ) whilst reducing the challenge of translating simulation to reality, we can instead start from reality, utilize system identification or other methods to capture the design space before returning to reality. Examples of this approach include using computer vision to extract the behavior of soft tentacles robot to generate a model which include information on the soft structure in the context of the environment, before controller optimization can be performed and then transferred back to reality ( Stella et al, 2022 ). Iterative approaches of cycles or real-sim-real have also shown potential ( Du et al, 2021 ).…”

Learning 3D shape proprioception for continuum soft robots with multiple magnetic sensors

“…To demonstrate the efficacy of the proposed method for higherorder kinematic models than PCC, we also conduct simulations of an affine curvature soft robot. The affine curvature kinematic parametrization 24 has been shown capable of representing the shape of soft tentacles 25,29 and provides a continuous function κ = κ 0 + κ 1 v to describe the curvature of the soft robot, where κ 0 , κ 1 are two configuration variables and v ∈ [0, 1] is the backbone coordinate. We allow for movement in 3D space by also specifying an azimuth bending angle φ and the elongation δ L. Please refer to Appendix A.2 for more implementation details about the affine curvature model.…”

“…Note, however, that the proposed proprioception algorithm applies to any finite-dimensional kinematic description of a soft robot. 5 In fact, we also specifically consider a robot with affine curvature 24,25 with its shape described by the configuration . We document this alternative kinematic model in Appendix A.2.…”

“…The affine curvature hypothesis 24,25 models the bending of the soft segment to be conforming to the affine function κ ( t , v ) = κ 0 ( t ) + κ 1 ( t ) v , where κ describes the local curvature of the backbone at the coordinate v ∈ [0,1] along the segment and κ 0 ( t ), κ 1 ( t ) are the zero-order and first-order term of the curvature polynomial respectively. 36 Specifically, we implement the recently proposed extension to 3D environments, 25 which specifies an azimuth angle of the bending direction ϕ ( t ) and additionally allows for an elongation δ L ( t ) of the segment. Accordingly, the configuration of the i th segment is described at any point in time byNow that the configuration space is defined, we aim to find a description of the forward kinematics.…”