Abstract
The complex nature of soft robot dynamics calls for the development of models specifically tailored on the control application. In this letter, we take a first step in this direction by proposing a dynamic model for slender soft robots, taking into account the fully infinite-dimensional dynamical structure of the system. We also contextually introduce a strategy to approximate this model at any level of detail through a finite dimensional system. First, we analyze the main mathematical properties of this model in the case of lightweight and non lightweight soft robots. Then, we prove that using the constant term of curvature as control output produces a minimum phase system, in this way providing the theoretical support that existing curvature control techniques lack, and at the same time opening up to the use of advanced nonlinear control techniques. Finally, we propose a new controller, i.e., the PD-poly, which exploits information on high order deformations, to achieve zero steady state regulation error in presence of gravity and generic nonconstant curvature conditions.
Highlights
I N SOFT robots, the standard paradigm of stiff robotics is reverted by artificial bodies fully made of continuously deformable and compliant materials [1]
As already discussed in the introduction, the main aim of this model is to provide a framework for advance model based control in soft robots, both in terms of controller design and theoretical assessment of structural properties
Following the proof that controlling the constant approximation of q produces a well defined problem, we propose here a controller to achieve this goal with zero error at steady state
Summary
I N SOFT robots, the standard paradigm of stiff robotics is reverted by artificial bodies fully made of continuously deformable and compliant materials [1]. This design choice endows soft robots with several advantages, as being inherently safe in the interaction with humans and other animals, or the ability of squeezing within narrow spaces This comes at the price of making much harder the development of effective model based algorithms for managing these systems. An approach going in this direction is proposed in [11], [12], where the order of very high dimensional FEM discretization of the robot is reduction to achieve model based regulation While promising, this approach lacks of interpretability of the results, and so far of nonlinear formulations. We discuss the structural properties of this model and we apply it for developing a high orderrcuArvnateuwremreogduellaitnogr To conclude, this technique suited letter contributes with for control purposes, allowing for a formulation of the dynamics with any level r r of precision - up to infinity. SANTINA AND RUS: CONTROL ORIENTED MODELING OF SOFT ROBOTS: THE POLYNOMIAL CURVATURE CASE
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