Fast, Generic, and Reliable Control and Simulation of Soft Robots Using Model Order Reduction

Abstract

Obtaining an accurate mechanical model of a soft deformable robot compatible with the computation time imposed by robotic applications is often considered as an unattainable goal. This paper should invert this idea. The proposed methodology offers the possibility to dramatically reduce the size and the online computation time of a Finite Element Model (FEM) of a soft robot. After a set of expensive offline simulations based on the whole model, we apply snapshot-proper orthogonal decomposition to sharply reduce the number of state variables of the soft robot model. To keep the computational efficiency, hyperreduction is used to perform the integration on a reduced domain. The method allows to tune the error during the two main steps of complexity reduction. The method handles external loads (contact, friction, gravity...) with precision as long as they are tested during the offline simulations. The method is validated on two very different examples of FE models of soft robots and on one real soft robot. It enables acceleration factors of more than 100, while saving accuracy, in particular compared to coarsely meshed FE models and provides a generic way to control soft robots.

Soft robots locomotion and manipulation control using FEM simulation and quadratic programming

“…If the number of DoFs and/or contacts is high, the computation of the matrix W may take time. To reduce this computation time we can use methods based on model order reduction [24]. Yet, for the examples given in this paper, the use of GPU was satisfactory enough.…”

Reduced Order Model Predictive Control For Setpoint Tracking

“…where δx f = x f − x f ∞ , δu = u − u ∞ , and P , Q, and R are positive definite cost matrices. The values of x f ∞ and u ∞ are given by a solution to the linear system (4). The terminal set, X f , along with the terminal cost P , are designed to provide stability properties to the algorithm.…”

“…Infinite-dimensional systems, commonly characterized by partial differential equations, arise in many realworld robotic applications. Examples include soft robotics [4], flexible structures and robotic manipulators [5], and autonomous systems with coupled fluid/rigid-body dynamics due to aerodynamics [6] or fluid sloshing [7].…”

Simulation of hyperelastic materials in real-time using deep learning

“…Thus, to keep the method numerically efficient in the case of non linear materials, hyperreduction can be used in order to further reduce the computation times while reducing the error (Ryckelynck, 2005). Goury and Duriez (2018) applied the hyperreduced POD to control and simulate soft robots with very good accuracy in 25 ms per time step. However the POD may be in some cases insufficient to capture correctly the high degrees of non linearity that can be found for example in biological soft tissues as it relies on a linear combination of few basis vectors (Bhattacharjee and Matous, 2016).…”