Computational time savings in multiscale fracture mechanics using model order reduction

Engineering problems are very often characterised by a large ratio between the scale of the structure and the scale at which the phenomena of interest need to be described. In fracture mechanics, the initiation and propagation of cracks is the result of localised microscopic phenomena. This local nature of fracture leads to large numerical models. Projection-based reduced order modelling is an increasingly popular technique for the fast solution of parametrised problems. However, traditional model order reduction methods are unable to reliably deal with either the initiation or the propagation of a crack or a local zone with high damage concentration. In this thesis, we look at the general problem of applying model order reduction to fracture/ damage mechanics, in the pursuit of rationalising the computational time involved in these kind of simulations. The first contribution of this thesis is the development of a reduced-order modelling for computational homogenisation, which is a general multiscale method used to take microscopic data into account when deriving an engineeringscale model. A specific strategy is used to reduce the cost of solving the representative element volume (RVE) boundary value problem traditionally formulated in this method. The second contribution was made by developing a partitioned reduced-order procedure for the case of parametrised nonlinear material deformations involving a local lack of correlation, which typically happens with fracture. The method allows to reduce the regions undergoing little non-linearities whilst computational work can be concentrated on regions of high non-linearity

Direct and inverse modeling of soft robots by learning a condensed FEM model

The Finite Element Method (FEM) is a powerful modeling tool for predicting the behavior of soft robots. However, its use for control can be difficult for non-specialists of numerical computation: it requires an optimization of the computation to make it real-time. In this paper, we propose a learning-based approach to obtain a compact but sufficiently rich mechanical representation. Our choice is based on nonlinear compliance data in the actuator/effector space provided by a condensation of the FEM model. We demonstrate that this compact model can be learned with a reasonable amount of data and, at the same time, be very efficient in terms of modeling, since we can deduce the direct and inverse kinematics of the robot. We also show how to couple some models learned individually in particular on an example of a gripper composed of two soft fingers. Other results are shown by comparing the inverse model derived from the full FEM model and the one from the compact learned version. This work opens new perspectives, namely for the embedded control of soft robots, but also for their design. These perspectives are also discussed in the paper

Projection-based model order reduction for real-time control of soft robots

International audienceSoft Robotics is a new field of robotics that deals with robots whose movements rely on the deformation of soft materials, such as silicone, rather than articulated rigid bodies in " traditional " robotics. Their design is often bio-inspired. Though having a great potential (for example in surgical applications, exploration of cavities, manipulation of fragile objects, etc…), one great challenge lies in their control since they are fundamentally equipped with a theoretically infinite number of degrees of freedom. Some works already proposed their control using a real-time finite element method [1]. The approach was limited by the real-time constraint which forced the use of relatively coarse meshes. This was good enough for a simple application with a unique effector. However, when considering complex geometries, more actuators and several effectors, finer meshes may be necessary, which would not be tractable in real-time. In this contribution, we attempt to perform real-time realistic simulation of the deformations of the soft robotics structures to achieve the real-time constraint with a converged mesh, meaning fine enough so that further refinement does not modify the result of the simulation. To this purpose, we use the snapshot-proper orthogonal decomposition (snapshot-POD), associated with an energy-conserving sampling and weighting (ECSW) method [2] to keep computational efficiency by only computing mechanical properties on a small subset of the finite elements. The parameter space explored in the offline stage is dictated by the range of the actuators of the soft-robot considered, as well as the possible contacts the robot may encounter. We show that we are able to achieve the real-time constraint with fine meshes. In further developments, if many actuators are involved, a specific sampling method based on Bayesian optimisation may be used to create the snapshot [3]. The main difficulty will lie on the fact that when the robot enters in contact with its environment, it may endure local deformations not captured by the reduced space. In this case, a partitioning strategy may be necessary [4], to allow for the computation of the local deformations with a full FEM model

Fast, generic and reliable control and simulation of soft robots using model order reduction

International audienceObtaining 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, hyperre-duction 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

On efficient black box optimization of systems defined by 100 or more parameters

In product development, the optimization of hectovariate systems (that is, depending on more than a hundred variables) is hard to handle with usual black box methods, since they require a huge number of experiments. That is an issue since each experiment can be both expensive and time-consuming. Furthermore, these methods can't even handle such big problems within a reasonable period of time. The Lean optimization algorithm [1] was one approach to overcome these difficulties. In this paper, we will come up with a new lean algorithm, inspired from [1] and developing new ideas. It will then be tested on some classical mathematical problems of various sizes and a practical example of combustion simulation engine issued from Volvo Technology. We will see that this new algorithm has a faster and more robust convergence, and is able to significantly improve most systems within a number of experiments less than the number of variables

An Open Source Design Optimization Toolbox Evaluated on a Soft Finger

In this paper, we introduce a novel open source toolbox for design optimization in Soft Robotics. We consider that design optimization is an important trend in Soft Robotics that is changing the way in which designs will be shared and adopted. We evaluate this toolbox on the example of a cable-driven, sensorized soft finger. For devices like these, that feature both actuation and sensing, the need for multi-objective optimization capabilities naturally arises, because at the very least, a trade-off between these two aspects has to be found. Thus, multi-objective optimization capability is one of the central features of the proposed toolbox. We evaluate the optimization of the soft finger and show that extreme points of the optimization trade-off between sensing and actuation are indeed far apart on actually fabricated devices for the established metrics. Furthermore, we provide an in depth analysis of the sim-to-real behavior of the example, taking into account factors such as the mesh density in the simulation, mechanical parameters and fabrication tolerances

Real-Time Simulation For Control Of Soft Robots With Self-Collisions Using Model Order Reduction For Contact Forces

International audienceIn rigid robotics, self-collision are usually avoided since it leads to a failure in the robot control and can also cause damage. In soft robotics, the situation is very different, and self-collisions may even be a desirable property, for example to gain artificial stiffness or to provide a natural limitation to the workspace. However, the modeling and simulation of self-collision is very costly as it requires first a collision detection algorithm to detect where collisions occur, and most importantly, it requires solving a constrained problem to avoid interpenetrations. When the number of contact points is large, this computation slows down the simulation dramatically. In this paper, we apply a numerical method to alleviate the contact response computation by reducing the contact space in a lowdimensional positive space obtained from experiments. We show good accuracy while speeding up dramatically the simulation. We apply the method in simulation on a cable-actuated finger and on a continuum manipulator performing exploration. We also show that the reduced contact method proposed can be used for inverse modeling. The method can therefore be used for control or design

Enabling the control of a new degree of freedom by using anisotropic material on a 6-DOF parallel soft robot

International audienceIn this paper, we design in simulation and build a parallel soft robot with a 6 degrees of freedom (DOF) endeffector. We show that by using a 3D-printed meso-structured material which displays an anisotropic behaviour, we can modify the kinematics of the structure in order to control one additional DOF which is not possible to achieve using a standard isotropic and homogeneous material like silicone. The behaviour of the robot is simulated using numerical homogenization and the finite element method (FEM), which runs in real-time and can be used for control. We finally show that the parallel soft robot we have built is controllable in open loop thanks to the use of inverse simulation. We demonstrate its maneuverability by guiding a marble in a maze game