We present a computational design system that assists users to model, optimize, and fabricate quad-robots with soft skins.Our system addresses the challenging task of predicting their physical behavior by fully integrating the multibody dynamics of the mechanical skeleton and the elastic behavior of the soft skin. The developed motion control strategy uses an alternating optimization scheme to avoid expensive full space time-optimization, interleaving space-time optimization for the skeleton and frame-by-frame optimization for the full dynamics. The output are motor torques to drive the robot to achieve a user prescribed motion trajectory.We also provide a collection of convenient engineering tools and empirical manufacturing guidance to support the fabrication of the designed quad-robot. We validate the feasibility of designs generated with our system through physics simulations and with a physically-fabricated prototype.
Our work is inspired by studies on how to drive the soft skin deformation with the underyling rigid skeletons or pseudo muscle force @cite_19 @cite_1 @cite_34 . Two-way coupling of rigid bodies and elastic bodies was considered in @cite_16 . Fast simulation and control of soft robots of various configurations and actuations has also been studied using finite element method and the reduced formulation of compliance matrix @cite_27 @cite_30 @cite_2 @cite_69 @cite_29 .
@cite_30 @cite_69 @cite_29 @cite_1 @cite_16 @cite_19 @cite_27 @cite_2 @cite_34
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Finite Element analysis can provide accurate deformable models for soft-robots. However, using such models is very difficult in a real-time system of control. In this paper, we introduce a generic solution that enables a high-rate control and that is compatible with strong real-time constraints. From a Finite Element analysis, computed at low rate, an inverse model of the robot outputs the setpoint values for the actuator in order to obtain a desired trajectory. This inverse problem uses a QP (quadratic-programming) algorithm based on the equations set by the Finite Element Method. To improve the update rate performances, we propose an asynchronous simulation framework that provides a better trade-off between the deformation accuracy and the computational burden. Complex computations such as accurate FEM deformations are done at low frequency while the control is performed at high frequency with strong real-time constraints. The two simulation loops (high frequency and low frequency loops) are mechanically coupled in order to guarantee mechanical accuracy of the system over time. Finally, the validity of the multi-rate simulation is discussed based on measurements of the evolution in the QP matrix and an experimental validation is conducted to validate the correctness of the high-rate inverse model on a real robot. The technological differences between traditional robotics and soft robotics have an impact on all of the modeling tools generally in use, including direct kinematics and inverse models, Jacobians, and dynamics. Due to the lack of precise modeling and control methods for soft robots, the promising concepts of using such design for complex applications (medicine, assistance, domestic robotics...) cannot be practically implemented. This paper presents a first unified software framework dedicated to modeling, simulation and control of soft robots. The framework relies on continuum mechanics for modeling the robotic parts and boundary conditions like actuators or contacts using a unified representation based on Lagrange multipliers. It enables the digital robot to be simulated in its environment using a direct model. The model can also be inverted online using an optimization-based method which allows to control the physical robots in the task space. To demonstrate the effectiveness of the approach, we present various soft robots scenarios including ones where the robot is interacting with its environment. The software has been built on top of SOFA, an open-source framework for deformable online simulation and is available at https: project.inria.fr softrobot Abstract This article presents a modeling methodology and experimental validation for soft manipulators to obtain forward kinematic model (FKM) and inverse kinematic model (IKM) under quasi-static conditions (in the literature, these manipulators are usually classified as continuum robots. However, their main characteristic of interest in this article is that they create motion by deformation, as opposed to the classical use of articulations). It offers a way to obtain the kinematic characteristics of this type of soft robots that is suitable for offline path planning and position control. The modeling methodology presented relies on continuum mechanics, which does not provide analytic solutions in the general case. Our approach proposes a real-time numerical integration strategy based on finite element method with a numerical optimization based on Lagrange multipliers to obtain FKM and IKM. To reduce the dimension of the problem, at each step, a projection of the model to the constraint space (gathering ... We propose a fast physically-based simulation system for skeleton-driven deformable body characters. Our system can generate realistic motions of self-propelled deformable body characters by considering the two-way interactions among the skeleton, the deformable body, and the environment in the dynamic simulation. It can also compute the passive jiggling behavior of a deformable body driven by a kinematic skelet al motion. We show that a well-coordinated combination of: (1) a reduced deformable body model with nonlinear finite elements, (2) a linear-time algorithm for skeleton dynamics, and (3) explicit integration can boost simulation speed to orders of magnitude faster than existing methods, while preserving modeling accuracy as much as possible. Parallel computation on the GPU has also been implemented to obtain an additional speedup for complicated characters. Detailed discussions of our engineering decisions for speed and accuracy of the simulation system are presented in the article. We tested our approach with a variety of skeleton-driven deformable body characters, and the tested characters were simulated in real time or near real time. We propose a framework for the full two-way coupling of rigid and deformable bodies, which is achieved with both a unified time integration scheme as well as individual two-way coupled algorithms at each point of that scheme. As our algorithm is two-way coupled in every fashion, we do not require ad hoc methods for dealing with stability issues or interleaving parts of the simulation. We maintain the ability to treat the key desirable aspects of rigid bodies (e.g. contact, collision, stacking, and friction) and deformable bodies (e.g. arbitrary constitutive models, thin shells, and self-collisions). In addition, our simulation framework supports more advanced features such as proportional derivative controlled articulation between rigid bodies. This not only allows for the robust simulation of a number of new phenomena, but also directly lends itself to the design of deformable creatures with proportional derivative controlled articulated rigid skeletons that interact in a life-like way with their environment. In this paper, we investigate the impact of the deformable bodies on the control algorithms for physically simulated characters. We hypothesize that ignoring the effect of deformable bodies at the site of contact negatively affects the control algorithms, leading to less robust and unnatural character motions. To verify the hypothesis, we introduce a compact representation for an articulated character with deformable soft tissue and develop a practical system to simulate two-way coupling between rigid and deformable bodies in a robust and efficient manner. We then apply a few simple and widely used control algorithms, such as pose-space tracking control, Cartesian-space tracking control, and a biped controller (SIMBICON), to simulate a variety of behaviors for both full-body locomotion and hand manipulation. We conduct a series of experiments to compare our results with the motion generated by these algorithms on a character comprising only rigid bodies. The evaluation shows that the character with soft contact can withstand larger perturbations in a more noisy environment, as well as produce more realistic motion. In this paper, we present a new method for the control of soft robots with elastic behavior, piloted by several actuators. The central contribution of this work is the use of the Finite Element Method (FEM), computed in real-time, in the control algorithm. The FEM based simulation computes the nonlinear deformations of the robots at interactive rates. The model is completed by Lagrange multipliers at the actuation zones and at the end-effector position. A reduced compliance matrix is built in order to deal with the necessary inversion of the model. Then, an iterative algorithm uses this compliance matrix to find the contribution of the actuators (force and or position) that will deform the structure so that the terminal end of the robot follows a given position. Additional constraints, like rigid or deformable obstacles, or the internal characteristics of the actuators are integrated in the control algorithm. We illustrate our method using simulated examples of both serial and parallel structures and we validate it on a real 3D soft robot made of silicone. This chapter presents new real-time and physics-based modeling methods dedicated to deformable soft robots. In this approach, continuum mechanics provides the partial derivative equations that govern the deformations, and Finite Element Method (FEM) is used to compute numerical solutions adapted to the robot. A formulation based on Lagrange Multipliers is used to model the behavior of the actuators as well as the contact with the environment. Direct and inverse kinematic models are also obtained for real-time control. Some experiments and numerical results are presented. We present a physically-based system to simulate and control the locomotion of soft body characters without skeletons. We use the finite element method to simulate the deformation of the soft body, and we instrument a character with muscle fibers to allow it to actively control its shape. To perform locomotion, we use a variety of intuitive controls such as moving a point on the character, specifying the center of mass or the angular momentum, and maintaining balance. These controllers yield an objective function that is passed to our optimization solver, which handles convex quadratic program with linear complementarity constraints. This solver determines the new muscle fiber lengths, and moreover it determines whether each point of contact should remain static, slide, or lift away from the floor. Our system can automatically find an appropriate combination of muscle contractions that enables a soft character to fulfill various locomotion tasks, including walking, jumping, crawling, rolling and balancing.