Dynamic simulation of articulated soft robots

Soft robots have recently drawn extensive attention thanks to their unique ability of adapting to complicated environments. Soft robots are designed in a variety of shapes of aiming for many different applications. However, accurate modelling and control of soft robots is still an open problem due to the complex robot structure and uncertain interaction with the environment. In fact, there is no unified framework for the modeling and control of generic soft robots. In this paper, we present a novel data-driven machine learning method for modeling a cable-driven soft robot. This machine learning algorithm, named deterministic learning (DL), uses soft robot motion data to train a radial basis function neural network (RBFNN). The soft robot motion dynamics are then guaranteed to be accurately identified, represented, and stored as an RBFNN model with converged constant neural network weights. To validate our method, We have built a simulated soft robot almost identical to our real inchworm soft robot, and we have tested the DL algorithm in simulation. Furthermore, a neural network weight combining technique is used which can extract and combine useful dynamics information from multiple robot motion trajectories.

Soft robots have been intensively investigated for manipulation and locomotion in recent years. However, the current state of soft robotics has significant design and development work but lags in modeling and control due to the difficulty in modeling them. In this paper, we present a physics-based analytical framework to model soft robots driven by Twisted-and-Coiled Actuators (TCAs), an artificial muscle that can be arranged in arbitrary shapes in the soft body of a soft robot to achieve programmable motions. The framework can model 1) the complicated routes of multiple TCAs in a soft body and 2) the coupling effect between the soft body and the TCAs during their actuation process. When not actuated, a TCA in the soft body is an antagonistic elastic element that restrains the magnitude of the motion and increases the stiffness of the robot. By stacking several modules together, we simulate the sequential motion of a soft robotic arm with three-dimensional bending, twisting, and grasping motion. The presented modeling and simulation approach will facilitate the design, optimization, and control of soft robots driven by TCAs or other types of artificial muscles.

Soft continuum robots are more and more used in various applications due to the multiple advantages offered by the properties of hyper-elastic soft materials, such as resilience, flexibility, etc. Despite all these essential properties that make the soft robots good candidates for some real-life needs (form enclosure grasping, obstacle-free navigation, etc.), controlling their shape remains challenging because of their hyper-redundancies. This letter investigates an inverse dynamics model-based shape control of soft continuum robots in the presence and absence of external efforts. To that end, modeling based on Pythagorean Hodograph (PH) curves with prescribed lengths is combined with Euler-Bernoulli modeling to reconstruct the robot shapes and then calculate the actuator inputs in the case of external efforts. Thus, a relationship between the actuator inputs and the PH control points is obtained. With the above strategy, the actuator inputs can be computed accordingly, and therefore, real-time shape control of the soft robots for various tasks becomes possible. The results of the proposed approach are validated both numerically and experimentally using two classes of soft continuum robots - a Fluidic Elastomeric Actuator (FEA), describing a 2D soft finger robot, with a single and multiple phalanges, and a 3D continuum manipulator, namely the Compact Bionic Handling Assistant (CBHA).

Soft robots made from soft materials can safely interact with humans and environments compared with the traditional rigid robots. However, the inherent compliance of the soft robots makes them difficult to realize the jumping motion. Although many soft robots can jump through the design of bistable structure. However, the existing soft robots need rigid spine to be embedded in the soft body. Therefore, it is still hard for the jumping of a soft robot with pure soft body. This paper offers the design method for the pure soft bistable robot with jumping ability. The critical buckling force and total elastic potential energy of the robot can be increased by designing the soft body with different thickness. We use the twisted artificial muscle (TAM) to realize the jumping motion of the soft bistable robot. The proposed robot can jump at a height nearly two times its body height. We envision that the design method will promote the application of the soft robot with pure soft body to realize more types of motion strategy.

Soft robots demonstrate superior flexibility and maneuverability than traditional rigid robots in many emerging applications. However, it is challenging to have a general modeling and control methodology to deal with soft body dynamics and its interactions with environment. We present a spline-based modeling and control framework for soft robotic systems. The dynamic model is built on non-uniform rational Bsplines (NURBS) that captures material and physical properties of soft body, while preserving exact geometric dynamics with environmental interactions. Using the NURBS-based dynamic model, the robotic optimal control based on general predictive control is designed through coordination among the finite number of control points. Therefore, the infinite-dimensional motion of soft body can be realized by significantly reduced finite particle motion control. We demonstrate the performance of the modeling and motion control framework using the snakeinspired robot simulations and experiments.

<p>Soft robots have become important members of the robot community with many potential applications owing to their unique flexibility and security embedded at the material level. An increasing number of researchers are interested in their designing, manufacturing, modeling, and control. However, the dynamic simulation of soft robots is difficult owing to their infinite degrees of freedom and nonlinear characteristics that are associated with soft materials and flexible geometric structures. In this study, a novel multi-flexible body dynamic modeling and simulation technique is introduced for soft robots. Various actuators for soft robots are modeled in a virtual environment, including soft cable-driven, spring actuation, and pneumatic driving. A pneumatic driving simulation was demonstrated by the bending modules with different materials. A cable-driven soft robot arm prototype and a cylindrical soft module actuated by shape memory alley springs inspired by an octopus were manufactured and used to validate the simulation model, and the experimental results demonstrated adequate accuracy. The proposed technique can be widely applied for the modeling and dynamic simulation of other soft robots, including hybrid actuated robots and rigid-flexible coupling robots. This study also provides a fundamental framework for simulating soft mobile robots and soft manipulators in contact with the environment.</p> <p> </p>

Simulating soft robots offers a cost-effective approach to exploring their design and control strategies. While current models, such as finite element analysis, are effective in capturing soft robotic dynamics, the field still requires a broadly applicable and efficient numerical simulation method. In this letter, we introduce a discrete differential geometry-based framework for the model-based inverse design of a novel snap-actuated jumping robot. Our findings reveal that the snapping beam actuator exhibits both symmetric and asymmetric dynamic modes, enabling tunable robot trajectories (e.g., horizontal or vertical jumps). Leveraging this bistable beam as a robotic actuator, we propose a physics-data hybrid inverse design strategy to endow the snap-jump robot with a diverse range of jumping capabilities. By utilizing a physical engine to examine the effects of design parameters on jump dynamics, we then use extensive simulation data to establish a data-driven inverse design solution. This approach allows rapid exploration of parameter spaces to achieve targeted jump trajectories, providing a robust foundation for the robot's fabrication. Our methodology offers a powerful framework for advancing the design and control of soft robots through integrated simulation and data-driven techniques.

The impressive capabilities of living organisms arise from the way autonomy is materialized by their bodies. Across scales, living beings couple computational or cognitive intelligence with physical intelligence through body morphology, material multifunctionality, and mechanical compliance. While soft robotics has advanced the design and fabrication of physically intelligent bodies, the integration of information‐processing capabilities for computational intelligence remains a challenge. Consequently, perception and control limitations have constrained how soft robots are built today. Progress toward untethered autonomy will require deliberate convergence in how the field codevelops new materials, fabrication methods, and control strategies for soft robots. Here, a new perspective is put forward: that researchers should use tasks alone to impose material and information constraints on soft robot design. A conceptual framework is proposed for a task‐first design paradigm that sidesteps limitations imposed by control strategies. This framework allows emergent synergies between material and information processing properties of soft matter to be readily exploited for task‐capable agents. Particular attention is paid to the scale dependence of solutions. Finally, an outlook is presented on emerging research opportunities for achieving autonomy in future soft robots as large as elephant trunks and as small as paramecia.

This research investigates designing a continuum soft robot and proposing a kinematic matching control to enable the robot to perform a specified medical task, which in this paper is the transesophageal echocardiography (TEE). A multi-chamber soft robot was designed and fabricated based on the molding of separate layers. The method of transformation matrices was used to develop the kinematic models, and a control method using Jacobian matrices was proposed to manipulate the robot. A prototype was made based on a multi-chamber multi-layer design. The system contains three segments that can be actuated independently to mimic the active bending part of the respective probe. Kinematic models were developed. Negative pressure (vacuum) was used as actuation input. An open-loop controller inspired by a redundancy resolution technique was proposed to make the soft robot tip follow the desired path, i.e.the path of the rigid ultrasound probe. It is concluded that the soft solution can perform the required task as the reachable points of the TEEtip cover the proposed robot workspace and the proposed control can be used for maneuvering in arbitrary trajectories.

Earthworms have entirely soft bodies mainly composed of circular and longitudinal muscle bundles but can handle the complexity of unstructured environments with exceptional multifunctionality. Soft robots are naturally appropriate for mimicking soft animal structures thanks to their inherent compliance. Here, we explore the new possibility of using this compliance to coordinate the actuation movements of single-type soft actuators for not only high adaptability but the simultaneous multifunctionality of soft robots. A cross-linked actuator coordination mechanism is proposed and explained with a novel conceptual design of a cross-linked network, characterization of modular coordinated kinematics, and a modular control strategy for multiple functions. We model and analyze the motion patterns for these functions, including grabbing, manipulation, and locomotion. This further enables the combination of simultaneous multi-functions with this very simple actuator network structure. In this way, a soft modular robot is developed with demonstrations of a novel continuous-transportation mode, for which multiple objects could be simultaneously transported in unstructured environments with either mobile manipulation or pick-and-place operation. A comprehensive workflow is presented to elaborate the cross-linked actuator coordination concept, analytical modeling, modular control strategy, experimental validation, and multi-functional applications. Our understanding of actuator coordination inspires new soft robotic designs for wider robotic applications.

SummaryA design and manufacturing method is described for creating a motor tendon–actuated soft foam robot. The method uses a castable, light, and easily compressible open-cell polyurethane foam, producing a structure capable of large (~70% strain) deformations while requiring low torques to operate (<0.2 N·m). The soft robot can change shape, by compressing and folding, allowing for complex locomotion with only two actuators. Achievable motions include forward locomotion at 13 mm/s (4.3% of body length per second), turning at 9◦/s, and end-over-end flipping. Hard components, such as motors, are loosely sutured into cavities after molding. This reduces unwanted stiffening of the soft body. This work is the first demonstration of a soft open-cell foam robot locomoting with motor tendon actuators. The manufacturing method is rapid (~30 min per mold), inexpensive (under $3 per robot for the structural foam), and flexible, and will allow a variety of soft foam robotic devices to be produced.

The imitation of the functions of soft animals has always been the goal of soft robotic design. However, most of the current soft terrestrial robots just imitate the basic gaits and are difficult to perform in three dimensional space. In this work, we present an inchworm-inspired soft robot that integrates the locomotion and manipulation functions together. The soft robot is able to move in the vertical plane from one pole to another or work as a soft manipulator. The two functions can switch between each other naturally. Besides, the soft robot is unfettered by gravity, which greatly expands the applications of the soft robot. The deformation and load capacities of the soft components were tested, and to enhance the stiffness of the whole soft robot, the rigid-frame reinforcement was used. The performance of the soft robot shows great potential of actual applications, such as spatial maintenance and agricultural picking. Most importantly, the combination of the locomotion and manipulation functions provides a new idea for designing more applicable soft robots.

Multimodal sensing using soft body dynamics plays a crucial role in controlling soft robotic motions. An intriguing application of such soft robot control is to mimic whiskers and digitize soft body motion through whisker dynamics. The challenge herein is to simultaneously monitor the directions, speed, force, and slip information of the whisker motion. The existing whisker-like sensors cannot detect slip information effectively. To address this challenge, this study develops a multitasking electronic brush (e-brush) composed of bundle of whiskers powered by reservoir computing (RC). Four pressure sensors are integrated into the brush to monitor its motion, speed, force, slip, and target surface. These sensors can provide long-term, low-pressure detection as low as 50 pascals, allowing for the precise monitoring of brush movements. A RC algorithm is developed to extract multiple brush motion parameters, including the slip. As a proof of concept for multitasking e-brush, the motion trajectory of handwriting is successfully detected.

Dynamic locomotion of a quadruped robot emerges from interaction between the robot body and the terrain. When the robot has a soft body, dynamic locomotion can be realized using a simple controller. This study investigates dynamic turning of a soft quadruped robot by changing the phase difference among the legs of the robot. We develop a soft quadruped robot driven by McKibben pneumatic artificial muscles. The phase difference between the hind and fore legs is fixed whereas that between the left and right legs is changed to enable the robot to turn dynamically. Since the robot legs are soft, the contact pattern between the legs and the terrain can be varied adaptively by simply changing the phase difference. Experimental results demonstrate that changes in the phase difference lead to changes in the contact time of the hind legs, and as a result, the soft robot can turn dynamically.

Soft robots are compliant and durable, and thus potentially better-suited for swimming or crawling over rough terrain than conventional rigid robots. Biomimetic locomotion strategies are often implemented on soft robots, but are difficult to tune because of the complexity of mapping nonlinear mechanical systems to specific gait patterns. We propose an approach to soft robot control in which the robot is designed to physically realize a shape space (mechanically predefined body poses) to follow a theoretically optimal gait. Specifically in this paper we present an entirely soft snake robot designed to implement the prerequisite shape space for slithering gaits. When coupled with a geometric mechanics model relating serpentine shape sequences to displacement, appropriate gait patterns can be selected analytically based on the system's Lie bracket. We developed a modular, two-link soft robot and used the geometric mechanics model to identify several cyclic gait patterns for producing forward displacement. The gait patterns were tested on the soft robot and observed with a motion capture system to measure displacement and monitor shape sequences. Relative performance of the gait patterns is consistent with the geometric “soap-bubble method” as a heuristic for gait optimization, which demonstrates the applicability of this approach to soft robot control and coordination.