Kinematic Controller of a Soft Continuum Robot Using Learned Forward Models

Continuum robots play the role of end effectors in various surgical robots and endoscopic devices. While soft continuum robots (SCRs) have proven advantages such as safety and compliance, more research and development are required to enhance their capability for specific medical scenarios. This research aims at designing a soft robot, considering the concepts of geometric and kinematic similarities. The chosen application is a semi-invasive medical application known as transesophageal echocardiography (TEE). The feasibility of fabrication of a soft endoscopic device derived from the Chorda dorsalis paragon was shown empirically by producing a three-segment pneumatic SCR. The main novelties include bioinspired design, modeling, and a navigation control strategy presented as a novel algorithm to maintain a kinematic similarity between the soft robot and the rigid counterpart. The kinematic model was derived based on the method of transformation matrices, and an algorithm based on a self-organizing map (SOM) network was developed and applied to realize kinematic similarity. The simulation results indicate that the control method forces the soft robot tip to follow the path of the rigid probe within the prescribed distance error (5 mm). The solution provides a soft robot that can surrogate and succeed the traditional rigid counterpart owing to size, workspace, and kinematics.

Soft robots are increasingly being explored and developed in various settings that demand safe and adaptable interactions between robots and their environments. In addition, soft robots exhibit passive compliant behavior and generate continuous deformations when engaging with the environment. This imposes challenges on achieving active, on-demand interaction force control, especially when feedback force-sensing devices are not available. Consequently, there is a need to explore new model-based force control paradigms for soft robots. In this article, we propose a (quasi-)static force control approach for soft robots based on compliance modeling, avoiding the necessity for feedback control loops or extensive training data collection. The proposed approach can deliver contact force control along three Cartesian axes when the robot is actuated into various configurations. The compliance matrix is derived from the robot configuration, which allows the calculation of desired deflection displacements needed to generate on-demand forces. The resulting force control is achieved by solving inverse kinematics problems based on these deflection displacements. The efficacy of our proposed controller is validated through experiments with both one- and two-segment pneumatic-driven soft continuum robots. The results demonstrate effective static force control performance, with mean control errors below 5% of the desired peak forces.

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 have been attracting much research attention in the past decades owing to their unique properties that are inherently different from conventional rigid robots. The intrinsic characteristics of soft robots, such as compliance and flexibility, have made them a promising supplement for many existing robotic applications. For instance, soft robots provide safer human-machine interaction and better adaptability to unexplored environments than the conventional rigid ones. However, their “soft” feature would conversely cause complex material deformation due to their high-DoF nature, which has made their kinematic or dynamic models more difficult to deduce. Logically, the process of designing model-based controllers would therefore suffer from the lack of efficient and accurate modeling methods. In this letter, through adopting Finite Element Method (FEM), we demonstrate a FEM-based nonlinear control method for a soft trunk robot to achieve trajectory tracking objectives. The proposed controller is developed by utilizing the essential information from the dynamic FE model of the studied robot. The details of deriving this nonlinear control method are demonstrated, then followed by 4 practical experiments on the soft truck robot to verify the feasibility of the control method. The corresponding experimental results are presented accordingly.

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.

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.

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 robotics technology can aid in achieving United Nations’ Sustainable Development Goals (SDGs) and the Paris Climate Agreement through development of autonomous, environmentally responsible machines powered by renewable energy. By utilizing soft robotics, we can mitigate the detrimental effects of climate change on human society and the natural world through fostering adaptation, restoration, and remediation. Moreover, the implementation of soft robotics can lead to groundbreaking discoveries in material science, biology, control systems, energy efficiency, and sustainable manufacturing processes. However, to achieve these goals, we need further improvements in understanding biological principles at the basis of embodied and physical intelligence, environment-friendly materials, and energy-saving strategies to design and manufacture self-piloting and field-ready soft robots. This paper provides insights on how soft robotics can address the pressing issue of environmental sustainability. Sustainable manufacturing of soft robots at a large scale, exploring the potential of biodegradable and bioinspired materials, and integrating onboard renewable energy sources to promote autonomy and intelligence are some of the urgent challenges of this field that we discuss in this paper. Specifically, we will present field-ready soft robots that address targeted productive applications in urban farming, healthcare, land and ocean preservation, disaster remediation, and clean and affordable energy, thus supporting some of the SDGs. By embracing soft robotics as a solution, we can concretely support economic growth and sustainable industry, drive solutions for environment protection and clean energy, and improve overall health and well-being.

Untethered small-scale soft robots have promising applications in minimally invasive surgery, targeted drug delivery, and bioengineering applications as they can access confined spaces in the human body. However, due to highly nonlinear soft continuum deformation kinematics, inherent stochastic variability during fabrication at the small scale, and lack of accurate models, the conventional control methods cannot be easily applied. Adaptivity of robot control is additionally crucial for medical operations, as operation environments show large variability, and robot materials may degrade or change over time, which would have deteriorating effects on the robot motion and task performance. Therefore, we propose using a probabilistic learning approach for millimeter-scale magnetic walking soft robots using Bayesian optimization (BO) and Gaussian processes (GPs). Our approach provides a data-efficient learning scheme to find controller parameters while optimizing the stride length performance of the walking soft millirobot robot within a small number of physical experiments. We demonstrate adaptation to fabrication variabilities in three different robots and to walking surfaces with different roughness. We also show an improvement in the learning performance by transferring the learning results of one robot to the others as prior information.

This paper proposes a novel decentralized approach to kinematic control of soft segmented continuum robots based on a consensus strategy. The robots under consideration deform in a plane according to a multi-segment Piecewise Constant Curvature (PCC) kinematic model in which each segment is represented as an equivalent rigid-link Revolute-Prismatic-Revolute (RPR) mechanism. In our approach, we assume that each segment of the robot is equipped with sensors to measure joint variables in its local coordinate frame and can communicate with its two adjacent segments. Our consensus-based decentralized control strategy provides an alternative to conventional control methods, which solve the inverse kinematic problem by using computationally intensive numerical methods to calculate the robot's Jacobian matrix at each time instant. We investigate the stability and convergence properties of proposed controllers for position regulation and trajectory tracking tasks and provide theoretical guarantees on the controllers' performance. We evaluate the controllers in simulation for scenarios in which the robot's tip must reach a certain position or follow a specified trajectory. We compare the performance of the position regulator for different controller gains, and we find that a simulated 15-link robot can track a complex reference trajectory with an average root-mean-square error of only 0.16% of the robot's initial length.

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.

Energy in Robotics: An Interdisciplinary Challenge

Current challenges in soft robotics include sensing and state awareness. Modern soft robotic systems require many more sensors than traditional robots to estimate pose and contact forces. Existing soft sensors include resistive, conductive, optical, and capacitive sensing, with each sensor requiring electronic circuitry and connection to a dedicated line to a data acquisition system, creating a rapidly increasing burden as the number of sensors increases. We demonstrate a network of fiber-based displacement sensors to measure robot state (bend, twist, elongation) and two microfluidic pressure sensors to measure overall and local pressures. These passive sensors transmit information from a soft robot to a nearby display assembly, where a digital camera records displacement and pressure data. We present a configuration in which one camera tracks 11 sensors consisting of nine fiber-based displacement sensors and two microfluidic pressure sensors, eliminating the need for an array of electronic sensors throughout the robot. Finally, we present a Cephalopod-chromatophore-inspired color cell pressure sensor. While these techniques can be used in a variety of soft robot devices, we present fiber and fluid sensing on an elastomeric finger. These techniques are widely suitable for state estimation in the soft robotics field and will allow future progress toward robust, low-cost, real-time control of soft robots. This increased state awareness is necessary for robots to interact with humans, potentially the greatest benefit of the emerging soft robotics field.

Model-based strategies are a promising solution to the grand challenge of equipping continuum soft robots with motor intelligence. However, finite-dimensional models of these systems are inherently inaccurate, thus posing pressing robustness concerns. Moreover, the actuation space of soft robots is usually limited. This article aims at solving both these challenges by proposing a robust model-based strategy for the shape control of soft robots with system uncertainty and input saturation. The proposed architecture is composed of two key components. First, we propose an observer that estimates deviations between the theoretical model and the soft robot, ensuring that the estimation error converges to zero within finite time. Second, we introduce a sliding mode controller to regulate the soft robot shape while fulfilling saturation constraints. This controller uses the observer's output to compensate for the deviations between the real system and the established model. We prove the convergence of the closed-loop with theoretical analysis and the method's effectiveness with simulations and experiments.

Soft robots are known for their ability to perform tasks with great adaptability, enabled by their distributed, non-uniform stiffness and actuation. Bending is the most fundamental motion for soft robot design, but creating robust, and easy-to-fabricate soft bending joint with tunable properties remains an active problem of research. In this work, we demonstrate an inflatable actuation module for soft robots with a defined bending plane enabled by forced partial wrinkling. This lowers the structural stiffness in the bending direction, with the final stiffness easily designed by the ratio of wrinkled and unwrinkled regions. We show the stiffness properties of the actuation module through a first-principle model validated by experimental characterization, and demonstrate the module's ability to maintain the kinematic constraint over a large range of loading conditions. We illustrate how these properties give the potential for complex actuation in a soft continuum robot and for decoupling actuation force and efficiency from load capacity. The module provides a novel method for embedding intelligent actuation into soft pneumatic robots.