Soft and continuum robots have unique advantages and capabilities useful in medical applications and confined environments due to their highly flexible structure. However, their underactuation and theoretically infinite degrees-of-freedom present significant challenges, particularly in control and state estimation. Prior work showed that a 2D discrete rod mechanics model, derived from the continuous partial differential equations of a Kirchhoff rod and expressed in maximal coordinates, can facilitate continuum robot state estimation and feedback-linearization-based control without conversion to a classical minimal robot dynamics form. We here extend that maximal-coordinate modeling approach to 3D, in a symmetric, constrained-Lagrangian form, using quaternions and Baumgarte constraint stabilization. We also formulate a physically intuitive, model-based observer to estimate the full state of a continuum robot by introducing virtual forces and moments. We validate both the open-loop model and the observer through optical tracking in experiments on a large tendon-driven continuum robot prototype, demonstrating the ability to accurately estimate the robot’s dynamic state during actuation.

Modeling soft robot dynamics is challenging due to their continuum structure and typically nonlinear dynamics. Creating models based on first-order principles is typically time-demanding, and their expressiveness is limited, whereas data-driven models lack interpretability and physical consistency. This work aims to overcome these challenges by introducing a port-Hamiltonian Gaussian Process Regression framework for learning and simulating the dynamics of planar, rod-like soft robots. In detail, the proposed model integrates Cosserat rod theory and Hamiltonian physics with data-driven inference to preserve the system's energy structure while accurately learning the rod dynamics. Numerical simulations show that we can achieve accurate and energy-consistent representations of a rod-like soft robot, showing the potential for a robust and interpretable pathway for modeling complex continuum mechanics.

This article presents three configurations of a pneumatically actuated, symmetric, wheeled soft robot that is able to locomote forwards, backwards, and in a circular trajectory on a planar surface. The robot can achieve 22 cm/s (1.38 body lengths/s) in straight-line speed. We also extend a modeling framework from previous work to express the dynamics of continuum robots and apply it to all three wheeled soft robot configurations. This dynamic model incorporates both holonomic and nonholonomic constraints and is able to capture the locomotion characteristics (configuration and velocity) of the 3D-printed robot. The model is formed by linking discrete rods with inertia, stiffness, and damping derived from constitutive beam bending equations and physical characterization of the robot. This formulation, based on a constrained Lagrangian approach, simplifies the equations of motion by kinematically chaining the rods to resemble the robot body and by constraining the velocity of the segments with wheels. Constraint enforcement is integrated into this formulation to mitigate accumulated errors from numerical integration. The configuration and velocity of the robot are characterized as a function of frequency both in simulation and experimentally, demonstrating a reasonably good match. This work presents and validates a modeling approach that is capable of capturing highly dynamic nonholonomic locomotion of fluid-powered soft robots that current state-of-the-art modeling frameworks cannot.

Soft actuators enable dexterous and compliant interaction, but closed-loop task-space control remains challenging due to strong nonlinearities, distributed deformation, and uncertainty in their dynamics. This paper presents a real-time dynamic-model-based task-space feedback and estimation framework based on a non-minimal coordinate discrete elastic rod model formulated in absolute coordinates with holonomic constraints. The resulting structure preserves distributed mechanics while maintaining computational efficiency through sparse system matrices, enabling real-time control with up to 10 discretized rods. A quasi-static feedforward inverse model is combined with a task-space PI controller and a dynamic observer that fuses measurement residuals as virtual forces, enabling full-state estimation from sparse sensing. The approach is experimentally validated on three planar pneumatic soft actuators with varying geometries. Across five tasks, including drawing the digits 0-9 across the workspace (3-18 mm/s tip speed), tracking periodic motion (up to 37 cm/s), cross-platform generalization, reduced sensing conditions, and real-time user-defined references, our method achieves 1.5-2.3 mm root mean square error (RMSE) for precision motions and 5.5-12.4 mm RMSE at 1-2 Hz. Results demonstrate that structured, non-minimal dynamic models can enable real-time, high-precision, moderate-bandwidth task-space control of planar soft pneumatic actuators in free space.

Soft pneumatic actuators offer inherent compliance and safe interaction but remain difficult to model and control because of their highly nonlinear, distributed dynamics. We present a control-oriented data-driven modeling and control framework that decomposes actuator behavior into a nonlinear static equilibrium model and a linear residual dynamics model identified using Extended Dynamic Mode Decomposition with control (EDMDc). This representation enables feedforward compensation, task-space feedback control, and local closed-loop stability analysis through an augmented linear model. Experiments achieve approximately 1 mm root mean square error (RMSE) during low-speed (approximately 10 mm/s) trajectory tracking and below 10 mm RMSE at higher speeds (approximately 100 mm/s). The framework further achieves stable tracking of highly dynamic user-generated references with peak accelerations exceeding 25 m/s^2 while simultaneously performing real-time obstacle avoidance. Finally, the proposed stability analysis is experimentally validated by accurately predicting stable, marginal, and unstable operating regimes. These results demonstrate that structured, control-oriented learning provides an accurate and practical framework for soft actuator control.

State-of-the-art soft manipulators are unable to vary stiffness continuously, are complex to manufacture, and have limited control bandwidth. In this work, we present a novel planar bidirectional pneumatically actuated soft manipulator that advances all three limitations-the stiffness is continuously tunable by a factor of 1.6, the actuator is manufactured from a single 3D print, and we are able to demonstrate free-space tracking of a time-varying signal. We are also able to modify the impedance of the actuator during a collision using a dynamic model-based feed-forward and feedback controller and demonstrate an increase in virtual stiffness by a factor of 4. The incorporation of feedback resulted in 0.7 mm tip position root-mean-square error (RMSE) (a reduction of 47% over the purely feed-forward controller) while tracking a 5 mm amplitude sinusoid up to 0.75 Hz across the entire stiffness range.

This work presents a novel geometry for a gerotor hydraulic pump integrated into the rotor of a brushless, direct-current, frameless motor. The design eliminates excess dynamic seals and produces a pump that is more compact, more efficient, higher bandwidth, and capable of greater pressure and flow performance than any servopump previously presented at this scale. Two pumps are presented, with one capable of achieving pressures in excess of 2.9 MPa, flows up to 1.6 L/min, output power levels of 31.5 W with 25% efficiency, and operation at bandwidths up to 37 Hz in a compact form weighing 265 g. Due to its compact size and high output, the proposed design achieved a peak power density of 119 W/kg. Variations of the second produced pressures up to 2500 kPa, flows over 4.5 L/min, hydraulic power of 25 W, and weighed 410 g. The proposed design was quiet in operation, with a maximum sound pressure level at 1 m of 55.8 dBA. Because the proposed design contains no external moving parts, a simple fabric wrap reduced pump noise to a maximum of 47.7 dBA. The pump was evaluated for positional-feedback control of representative systems via integration into two setups: one driving standard rigid hydraulic pistons and one driving a soft robotic actuator. The pump was able to control these setups with positional accuracy on the order of 1 mm and angular accuracy of 2 deg, respectively.

Cosserat rod models are widely used to simulate, design, and control soft robots. The Cosserat framework accounts for bending, torsion, transverse shear, and elongation of a long, slender structure and correctly handles large rotations and deflections in 3D, while being far less computationally expensive than full 3D elasticity models using finite elements. However, the Cosserat model is not always appropriate for soft robotic structures since it assumes the cross sections never change size or shape. In this letter, we extend the standard Cosserat rod model to include cross-sectional deformation while retaining much of its simplicity. We add to the Cosserat model additional degrees of freedom that parameterize stretch and shear in the cross-sectional plane and their rates of change along the rod length. We then formulate several possible constitutive laws on the state variables (one linear and one non-linear) and compare them to the standard Cosserat energy expressions to gain insight. We further show how fluidic actuation and tendon actuation can be incorporated into the model, and we compare the extended Cosserat models to 3D nonlinear finite-element simulations with good agreement. Finally, we demonstrate use of this model in a robotics context to control the path-following gait of a peristaltic worm-inspired soft robot.

Prior models of continuously flexible robots typically assume uniform stiffness, and in this paper we relax this assumption. Geometrically varying stiffness profiles provide additional design freedom to influence the motions and workspaces of continuum robots. These results are timely, because with recent rapid advancements in multimaterial additive manufacturing techniques, it is now straightforward to create more complex stiffness profiles in robots. The key insight of this paper is to project forces and moments applied to the robot onto its center of stiffness (i.e. the Young’s modulus-weighted center of each cross section). We show how the center of stiffness can be thought of as analogous to a “precurved backbone” in a robot with uniform stiffness. This analogy enables a large body of prior work in Cosserat Rod modeling of such robots to be applied directly to those with stiffness variations. We experimentally validate this approach using multimaterial, soft, tendon-actuated robots. Lastly, to illustrate how these results can be used in practice, we investigate how stiffness variation can improve performance in a neurosurgical task.

In pursuit of compact electrohydraulic systems, including soft robots, which contain large numbers of controlled degrees of freedom, it is necessary to evaluate designs of valves which are compact and simple to manufacture. This paper presents simulation and initial experimental investigation of a novel frequency-addressable valve for distributed actuation of fluidic robots. The valve consists of only one compliant moving part which can be actuated using an external oscillatory source such as an acoustic transducer. Cantilevers are evaluated using a constrained Lagrangian model formulation and shown to resonate under sinusoidal forcing at frequencies between 7 and 40 Hz depending on beam geometry. This modeling framework allows a broad design space of complex shapes, mass distributions, and applications of non-geometrically-uniform excitation forces and torques. This framework allows for the consideration of beams which are created with complex shapes via methods such as additive-manufacturing. The simulations show that different geometries are capable of forming distinct, appreciably non-overlapping peaks in the frequency domain, which indicate the potential of each valve to operate in a bandpass mode. An experimental evaluation of three proof-of-concept beams made of nitinol wires submerged in water show distinct frequency-addressability at closely-spaced excitation frequencies of 94.8, 103.9, and 122.3 Hz with tip displacements between 0.5 and 1.5 mm.

In contrast to soft robots, typical electromechanical robotic systems are able to leverage a wide range of available brushless servomotors and compatible gear reduction devices. This makes the selection of components to suit the desired application using commercial devices possible and relatively straightforward. However, for fluidic soft robotics and other electrohydraulic systems, there is a relative lack of servomotor equivalents that are low-weight, high-bandwidth, and that can provide sufficient performance at power levels of 10 to 100 W. This work presents a rapidly-producible 3D-printed gerotor pump design created using fused-filament fabrication, which can be mounted to standard brushless, direct-current motors. Factors that may affect the efficacy of a 3D-printed gerotor pump are evaluated. The proposed design is demonstrated to be capable of pro- ducing pressure differentials of more than 1500 kPa, flows up to 2 L/min, and an actuation bandwidth of up to 20 Hz. The mass of the pump was 36 g excluding the motor. The presented pump is designed for use in small-scale electrohydraulic mechanisms and robots, especially fluidic soft robots as a ‘servopump’ in applications which require a high- bandwidth, low-weight solution for the provision of hydraulic power.

In contrast to soft robots, typical electromechanical robotic systems are able to leverage a wide range of available brushless servomotors and compatible gear reduction devices. This makes the selection of components to suit the desired application using commercial devices possible and relatively straightforward. However, for fluidic soft robotics and other electrohydraulic systems, there is a relative lack of servomotor equivalents that are low-weight, high-bandwidth, and that can provide sufficient performance at power levels of 10 to 100 W. This work presents a rapidly producible 3D-printed gerotor pump design created using fused-filament fabrication (FFF), which can be mounted to standard brushless, direct-current motors. Factors that may affect the efficacy of a 3D-printed gerotor pump are evaluated. The proposed design is demonstrated to be capable of producing pressure differentials of more than 1500 kPa, flows up to 2 L/min, and an actuation bandwidth of up to 20 Hz. The mass of the pump was 36 g excluding the motor. The presented pump is designed for use in small-scale electrohydraulic mechanisms and robots, especially fluidic soft robots as a "servopump" in applications which require a high-bandwidth, low-weight solution for the provision of hydraulic power.

Electropermanent magnetic (EPM) valves consist of two permanent magnets, one with high coercivity and one with relatively low coercivity, which are able to rapidly redirect the flux within a magnetic circuit. When combined with magnetorheological (MR) fluid, they provide the ability to rapidly switch flow in a hydraulic circuit on or off. EPM valves contain no moving parts and draw no power except when changing state. These facts, along with their scalability, make them an attractive option for distributed flow control in small hydraulic systems. Current examples of EPM valves are often restricted to relatively low-pressure or low-flow operation. Miniaturization of small-scale hydraulic robots, both soft and rigid, is limited by the availability of sufficiently lightweight, compact, and efficient components which are capable of directing fluid at pressures greater than 700 kPa. This research proposes an EPM valve which leverages the magnetic properties of MR fluid to channel magnetic flux through the fluid. To evaluate the proposed geometry, an exploratory prototype was constructed and evaluated using a test-bench capable of evaluating the valve as a flow resistance. Simulations were conducted to evaluate the design and validate the use of simulation for future design iteration. To be of use in robotic systems, this valve needs to be capable of rapidly switching relatively high pressures while maintaining a highly compact and easily manufactured form factor. Due to its size and low power consumption, it is suitable for distributed hydraulic control in miniature systems such as hydraulically-actuated robots, including soft robots.

Goal: We present a new framework for in vivo image guidance evaluation and provide a case study on robotic partial nephrectomy. Methods: This framework (called the “bystander protocol”) involves two surgeons, one who solely performs the therapeutic process without image guidance, and another who solely periodically collects data to evaluate image guidance. This isolates the evaluation from the therapy, so that in-development image guidance systems can be tested without risk of negatively impacting the standard of care. We provide a case study applying this protocol in clinical cases during robotic partial nephrectomy surgery. Results: The bystander protocol was performed successfully in 6 patient cases. We find average lesion centroid localization error with our IGS system to be 6.5 mm in vivo compared to our prior result of 3.0 mm in phantoms. Conclusions : The bystander protocol is a safe, effective method for testing in-development image guidance systems in human subjects.

This work studies upper-limb impairment resulting from stroke or traumatic brain injury and presents a simple technological solution for a subset of patients: a soft, active stretching aid for at-home use. To better understand the issues associated with existing associated rehabilitation devices, customer discovery conversations were conducted with 153 people in the healthcare ecosystem (60 patients, 30 caregivers, and 63 medical providers). These patients fell into two populations: spastic (stiff, clenched hands) and flaccid (limp hands). Focusing on the first category, a set of design constraints was developed based on the information collected from the customer discovery. With these constraints in mind, a powered wrist-hand stretching orthosis (exoskeleton) was designed and prototyped as a preclinical study (T0 basic science research) to aid in recovery. The orthosis was tested on two patients for proof-of-concept, one survivor of stroke and one of traumatic brain injury. The prototype was able to consistently open both patients’ hands. A mathematical model was developed to characterize joint stiffness based on experimental testing. Donning and doffing times for the prototype averaged 76 and 12.5 s, respectively, for each subject unassisted. This compared favorably to times shown in the literature. This device benefits from simple construction and low-cost materials and is envisioned to become a therapy device accessible to patients in the home. This work lays the foundation for phase 1 clinical trials and further device development.

Stroke causes neurological and physical impairment in millions of people around the world every year. To better comprehend the upper-limb needs and challenges stroke survivors face and the issues associated with existing technology and formulate ideas for a technological solution, the authors conversed with 153 members of the ecosystem (60 neuro patients, 30 caregivers, and 63 medical providers). Patients fell into two populations depending on their upper-limb impairment: spastic (stiff, clenched hands) and flaccid (limp hands). For this work, the authors chose to focus on the second category and developed a set of design constraints based on the information collected through customer discovery. With these in mind, they designed and prototyped a 3D-printed powered wrist-hand grasping orthosis (exoskeleton) to aid in recovery. The orthosis is easily custom-sized based on two parameters and derived anatomical relationships. The researchers tested the prototype on a survivor of stroke and modeled the kinematic behavior of the orthosis with and without load. The prototype neared or exceeded the target design constraints and was able to grasp objects consistently and stably, as well as exercise the patients' hands. In particular, donning time was only 42 s, as compared to the next fastest time of 3 min reported in literature. This device has the potential for effective neurorehabilitation in a home setting, and it lays the foundation for clinical trials and further device development.

Epilepsy affects more than 50 million people world- wide, afflicting patients with debilitating seizures. While antiepileptic drugs are available, 20-40% of patients remain medically refractory, leaving surgical interven- tion as the remaining option [1]. Hippocampal resec- tion is the gold standard surgical therapy, while laser interstitial thermal therapy (LITT) offers a minimally invasive alternative. Current LITT interventions involve delivery of thermal energy via a straight laser probe through a burr hole in the back of the skull under the guidance of magnetic resonance imaging (MRI). LITT has been associated with lower seizure freedom rates which we hypothesize is related to the use of straight line trajectories in a naturally curved structure. Our previous work proposed a percutaneous approach whereby a helically precurved needle is deployed through the foramen ovale to ablate along the hippocampal midline gripper capable of directly grasping needles. (c) De- maximizing tissue coverage [2]. This approach demands a safe, compact, and accurate actuation system capable of operating within the MRI scanner.

This paper presents an inherently safe, compact, 3D-printed, fluid-powered stepper actuation system enabling surgical precision within the demanding and confined space of a magnetic resonance imaging (MRI) scanner. The intense magnetic field and limited workspace of an MRI excludes the use of traditional, ferromagnetic robotics. Additionally, scanner image quality is sensitive to interference, creating a strict constraint on the electromagnetic and ferromagnetic signature of the actuator. While non-ferromagnetic, fluid powered actuators exist, they are often bulky and difficult to control. Using high resolution, material jetting technology, we’re able to 3D print small, standalone multi-material designs with variable rigidity. Leveraging these advances in additive manufacturing technology, we have developed a modular set of miniature flexible fluidic actuators (FFAs). These actuators are capable of translating, rotating, and gripping a slender rod and are inherently safe to valve, control, or pressure faults, due to the stepping sequence. Using a specific clinical application as a use case, we assembled these components into a highly compact needle steering system for MRI-guided neurosurgery. This two-degree-of-freedom actuation system is driven pneumatically, taking advantage of sterile, hospital instrument air and is electromagnetically transparent to the MRI scanner. In addition to detailing the actuator system design, this paper also demonstrates a robust, nonlinear control strategy for precision sub-step motion control. This paper reports the actuator system’s operating pressure and bandwidth, translational and rotational accuracy, and maximum force and torque capabilities.