arXiv subjects

Andrew P. Sabelhaus

Publications and source records attributed to Andrew P. Sabelhaus.

At least 19 recordsLinked to original sources

arXiv2026

Design Optimization for Large High-Force Soft Robot Manipulators Under Gravitational Loads

Designing large soft robots capable of generating high forces for physical human-robot interaction remains a significant challenge in soft robotics. Prior work in large soft robots has focused on proof-of-concept prototypes, and no systematic framework exists for determining the suitability of a design paradigm for a desired task. This manuscript introduces a method for optimizing the geometry of a soft robot limb, maximizing its blocking force subject to an anti-bucking constraint under its own gravitational loading. We demonstrate that an explicit solution exists to the proposed optimization problem under certain assumptions. Experiments with three geometries of a large, soft, pneumatically-actuated manipulator demonstrate that the method correctly predicts which designs meet constraints and which produces the largest end-effector forces. This method, with its closed-form solution, can allow designers to determine a-priori if an intended class of soft manipulators is an appropriate choice for physical interaction at large size scales.

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arXiv2026

Trajectory Generation for Underactuated Soft Robot Manipulators using Discrete Elastic Rod Dynamics

Soft robots are well suited for contact-rich tasks due to their compliance, yet this property makes accurate and tractable modeling challenging. Planning motions with dynamically-feasible trajectories requires models that capture arbitrary deformations, remain computationally efficient, and are compatible with underactuation. However, existing approaches balance these properties unevenly: continuum rod models provide physical accuracy but are computationally demanding, while reduced-order approximations improve efficiency at the cost of modeling fidelity. To address this, our work introduces a control-oriented reformulation of Discrete Elastic Rod (DER) dynamics for soft robots, and a method to generate trajectories with these dynamics. The proposed formulation yields a control-affine representation while preserving certain first-principles force-deformation relationships. As a result, the generated trajectories are both dynamically feasible and consistent with the underlying actuation assumptions. We present our trajectory generation framework and validate it experimentally on a pneumatic soft robotic limb. Hardware results demonstrate consistently improved trajectory tracking performance over a constant-curvature-based baseline, particularly under complex actuation conditions.

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arXiv2025

Force-Safe Environment Maps and Real-Time Detection for Soft Robot Manipulators

Soft robot manipulators have the potential for deployment in delicate environments to perform complex manipulation tasks. However, existing obstacle detection and avoidance methods do not consider limits on the forces that manipulators may exert upon contact with delicate obstacles. This work introduces a framework that maps force safety criteria from task space (i.e. positions along the robot's body) to configuration space (i.e. the robot's joint angles) and enables real-time force safety detection. We incorporate limits on allowable environmental contact forces for given task-space obstacles, and map them into configuration space (C-space) through the manipulator's forward kinematics. This formulation ensures that configurations classified as safe are provably below the maximum force thresholds, thereby allowing us to determine force-safe configurations of the soft robot manipulator in real-time. We validate our approach in simulation and hardware experiments on a two-segment pneumatic soft robot manipulator. Results demonstrate that the proposed method accurately detects force safety during interactions with deformable obstacles, thereby laying the foundation for real-time safe planning of soft manipulators in delicate, cluttered environments.

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arXiv2025

Safe Autonomous Environmental Contact for Soft Robots using Control Barrier Functions

Robots built from soft materials will inherently apply lower environmental forces than their rigid counterparts, and therefore may be more suitable in sensitive settings with unintended contact. However, these robots' applied forces result from both their design and their control system in closed-loop, and therefore, ensuring bounds on these forces requires controller synthesis for safety as well. This article introduces the first feedback controller for a soft manipulator that formally meets a safety specification with respect to environmental contact. In our proof-of-concept setting, the robot's environment has known geometry and is deformable with a known elastic modulus. Our approach maps a bound on applied forces to a safe set of positions of the robot's tip via predicted deformations of the environment. Then, a quadratic program with Control Barrier Functions in its constraints is used to supervise a nominal feedback signal, verifiably maintaining the robot's tip within this safe set. Hardware experiments on a multi-segment soft pneumatic robot demonstrate that the proposed framework successfully maintains a positive safety margin. This framework represents a fundamental shift in perspective on control and safety for soft robots, implementing a formally verifiable logic specification on their pose and contact forces.

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arXiv2025

Koopman Control Factorization: Data-Driven Convex Controller Design for a Class of Nonlinear Systems

Although Koopman operators provide a global linearization for autonomous dynamical systems, nonautonomous systems are not globally linear in the inputs. State (or output) feedback controller design therefore remains nonconvex in typical formulations, even with approximations via bilinear control-affine terms. We address this gap by introducing the Koopman Control Factorization, a novel parameterization of control-affine dynamical systems combined with a feedback controller defined as a linear combination of nonlinear measurements. With this choice, the Koopman operator of the closed-loop system is a bilinear combination of the coefficients in two matrices: one representing the system, and the other the controller. We propose a set of sufficient conditions such that the factorization holds. Then, we present an algorithm that calculates the feedback matrix via semi-definite programming, producing a Lyapunov-stable closed-loop system with convex optimization. We evaluate the proposed controllers on two canonical examples of control-affine nonlinear systems (inverted pendulums), and show that our factorization and controller successfully stabilize both under properly-chosen basis functions. This manuscript introduces a broadly generalizable control synthesis method for stabilization of nonlinear systems that is quick-to-compute, verifiably stable, data-driven, and does not rely on approximations.

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arXiv2025

Soft Robotic Delivery of Coiled Anchors for Cardiac Interventions

Trans-catheter cardiac intervention has become an increasingly available option for high-risk patients without the complications of open heart surgery. However, current catheterbased platforms suffer from a lack of dexterity, force application, and compliance required to perform complex intracardiac procedures. An exemplary task that would significantly ease minimally invasive intracardiac procedures is the implantation of anchor coils, which can be used to fix and implant various devices in the beating heart. We introduce a robotic platform capable of delivering anchor coils. We develop a kineto-statics model of the robotic platform and demonstrate low positional error. We leverage the passive compliance and high force output of the actuator in a multi-anchor delivery procedure against a motile in-vitro simulator with millimeter level accuracy.

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arXiv2024

Real-Time Trajectory Generation for Soft Robot Manipulators Using Differential Flatness

Soft robots have the potential to interact with sensitive environments and perform complex tasks effectively. However, motion plans and trajectories for soft manipulators are challenging to calculate due to their deformable nature and nonlinear dynamics. This article introduces a fast real-time trajectory generation approach for soft robot manipulators, which creates dynamically-feasible motions for arbitrary kinematically-feasible paths of the robot's end effector. Our insight is that piecewise constant curvature (PCC) dynamics models of soft robots can be differentially flat, therefore control inputs can be calculated algebraically rather than through a nonlinear differential equation. We prove this flatness under certain conditions, with the curvatures of the robot as the flat outputs. Our two-step trajectory generation approach uses an inverse kinematics procedure to calculate a motion plan of robot curvatures per end-effector position, then, our flatness diffeomorphism generates corresponding control inputs that respect velocity. We validate our approach through simulations of our representative soft robot manipulator along three different trajectories, demonstrating a margin of 23x faster than real-time at a frequency of 100 Hz. This approach could allow fast verifiable replanning of soft robots' motions in safety-critical physical environments, crucial for deployment in the real world.

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arXiv2024

Self-Sensing for Proprioception and Contact Detection in Soft Robots Using Shape Memory Alloy Artificial Muscles

Estimating a soft robot's pose and applied forces, also called proprioception, is crucial for safe interaction of the robot with its environment. However, most solutions for soft robot proprioception use dedicated sensors, particularly for external forces, which introduce design trade-offs, rigidity, and risk of failure. This work presents an approach for pose estimation and contact detection for soft robots actuated by shape memory alloy (SMA) artificial muscles, using no dedicated force sensors. Our framework uses the unique material properties of SMAs to self-sense their internal stress, via offboard measurements of their electrical resistance and in-situ temperature readings, in an existing fully-soft limb design. We demonstrate that a simple polynomial regression model on these measurements is sufficient to predict the robot's pose, under no-contact conditions. Then, we show that if an additional measurement of the true pose is available (e.g. from an already-in-place bending sensor), it is possible to predict a binary contact/no-contact using multiple combinations of self-sensing signals. Our hardware tests verify our hypothesis via a contact detection test with a human operator. This proof-of-concept validates that self-sensing signals in soft SMA-actuated soft robots can be used for proprioception and contact detection, and suggests a direction for integrating proprioception into soft robots without design compromises. Future work could employ machine learning for enhanced accuracy.

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arXiv2024

Maximizing Consistent Force Output for Shape Memory Alloy Artificial Muscles in Soft Robots

Soft robots have immense potential given their inherent safety and adaptability, but challenges in soft actuator forces and design constraints have limited scaling up soft robots to larger sizes. Electrothermal shape memory alloy (SMA) artificial muscles have the potential to create these large forces and high displacements, but consistently using these muscles under a well-defined model, in-situ in a soft robot, remains an open challenge. This article provides a system for maintaining the highest-possible consistent SMA forces, over long lifetimes, by combining a fatigue testing protocol with a supervisory control system for the muscles' internal temperature state. We propose a design of a soft limb with swap-able SMA muscles, and deploy the limb in a blocked-force test to quantify the relationship between the measured maximum force at different temperatures over different lifetimes. Then, by applying an invariance-based control system to maintain temperatures under our long-life limit, we demonstrate consistent high forces in a practical task over hundreds of cycles. The method we developed allows for practical implementation of SMAs in soft robots through characterizing and controlling their behavior in-situ, and provides a method to impose limits that maximize their consistent, repeatable behavior.

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arXiv2022

Safe Balancing Control of a Soft Legged Robot

Legged robots constructed from soft materials are commonly claimed to demonstrate safer, more robust environmental interactions than their rigid counterparts. However, this motivating feature of soft robots requires more rigorous development for comparison to rigid locomotion. This article presents a soft legged robot platform, Horton, and a feedback control system with safety guarantees on some aspects of its operation. The robot is constructed using a series of soft limbs, actuated by thermal shape memory alloy (SMA) wire muscles, with sensors for its position and its actuator temperatures. A supervisory control scheme maintains safe actuator states during the operation of a separate controller for the robot's pose. Experiments demonstrate that Horton can lift its leg and maintain a balancing stance, a precursor to locomotion. The supervisor is verified in hardware via a human interaction test during balancing, keeping all SMA muscles below a temperature threshold. This work represents the first demonstration of a safety-verified feedback system on any soft legged robot.

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arXiv2022

Safe Supervisory Control of Soft Robot Actuators

Although soft robots show safer interactions with their environment than traditional robots, soft mechanisms and actuators still have significant potential for damage or degradation particularly during unmodeled contact. This article introduces a feedback strategy for safe soft actuator operation during control of a soft robot. To do so, a supervisory controller monitors actuator state and dynamically saturates control inputs to avoid conditions that could lead to physical damage. We prove that, under certain conditions, the supervisory controller is stable and verifiably safe. We then demonstrate completely onboard operation of the supervisory controller using a soft thermally-actuated robot limb with embedded shape memory alloy (SMA) actuators and sensing. Tests performed with the supervisor verify its theoretical properties and show stabilization of the robot limb's pose in free space. Finally, experiments show that our approach prevents overheating during contact (including environmental constraints and human contact) or when infeasible motions are commanded. This supervisory controller, and its ability to be executed with completely onboard sensing, has the potential to make soft robot actuators reliable enough for practical use.

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arXiv2022

Trajectory Optimization for Thermally-Actuated Soft Planar Robot Limbs

Practical use of robotic manipulators made from soft materials requires generating and executing complex motions. We present the first approach for generating trajectories of a thermally-actuated soft robotic manipulator. Based on simplified approximations of the soft arm and its antagonistic shape-memory alloy actuator coils, we justify a dynamics model of a discretized rigid manipulator with joint torques proportional to wire temperature. Then, we propose a method to calibrate this model from experimental data and demonstrate that the simulation aligns well with a hardware test. Finally, we use a direct collocation optimization with the robot's nonlinear dynamics to generate feasible state-input trajectories from a desired reference. Three experiments validate our approach for a single-segment robot in hardware: first using a hand-derived reference trajectory, then with two teach-and-repeat tests. The results show promise for both open-loop motion generation as well as for future applications with feedback.

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arXiv2022

In-Situ Sensing and Dynamics Predictions for Electrothermally-Actuated Soft Robot Limbs

Untethered soft robots that locomote using electrothermally-responsive materials like shape memory alloy (SMA) face challenging design constraints for sensing actuator states. At the same time, modeling of actuator behaviors faces steep challenges, even with available sensor data, due to complex electrical-thermal-mechanical interactions and hysteresis. This article proposes a framework for in-situ sensing and dynamics modeling of actuator states, particularly temperature of SMA wires, which is used to predict robot motions. A planar soft limb is developed, actuated by a pair of SMA coils, that includes compact and robust sensors for temperature and angular deflection. Data from these sensors are used to train a neural network based on the long short-term memory (LSTM) architecture to model both unidirectional (single SMA) and bidirectional (both SMAs) motion. Predictions from the model demonstrate that data from the temperature sensor, combined with control inputs, allow for dynamics predictions over extraordinarily long open-loop timescales (10 minutes) with little drift. Prediction errors are on the order of the soft deflection sensor's accuracy. This architecture allows for compact designs of electrothermally-actuated soft robots that include sensing sufficient for motion predictions, helping to bring these robots into practical application.

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arXiv2021

Robust Control of a Multi-Axis Shape Memory Alloy-Driven Soft Manipulator

Control of soft robotic manipulators remains a challenge for designs with advanced capabilities and novel actuation. Two significant limitations are multi-axis, three-dimensional motion of soft bodies alongside actuator dynamics and constraints, both of which are present in shape-memory-alloy (SMA)-powered soft robots. This article addresses both concerns with a robust feedback control scheme, demonstrating state tracking control for a soft robot manipulator of this type. Our controller uses a static beam bending model to approximate the soft limb as an LTI system, alongside a singular-value-decomposition compensator approach to decouple the multi-axial motion and an anti-windup element for the actuator saturation. We prove stability and verify robustness of our controller, with robustness intended to account for the unmodeled dynamics. Our implementation is verified in hardware tests of a soft SMA-powered limb, showing low tracking error, with promising results for future multi-limbed robots.

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arXiv2020

An Untethered Brittle Star-Inspired Soft Robot for Closed-Loop Underwater Locomotion

Soft robots are capable of inherently safer interactions with their environment than rigid robots since they can mechanically deform in response to unanticipated stimuli. However, their complex mechanics can make planning and control difficult, particularly with tasks such as locomotion. In this work, we present a mobile and untethered underwater crawling soft robot, PATRICK, paired with a testbed that demonstrates closed-loop locomotion planning. PATRICK is inspired by the brittle star, with five flexible legs actuated by a total of 20 shape-memory alloy (SMA) wires, providing a rich variety of possible motions via its large input space. We propose a motion planning infrastructure based on a simple set of PATRICK's motion primitives, and provide experiments showing that the planner can command the robot to locomote to a goal state. These experiments contribute the first examples of closed-loop, state-space goal seeking of an underwater, untethered, soft crawling robot, and make progress towards full autonomy of soft mobile robotic systems.

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arXiv2020

Inverse Statics Optimization for Compound Tensegrity Robots

Robots built from cable-driven tensegrity (`tension-integrity') structures have many of the advantages of soft robots, such as flexibility and robustness, while still obeying simple statics and dynamics models. However, existing tensegrity modeling approaches cannot natively describe robots with arbitrary rigid bodies in their tension network. This work presents a method to calculate the cable tensions in static equilibrium for such tensegrity robots, here defined as compound tensegrity. First, a static equilibrium model for compound tensegrity robots is reformulated from the standard force density method used with other tensegrity structures. Next, we pose the problem of calculating tension forces in the robot's cables under our proposed model. A solution is proposed as a quadratic optimization problem with practical constraints. Simulations illustrate how this inverse statics optimization problem can be used for both the design and control of two different compound tensegrity applications: a spine robot and a quadruped robot built from that spine. Finally, we verify the accuracy of the inverse statics model through a hardware experiment, demonstrating the feasibility of low-error open-loop control using our proposed methodology.

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arXiv2019

Model-Predictive Control with Inverse Statics Optimization for Tensegrity Spine Robots

Robots with flexible spines based on tensegrity structures have potential advantages over traditional designs with rigid torsos. However, these robots can be difficult to control due to their high-dimensional nonlinear dynamics and actuator constraints. This work presents two controllers for tensegrity spine robots, using model-predictive control (MPC) and inverse statics optimization. The controllers introduce two different approaches to making the control problem computationally tractable. The first utilizes smoothing terms in the MPC problem. The second uses a new inverse statics optimization algorithm, which gives the first feasible solutions to the problem for certain tensegrity robots, to generate reference input trajectories in combination with MPC. Tracking the inverse statics reference input trajectory significantly reduces the number of tuning parameters. The controllers are validated against simulations of two-dimensional and three-dimensional tensegrity spines. Both approaches show noise insensitivity and low tracking error, and can be used for different control goals. The results here demonstrate the first closed-loop control of such structures.

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arXiv2018

Design, Simulation, and Testing of a Flexible Actuated Spine for Quadruped Robots

Walking quadruped robots face challenges in positioning their feet and lifting their legs during gait cycles over uneven terrain. The robot Laika is under development as a quadruped with a flexible, actuated spine designed to assist with foot movement and balance during these gaits. This paper presents the first set of hardware designs for the spine of Laika, a physical prototype of those designs, and tests in both hardware and simulations that show the prototype's capabilities. Laika's spine is a tensegrity structure, used for its advantages with weight and force distribution, and represents the first working prototype of a tensegrity spine for a quadruped robot. The spine bends by adjusting the lengths of the cables that separate its vertebrae, and twists using an actuated rotating vertebra at its center. The current prototype of Laika has stiff legs attached to the spine, and is used as a test setup for evaluation of the spine itself. This work shows the advantages of Laika's spine by demonstrating the spine lifting each of the robot's four feet, both as a form of balancing and as a precursor for a walking gait. These foot motions, using specific combinations of bending and rotation movements of the spine, are measured in both simulation and hardware experiments. Hardware data are used to calibrate the simulations, such that the simulations can be used for control of balancing or gait cycles in the future. Future work will attach actuated legs to Laika's spine, and examine balancing and gait cycles when combined with leg movements.

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