Andrew P. Sabelhaus

Andrew P. Sabelhaus, Huajing Zhao, Edward L. Zhu et al.

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.

Beibei Liu, Akua K. Dickson, Ran Jing et al.

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.

Andrew P. Sabelhaus, Rohan K. Mehta, Anthony T. Wertz et al.

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.

Zach J. Patterson, Andrew P. Sabelhaus, Carmel Majidi

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.

Anthony Wertz, Andrew P. Sabelhaus, Carmel Majidi

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.

Zach J. Patterson, Andrew P. Sabelhaus, Keene Chin et al.

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.

Andrew P. Sabelhaus, Shirley Huajing Zhao, Mallory C. Daly et al.

The Underactuated Lightweight Tensegrity Robotic Assistive Spine (ULTRA Spine) project is an ongoing effort to develop a flexible, actuated backbone for quadruped robots. In this work, model-predictive control is used to track a trajectory in the robot's state space, in simulation. The state trajectory used here corresponds to a bending motion of the spine, with translations and rotations of the moving vertebrae. Two different controllers are presented in this work: one that does not use a reference input but includes smoothing constrants, and a second one that uses a reference input without smoothing. For the smoothing controller, without reference inputs, the error converges to zero, while the simpler-to-tune controller with an input reference shows small errors but not complete convergence. It is expected that this controller will converge as it is improved further.

Andrew P. Sabelhaus, Albert H. Li, Kimberly A. Sover et al.

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.

Andrew P. Sabelhaus, Lara Janse van Vuuren, Ankita Joshi et al.

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.