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1. Using First Principles for Deep Learning and Model-Based Control of Soft Robots

   https://doi.org/10.3389/frobt.2021.654398  

   Johnson, Curtis C.; Quackenbush, Tyler; Sorensen, Taylor; Wingate, David; Killpack, Marc D. (May 2021, Frontiers in Robotics and AI)

   Model-based optimal control of soft robots may enable compliant, underdamped platforms to operate in a repeatable fashion and effectively accomplish tasks that are otherwise impossible for soft robots. Unfortunately, developing accurate analytical dynamic models for soft robots is time-consuming, difficult, and error-prone. Deep learning presents an alternative modeling approach that only requires a time history of system inputs and system states, which can be easily measured or estimated. However, fully relying on empirical or learned models involves collecting large amounts of representative data from a soft robot in order to model the complex state space–a task which may not be feasible in many situations. Furthermore, the exclusive use of empirical models for model-based control can be dangerous if the model does not generalize well. To address these challenges, we propose a hybrid modeling approach that combines machine learning methods with an existing first-principles model in order to improve overall performance for a sampling-based non-linear model predictive controller. We validate this approach on a soft robot platform and demonstrate that performance improves by 52% on average when employing the combined model. 

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2. Modeling, Reduction, and Control of a Helically Actuated Inertial Soft Robotic Arm via the Koopman Operator

   David A. Haggerty, Michael J. (January 2021, ArXivorg)

   null (Ed.)

   Soft robots promise improved safety and capabil- ity over rigid robots when deployed in complex, delicate, and dynamic environments. However the infinite degrees of freedom and highly nonlinear dynamics of these systems severely com- plicate their modeling and control. As a step toward addressing this open challenge, we apply the data-driven, Hankel Dynamic Mode Decomposition (HDMD) with time delay observables to the model identification of a highly inertial, helical soft robotic arm with a high number of underactuated degrees of freedom. The resulting model is linear and hence amenable to control via a Linear Quadratic Regulator (LQR). Using our test bed device, a dynamic, lightweight pneumatic fabric arm with an inertial mass at the tip, we show that the combination of HDMD and LQR allows us to command our robot to achieve arbitrary poses using only open loop control. We further show that Koopman spectral analysis gives us a dimensionally reduced basis of modes which decreases computational complexity without sacrificing predictive power. 

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3. Control of soft robots with inertial dynamics

   https://doi.org/10.1126/scirobotics.add6864  

   Haggerty, David A.; Banks, Michael J.; Kamenar, Ervin; Cao, Alan B.; Curtis, Patrick C.; Mezić, Igor; Hawkes, Elliot W. (August 2023, Science Robotics)

   Soft robots promise improved safety and capability over rigid robots when deployed near humans or in complex, delicate, and dynamic environments. However, infinite degrees of freedom and the potential for highly nonlinear dynamics severely complicate their modeling and control. Analytical and machine learning methodologies have been applied to model soft robots but with constraints: quasi-static motions, quasi-linear deflections, or both. Here, we advance the modeling and control of soft robots into the inertial, nonlinear regime. We controlled motions of a soft, continuum arm with velocities 10 times larger and accelerations 40 times larger than those of previous work and did so for high-deflection shapes with more than 110° of curvature. We leveraged a data-driven learning approach for modeling, based on Koopman operator theory, and we introduce the concept of the static Koopman operator as a pregain term in optimal control. Our approach is rapid, requiring less than 5 min of training; is computationally low cost, requiring as little as 0.5 s to build the model; and is design agnostic, learning and accurately controlling two morphologically different soft robots. This work advances rapid modeling and control for soft robots from the realm of quasi-static to inertial, laying the groundwork for the next generation of compliant and highly dynamic robots. 

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4. Tractable and Intuitive Dynamic Model for Soft Robots via the Recursive Newton-Euler Algorithm

   https://doi.org/10.1109/RoboSoft54090.2022.9762215  

   Jensen, Spencer W.; Johnson, Curtis C.; Lindberg, Alexa M.; Killpack, Marc D. (April 2022, IEEE International Conference on Soft Robotics (RoboSoft))

   Because of the complex nature of soft robots, formulating dynamic models that are simple, efficient, and sufficiently accurate for simulation or control is a difficult task. This paper introduces an algorithm based on a recursive Newton-Euler (RNE) approach that enables an accurate and tractable lumped parameter dynamic model. This model scales linearly in computational complexity with the number of discrete segments. We validate this model by comparing it to actual hardware data from a three-joint continuum soft robot (with six degrees of freedom represented in a constant curvature kinematic model). The results show that this RNE-based model can be computed faster than real-time. We also show that with minimal system identification, a simulation performed using the dynamic model matches the real robot data with a median error of 3.15 degrees. 

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5. Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networks

   Neary, Cyrus; Topcu, Ufuk (June 2023, Learning for Dynamics and Control Conference)

   Matni, Nikolai; Morari, Manfred; Pappas, George J (Ed.)

   Many dynamical systems—from robots interacting with their surroundings to large-scale multi-physics systems—involve a number of interacting subsystems. Toward the objective of learning composite models of such systems from data, we present i) a framework for compositional neural networks, ii) algorithms to train these models, iii) a method to compose the learned models, iv) theoretical results that bound the error of the resulting composite models, and v) a method to learn the composition itself, when it is not known a priori. The end result is a modular approach to learning: neural network submodels are trained on trajectory data generated by relatively simple subsystems, and the dynamics of more complex composite systems are then predicted without requiring additional data generated by the composite systems themselves. We achieve this compositionality by representing the system of interest, as well as each of its subsystems, as a port-Hamiltonian neural network (PHNN)—a class of neural ordinary differential equations that uses the port-Hamiltonian systems formulation as inductive bias. We compose collections of PHNNs by using the system’s physics-informed interconnection structure, which may be known a priori, or may itself be learned from data. We demonstrate the novel capabilities of the proposed framework through numerical examples involving interacting spring-mass-damper systems. Models of these systems, which include nonlinear energy dissipation and control inputs, are learned independently. Accurate compositions are learned using an amount of training data that is negligible in comparison with that required to train a new model from scratch. Finally, we observe that the composite PHNNs enjoy properties of port-Hamiltonian systems, such as cyclo-passivity—a property that is useful for control purposes. 

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