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Drifters are energy-efficient platforms for monitoring rivers and oceans. Prior work largely focused on free-floating drifters that drift passively with flow and have little or no controllability. In this paper we propose steerable drifters that use multiple rudders for modulating the hydrodynamic forces and thus maneuvering. A dynamic model for drifters with multiple rudders is presented. Simulation is conducted to examine the behavior of the drifter in two different flow conditions, uniform flow and parabolic flow. When there is no difference in relative flow between the rudders, as in uniform flow, the drifter can only be controlled until its velocity approaches that of the water. However, when present, local flow differentials can be exploited to initiate motion lateral to the ambient flow and control the trajectory of the drifter to some degree. The motion of the drifter is further classified as belonging to one of three major modes, rotational, oscillatory, and stable. The behavior of the drifter in a simulated river was mapped for different rudder angles. Identifying the parameters that induce each mode lays the groundwork for developing a feedback control scheme for the drifter.

 

This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using higher order derivatives of general nonlinear dynamics that need not be known, we construct a Koopman operator-based linear representation and utilize Taylor series accuracy analysis to derive an error bound. The resulting error formula is used to choose the order of derivatives in the basis functions and obtain a data-driven Koopman model using a closed-form expression that can be computed in real time. Using the inverted pendulum system, we illustrate the robustness of the error bounds given noisy measurements of unknown dynamics, where the derivatives are estimated numerically. When combined with control, the Koopman representation of the nonlinear system has marginally better performance than competing nonlinear modeling methods, such as SINDy and NARX. In addition, as a linear model, the Koopman approach lends itself readily to efficient control design tools, such as LQR, whereas the other modeling approaches require nonlinear control methods. The efficacy of the approach is further demonstrated with simulation and experimental results on the control of a tail-actuated robotic fish. Experimental results show that the proposed data-driven control approach outperforms a tuned PID (Proportional Integral Derivative) controller and that updating the data-driven model online significantly improves performance in the presence of unmodeled fluid disturbance. This paper is complemented with a video: https://youtu.be/9 wx0tdDta0. 

Interest in soft robotics has increased in recent years due to their potential in a myriad of applications. A wide variety of soft robots has emerged, including bio-inspired robotic swimmers such as jellyfish, rays, and robotic fish. However, the highly nonlinear fluid-structure interactions pose considerable challenges in the analysis, modeling, and feedback control of these soft robotic swimmers. In particular, developing models that are of high fidelity but are also amenable to control for such robots remains an open problem. In this work, we pro- pose a data-driven approach that exploits Koopman operators to obtain a linear representation of the soft swimmer dynamics. Specifically, two methodologies are explored for obtaining the basis functions of the the operator, one based on data-based derivatives estimated using high-gain observers, and the other based on the dynamics structure of a tail-actuated rigid-body robotic fish. The resulting approximate finite-dimensional operators are trained and evaluated using data from high-fidelity CFD simulations that incorporate fluid-structure interactions. Validation results demonstrate that, while both methods are promising in producing control-oriented models, the approach based on derivative estimates shows higher accuracy in state prediction.