Model Predictive Control-Based Path-Following for Tail-Actuated Robotic Fish

Abstract

There has been an increasing interest in the use of autonomous underwater robots to monitor freshwater and marine environments. In particular, robots that propel and maneuver themselves like fish, often known as robotic fish, have emerged as mobile sensing platforms for aquatic environments. Highly nonlinear and often under-actuated dynamics of robotic fish present significant challenges in control of these robots. In this work, we propose a nonlinear model predictive control (NMPC) approach to path-following of a tail-actuated robotic fish that accommodates the nonlinear dynamics and actuation constraints while minimizing the control effort. Considering the cyclic nature of tail actuation, the control design is based on an averaged dynamic model, where the hydrodynamic force generated by tail beating is captured using Lighthill's large-amplitude elongated-body theory. A computationally efficient approach is developed to identify the model parameters based on the measured swimming and turning data for the robot. With the tail beat frequency fixed, the bias and amplitude of the tail oscillation are treated as physical variables to be manipulated, which are related to the control inputs via a nonlinear map. A control projection method is introduced to accommodate the sector-shaped constraints of the control inputs while minimizing the optimization complexity in solving the NMPC problem. Both simulation and experimental results support the efficacy of the proposed approach. In particular, the advantages of the control projection method are shown via comparison with alternative approaches.

Local Koopman Operators for Data-Driven Control of Robotic Systems

“…Parameter m b is the mass of the robotic fish, m ax and m ay are the hydrodynamic derivatives that represent the added masses of the robotic fish along the x and y directions, respectively, J az and J bz are the added inertia effect and the inertia of the body about the z-axis, respectively, m is the mass of the water displaced by the tail per unit length, ρ is the water density, L is the tail length, c is the distance from the body center to the pivot point of the actuated tail, C D , C L , K D are drag force, lift, and drag moment coefficients, respectively, and K f and K m are scaling coefficients that are measured experimentally [39].…”

“…Proof: For the derivation of the error expression (21), see Appendix V-A. For the derivation of the error bound formula (22), see Appendix V-B.…”

“…In fact, several of these methods have already been explored in underwater tasks using robotic fish of different morphologies. Researchers have performed maneuvering, speed and orientation control, collision-avoidance, point-to-point navigation as well as velocity and position tracking using a myriad of control schemes, such as PID [12], [13], LQR [14], SAC [11], [15], fuzzy control [16], [17], geometric control [18], [19], sliding mode control [20], NMPC [21], feedback linearization [22], backstepping control [23] or even a combination of the above [24], [25]. However, the aforementioned methods are either system-specific, apply to dynamics with certain structures, or are computationally prohibitive for real-time identification and control of resource-constrained robots.…”

Computational load reduction of the agent guidance problem using Mixed Integer Programming

“…Applications of MIP in the literature are plentiful, whether in terrestrial [1, 5-8, 18, 19], aquatic [27][28][29], aerial [2,4,9,16,[30][31][32] or even spatial [33] environments. For instance, the authors propose in [14] an approximate model of aircraft dynamics using linear constraints and they apply a MIP approach to the trajectory planning of airplanes.…”

Innovation Concept Model and Prototype Validation of Robotic Fish with a Spatial Oscillating Rigid Caudal Fin

“…After nearly thirty years of research on bionic carangiform fish, the fish motion could be simplified into one joint, double joints or more joints, and corresponding biofish prototypes were developed [8][9][10]. When compared to real fish's thrust generation, simplified swimming, controlling models and optimization are reasonably accurate and useful [11][12][13][14][15]. The hydrodynamics of different caudal fins' shapes vary considerably among each other [16][17][18].…”