Soft robotics has advanced rapidly, yet its control methods remain fragmented: different morphologies and actuation schemes still require task-specific controllers, hindering theoretical integration and large-scale deployment. A generic control framework is therefore essential, and a key obstacle lies in the persistent use of rigid-body control logic, which relies on precise models and strict low-level execution. Such a paradigm is effective for rigid robots but fails for soft robots, where the ability to tolerate and exploit approximate action representations, i.e., control compliance, is the basis of robustness and adaptability rather than a disturbance to be eliminated. Control should thus shift from suppressing compliance to explicitly exploiting it. Human motor control exemplifies this principle: instead of computing exact dynamics or issuing detailed muscle-level commands, it expresses intention through high-level movement tendencies, while reflexes and biomechanical mechanisms autonomously resolve local details. This architecture enables robustness, flexibility, and cross-task generalization. Motivated by this insight, we propose a generic soft-robot control framework grounded in control compliance and validate it across robots with diverse morphologies and actuation mechanisms. The results demonstrate stable, safe, and cross-platform transferable behavior, indicating that embracing control compliance, rather than resisting it, may provide a widely applicable foundation for unified soft-robot control.

The efficient optimization of actuated soft structures, particularly under complex nonlinear forces, remains a critical challenge in advancing robotics. Simulations of nonlinear structures, such as soft-bodied robots modeled using the finite element method (FEM), often demand substantial computational resources, especially during optimization. To address this challenge, we propose a novel optimization algorithm based on a tensorial parametric reduced order model (PROM). Our algorithm leverages dimensionality reduction and solution approximation techniques to facilitate efficient solving of nonlinear constrained optimization problems. The well-structured tensorial approach enables the use of analytical gradients within a specifically chosen reduced order basis (ROB), significantly enhancing computational efficiency. To showcase the performance of our method, we apply it to optimizing soft robotic swimmer shapes. These actuated soft robots experience hydrodynamic forces, subjecting them to both internal and external nonlinear forces, which are incorporated into our optimization process using a data-free ROB for fast and accurate computations. This approach not only reduces computational complexity but also unlocks new opportunities to optimize complex nonlinear systems in soft robotics, paving the way for more efficient design and control.

Aquatic organisms are known for their ability to generate efficient propulsion with low energy expenditure. While existing research has sought to leverage bio-inspired structures to reduce energy costs in underwater robotics, the crucial role of control policies in enhancing efficiency has often been overlooked. In this study, we optimize the motion of a bio-mimetic robotic fish using deep reinforcement learning (DRL) to maximize propulsion efficiency and minimize energy consumption. Our novel DRL approach incorporates extended pressure perception, a transformer model processing sequences of observations, and a policy transfer scheme. Notably, significantly improved training stability and speed within our approach allow for end-to-end training of the robotic fish. This enables agiler responses to hydrodynamic environments and possesses greater optimization potential compared to pre-defined motion pattern controls. Our experiments are conducted on a serially connected rigid robotic fish in a free stream with a Reynolds number of 6000 using computational fluid dynamics (CFD) simulations. The DRL-trained policies yield impressive results, demonstrating both high efficiency and propulsion. The policies also showcase the agent's embodiment, skillfully utilizing its body structure and engaging with surrounding fluid dynamics, as revealed through flow analysis. This study provides valuable insights into the bio-mimetic underwater robots optimization through DRL training, capitalizing on their structural advantages, and ultimately contributing to more efficient underwater propulsion systems.

Fish have endured millions of years of evolution, and their distinct rigid-flexible body structures offer inspiration for overcoming challenges in underwater robotics, such as limited mobility, high energy consumption, and adaptability. This paper introduces SpineWave, a biomimetic robotic fish featuring a fish-spine-like rigid-flexible transition structure. The structure integrates expandable fishbone-like ribs and adjustable magnets, mimicking the stretch and recoil of fish muscles to balance rigidity and flexibility. In addition, we employed an evolutionary algorithm to optimize the hydrodynamics of the robot, achieving significant improvements in swimming performance. Real-world tests demonstrated robustness and potential for environmental monitoring, underwater exploration, and industrial inspection. These tests established SpineWave as a transformative platform for aquatic robotics.

Fish use their lateral lines to sense flows and pressure gradients, enabling them to detect nearby objects and organisms. Towards replicating this capability, we demonstrated successful leader-follower formation swimming using flow pressure sensing in our undulatory robotic fish ($\mu$Bot/MUBot). The follower $\mu$Bot is equipped at its head with bilateral pressure sensors to detect signals excited by both its own and the leader's movements. First, using experiments with static formations between an undulating leader and a stationary follower, we determined the formation that resulted in strong pressure variations measured by the follower. This formation was then selected as the desired formation in free swimming for obtaining an expert policy. Next, a long short-term memory neural network was used as the control policy that maps the pressure signals along with the robot motor commands and the Euler angles (measured by the onboard IMU) to the steering command. The policy was trained to imitate the expert policy using behavior cloning and Dataset Aggregation (DAgger). The results show that with merely two bilateral pressure sensors and less than one hour of training data, the follower effectively tracked the leader within distances of up to 200 mm (= 1 body length) while swimming at speeds of 155 mm/s (= 0.8 body lengths/s). This work highlights the potential of fish-inspired robots to effectively navigate fluid environments and achieve formation swimming through the use of flow pressure feedback.

Miniature underwater robots play a crucial role in the exploration and development of marine resources, particularly in confined spaces and high-pressure deep-sea environments. This study presents the design, optimization, and performance of a miniature robotic fish, powered by the oscillation of bio-inspired fins. These fins feature a rigid-flexible hybrid structure and use an eccentric rotating mass (ERM) vibration motor as the excitation source to generate high-frequency unidirectional oscillations that induce acoustic streaming for propulsion. The drive mechanism, powered by miniature ERM vibration motors, eliminates the need for complex mechanical drive systems, enabling complete isolation of the entire drive system from the external environment and facilitating the miniaturization of the robotic fish. A compact, untethered robotic fish, measuring 85*60*45 mm^3, is equipped with three bio-inspired fins located at the pectoral and caudal positions. Experimental results demonstrate that the robotic fish achieves a maximum forward swimming speed of 1.36 body lengths (BL) per second powered by all fins and minimum turning radius of 0.6 BL when powered by a single fin. These results underscore the significance of employing the ERM vibration motor in advancing the development of highly maneuverable, miniature untethered underwater robots for various marine exploration tasks.

Scombrid fishes and tuna are efficient swimmers capable of maximizing performance to escape predators and save energy during long journeys. A key aspect in achieving these goals is the flexibility of the tail, which the fish optimizes during swimming. Though, the robotic counterparts, although highly efficient, have partially investigated the importance of flexibility. We have designed and tested a fish-like robotic platform (of 30 cm in length) to quantify performance with a tail made flexible through a torsional spring placed at the peduncle. Body kinematics, forces, and power have been measured and compared with real fish. The platform can vary its frequency between 1 and 3 Hz, reaching self-propulsion conditions with speed over 1 BL/s and Strouhal number in the optimal range. We show that changing the frequency of the robot can influence the thrust and power achieved by the fish-like robot. Furthermore, by using appropriately tuned stiffness, the robot deforms in accordance with the travelling wave mechanism, which has been revealed to be the actual motion of real fish. These findings demonstrate the potential of tuning the stiffness in fish swimming and offer a basis for investigating fish-like flexibility in bio-inspired underwater vehicles.

The pursuit of agile and efficient underwater robots, especially bio-mimetic robotic fish, has been impeded by challenges in creating motion controllers that are able to fully exploit their hydrodynamic capabilities. This paper addresses these challenges by introducing a novel, model-free, end-to-end control framework that leverages Deep Reinforcement Learning (DRL) to enable agile and energy-efficient swimming of robotic fish. Unlike existing methods that rely on predefined trigonometric swimming patterns like Central Pattern Generators (CPG), our approach directly outputs low-level actuator commands without strong constraint, enabling the robotic fish to learn agile swimming behaviors. In addition, by integrating a high-performance Computational Fluid Dynamics (CFD) simulator with innovative sim-to-real strategies, such as normalized density matching and servo response matching, the proposed framework significantly mitigates the sim-to-real gap, facilitating direct transfer of control policies to real-world environments without fine-tuning. Comparative experiments demonstrate that our method achieves faster swimming speeds, smaller turning radii, and reduced energy consumption compared to the conventional CPG-PID-based controllers. Furthermore, the proposed framework shows promise in addressing complex tasks in diverse scenario, paving the way for more effective deployment of robotic fish in real aquatic environments.

Robotic fish is one of the most promising directions of the new generation of underwater vehicles. Traditional biomimetic fish often mimic fish joints using tandem components like servos, which leads to increased volume, weight and control complexity. In this paper, a new double-joint robotic fish using a composite linkage was designed, where the propulsion mechanism transforms the single-degree-of-freedom rotation of the motor into a double-degree-of-freedom coupled motion, namely caudal peduncle translation and caudal fin rotation. Motion analysis of the propulsion mechanism demonstrates its ability to closely emulate the undulating movement observed in carangiform fish. Experimental results further validate the feasibility of the proposed propulsion mechanism. To improve propulsion efficiency, an analysis is conducted to explore the influence of swing angle amplitude and swing frequency on the swimming speed of the robotic fish. This examination establishes a practical foundation for future research on such robotic fish systems.

Median fins of fish-like swimmers play a crucial role in linear acceleration and maneuvering processes. However, few research focused on untethered robotic fish experiments. Imitating the behaviour of real tuna, we developed a free-swimming bionic tuna with a foldable dorsal fin. The erection of dorsal fin, at proper conditions, can reduce head heave by 50%, enhance linear acceleration by 15.7%, increase turning angular velocity by 32.78%, and turning radius decreasing by 33.13%. Conversely, erecting the dorsal fin increases the wetted surface area, resulting in decreased maximum speed and efficiency during steady swimming phase. This finding partially explains why tuna erect their median fins during maneuvers or acceleration and fold them afterward to reduce drag. In addition, we verified that folding the median fins after acceleration does not significantly affect locomotion efficiency. This study supports the application of morphing median fins in undulating underwater robots and helps to further understand the impact of median fins on fish locomotion.