In nature, through millions of years of evolution, fish and cetaceans have developed fast efficient and highly manoeuvrable methods of marine propulsion. A recent explosion in demand for sub sea robotics, for conducting tasks such as sub sea exploration and survey has left developers desiring to capture some of the novel mechanisms evolved by fish and cetaceans to increase the efficiency of speed and manoeuvrability of sub sea robots. Research has revealed that interactions with vortices and other unsteady fluid effects play a significant role in the efficiency of fish and cetaceans. However attempts to duplicate this with robotic fish have been limited by the difficulty of predicting or sensing such uncertain fluid effects. This study aims to develop a gait generation method for a robotic fish with a degree of passivity which could allow the body to dynamically interact with and potentially synchronise with vortices within the flow without the need to actually sense them. In this study this is achieved through the development of a novel energy based gait generation tactic, where the gait of the robotic fish is determined through regulation of the state energy rather than absolute state position. Rather than treating fluid interactions as undesirable disturbances and `fighting' them to maintain a rigid geometric defined gait, energy based control allows the disturbances to the system generated by vortices in the surrounding flow to contribute to the energy of the system and hence the dynamic motion. Three different energy controllers are presented within this thesis, a deadbeat energy controller equivalent to an analytically optimised model predictive controller, a $H_\infty$ disturbance rejecting controller with a novel gradient decent optimisation and finally a error feedback controller with a novel alternative error metric. The controllers were tested on a robotic fish simulation platform developed within this project. The simulation platform consisted of the solution of a series of ordinary differential equations for solid body dynamics coupled with a finite element incompressible fluid dynamic simulation of the surrounding flow. results demonstrated the effectiveness of the energy based control approach and illustrate the importance of choice of controller in performance.

Soft robotics are robots, manipulators, and technologies using soft/compliant materials as the key elements of the robotic bodies instead of traditional rigid materials like metals. However, they face problems in the following areas: 1. Low energy density. In many cases of soft robots, the large blocks of elastomer are barely stiff enough for self-supporting and working as end-effectors, let alone high-speed motion or high-force manipulation. 2. Inconvenient actuation methods. The most widely used actuation method of soft robots is fluidic pumping to the elastomeric bodies, which is called pneumatic networks (Pneu-Nets). However, the tube and pipe system dissipate too much energy via viscous friction, leading to a low energy efficiency, especially when the actuation frequency is high. 3. Difficulty in estimating robotic morphology or motion trajectory. The elastic body of a soft robot is usually made of an infinite number of tiny elastic cubes that deform continuously. Each of the cubes has six degrees of freedom (DOF), and they all together form an integrated constitutive equation that has a number of six times DOF coefficients, even if we only consider statics or pseudo-statics. During dynamic analysis, the comparable magnitudes of elastic energy, kinetic energy, and gravitational energy make the calculations even harder. With the inspiration from the prestressing assembly and the snapping of a steel hair clip, this work proposes that we use a prestressed bistable self-interacting kinked ribbon, which we term hair clip mechanism (HCM), made from paper, plastic, metal, carbon-fiber-reinforced plastic (CFRP) plates, etc., as the force amplifier to increase the functionalities of soft/compliant robots and manipulators. The efforts and contributions in this research include all three aspects of theory, simulation, and applications: 1. New mathematical model and solutions (theory). The assembly and actuation of HCMs include the processes of lateral-torsional buckling, post-buckling morphing, and snap-through bucking, which are highly non-linear. To calculate and estimate the deformation of such mechanisms, a mathematical model based on elastic instability and Euler-Bernoulli beam theory is derived and used for analyses and applications. Corresponding design algorithms for HCM robots are derived based on the theory. 2. Finite-element (FE) simulation and verification. To ensure the accuracy of the theoretical solutions and the correctness of the experiments, FE software is used to replicate the processes of lateral-torsional buckling, post-buckling morphing, snap-through buckling, specific robotic applications, etc. 3. Robotic applications of HCMs. The energy-storing-and-releasing properties of HCMs make them very suitable for increasing the controllability and controllability of soft robots/manipulators. Different from both rigid materials and elastomeric soft materials, HCMs and their major materials were termed “compliant mechanisms/materials.” These materials have moduli comparable to rigid materials but are compliant and deformable thanks to their small out-of-plane bending stiffness. Because of the small deformation assumption used, the mathematical model and solutions built and derived in this work are only a first approximation with qualitative-level correctness. However, they offer an estimation error within 5% compared to the experiments and FE simulation data in the specific problem of the assembly of HCMs involving lateral-torsional buckling and post-buckling responses. To calculate the snap-through buckling, they give an error of ~10% because of the additional assumption of the snapping trajectory used. As for applications, the bistable HCMs are mounted on a soft gripper, a terrestrial galloping runner, and three different soft robotic fish. The motor-driven snapping soft gripper exploits the elastic instability of HCMs to achieve rapid closing within 46ms and reversible operation over a span of 86mm, 2.7 times and 10.9 times better than the reference gripper, respectively. The single-actuated untethered terrestrial soft crawler is capable of jumping off and can gallop at a speed of 313 mm/s or 1.56 body length per second (BL/s), faster than most previous soft crawlers in mm/s and BL/s. The pneumatic HCM fish swim at 26.54 cm/s or 1.40BL/s in a lab-condition aquarium tank, about twice as fast as its reference group. The motor-driven HCM fish has a speed of 2.03 BL/s or 42.6 cm/s, 2-3 times faster than previous untethered soft robotic fish. The newest HCM fish robot uses CFRP as its material, herein referred to as “CarbonFish.” Preliminary evaluations of CarbonFish have evidenced an undulation frequency approaching 10~13 Hz and an operating time of about 40 min, suggesting its potential to outperform other biologically inspired aquatic entities and real fish.