Computational Optimisation of Robotic Swimmers

Robotic swimmers offer innovative solutions for a range of problems in Science and Engineering. Soft robotic micro-swimmers can be actuated by external magnetic or acoustic fields and are investigated for targeted drug delivery. Robotic fish has applications in marine conservation where it can be used to study animal behaviour and aid the exploration of areas that are difficult to access. Autonomous underwater robotic swimmers can undertake surveillance tasks and support the maintenance of marine engineering structures ranging from military applications to renewable energy. Devices should be energy efficient and highly manoeuvrable. This poses an optimisation problem for the shape and control of the robotic swimmer. It is the objective of this project to develop, implement and test suitable computational strategies for this optimisation problem. The propulsion of robotic swimmers is based on its interaction with the surrounding fluid and generally involves periodic motion. While analytical models are available for some micro-swimmers in the viscous limit, simulating swimming at moderate or large Reynolds numbers must be based on numerical methods and on a strategy to resolve the coupling between the fluid and solid sub-solvers. Optimisation requires that this fluid-structure interaction (FSI) solver is executed many times and for a range of geometric configurations and control parameters. The viability of the optimisation procedure therefore depends on the accuracy, robustness and computational efficiency of the FSI solver at its heart. The investigator, Professor Dettmer, has extensive expertise in numerical FSI solution strategies and is well-placed to take his work to the next stage, namely its integration in shape and time-distributed control optimisation for dynamic FSI. This is an emerging field, and methodologies applicable to real-world problems are not available. Two different approaches are considered: The motion of the swimmer and the induced fluid flow are generally smooth. Therefore gradient-based methods are considered. Yet, a strategy based on exact sensitivities is likely to be prohibitively expensive for realistic three-dimensional models. It requires that several forward and backward passes in time are performed. The backward passes must be provided with the state of the system in every time step of the preceding forward pass. Hence, the fluid velocities and pressures in each time step must be stored, quickly resulting in excessive memory requirements. Therefore, strategies for obtaining approximate sensitivities will be developed, tailored to specific FSI solvers. In particular, the optimally efficient, staggered solution techniques, proposed by Professor Dettmer, tested and proven in academic and industrial contexts, will be exploited. A hybrid approach based on direct and adjoint sensitivities will be investigated, seeking to avoid the need for excessive data storage. In the second approach, black box optimisation procedures will be applied, interacting with the FSI solver only in terms of input (shape and control parameters) and output (swimming speed and energy). The parameterisation of the shape and control must be undertaken carefully such that the number of optimisation variables remains moderate. The focus will be on Bayesian optimisation strategies and on approximate gradient descent. Bayesian optimisation is restricted to a relatively small number of free parameters and has been applied successfully in robotics. Approximate gradient descent strategies based on gradient recovery from small point clouds have proven promising in recent research of the investigator on problems with larger sets of design variables and will be further developed in this project.