PhD Defence Yannik Wotte | Geometric methods for dynamics optimization and model order reduction

Geometric methods for dynamics optimization and model order reduction

Yannik Wotte is a PhD student in the Department of Robotics and Mechatronics. (Co)promotors are prof.dr.ir. S. Stramigioli and dr. F. Califano from the Faculty of Electrical Engineering, Mathematics and Computer Science.

Distributed multi-physical robotics systems are at the frontier of robotics research: soft robots deform in response to external stimuli; drones and robotic birds rely on increasingly complex fluid-structure interactions. Each benefits from energy-efficient motion, which reduces power demands and thus the weight, size and cost of motors and batteries. Control optimization promises to enable this energy-efficiency. However, complex dynamics make the above systems cumbersome to simulate. This significantly slows iterative optimization, which relies on repeated simulation. Finally, what classifies as energy-efficient motion is strongly system-dependent and not necessarily useful: for example, it may be energy-efficient for a robot to simply fall over. 

This thesis aims to address the above problems by geometric and computational methods in three distinct topics: model order reduction, dynamics optimization, and nonlinear dynamics. 

First, model order reduction via Lie groups was formalized and implemented. The framework recovers popular model reduction methods as special cases and outperforms existing techniques on practically relevant datasets. The method applies to multi-physical, port-Hamiltonian systems: it is shown to preserve energetic structure, input and output ports in the reduced-order system, meaning the simplified model follows physical laws similar to the original. 

Second, a generalized geometric adjoint method for the optimization of parameterized dynamical systems on manifolds and Lie groups was developed. This resulted in a general framework for control and dynamics optimization and enabled optimizing an inherently passive, nonlinear state-feedback controller for a 3D rigid body. 

Third, periodic motions of mechanical systems are applied as energy-efficient target trajectories for periodic tasks. It is shown that Lyapunov subcenter manifolds, particular families of periodic oscillations, acquire stronger properties in conservative mechanical systems, becoming Eigenmanifolds. Periodic motions on Eigenmanifolds are optimized for energy-efficient pick-and-place tasks. 

Together, the three parts form a toolkit that simplifies complex systems, optimizes their behavior, and discovers efficient motions within them.