Optimal Design of Neuro-Mechanical Networks

Abstract: Many biological and artificial systems are made up from similar, relatively simple elements that interact directly with their nearest neighbors. Despite the simplicity of the individual building blocks, systems of this type, network systems, often display complex behavior — an observation which has inspired disciplines such as artificial neural networks and modular robotics. Network systems have several attractive properties, including distributed functionality, which enables robustness, and the possibility to use the same elements in different configurations. The uniformity of the elements should also facilitate development of efficient methods for system design, or even self-reconfiguration. These properties make it interesting to investigate the idea of constructing mechatronic systems based on networks of simple elements.This thesis concerns modeling and optimal design of a class of active mechanical network systems referred to as Neuro-Mechanical Networks (NMNs). To make matters concrete, a mathematical model that describes an actuated truss with an artificial recurrent neural network superimposed onto it is developed and used. A typical NMN is likely to consist of a substantial number of elements, making design of NMNs for various tasks a complex undertaking. For this reason, the use of numerical optimization methods in the design process is advocated. Application of such methods is exemplified in four appended papers that describe optimal design of NMNs which should take on static configurations or follow time-varying trajectories given certain input stimuli. The considered optimization problems are nonlinear, non-convex, and potentially large-scale, but numerical results indicate that useful designs can be obtained in practice.The last paper in the thesis deals with a solution method for optimization problems with matrix inequality constraints. The method described was developed primarily for solving optimization problems stated in some of the other appended papers, but is also applicable to other problems in control theory and structural optimization.