Geometric analysis of gaits and optimal control for three-link kinematic swimmers

Many robotic systems locomote using gaits - periodic changes of internal shape, whose mechanical interaction with the robot's environment generate characteristic net displacements. Prominent examples with two shape variables are the low Reynolds number 3-link "Purcell swimmer" with inputs of 2 joint angles and the "ideal fluid" swimmer. Gait analysis of these systems allows for intelligent decisions to be made about the swimmer's locomotive properties, increasing the potential for robotic autonomy. In this work, we present comparative analysis of gait optimization using two different methods. The first method is variational approach of "Pontryagin's maximum principle" (PMP) from optimal control theory. We apply PMP for several variants of 3-link swimmers, with and without incorporation of bounds on joint angles. The second method is differential-geometric analysis of the gaits based on curvature (total Lie bracket) of the local connection for 3-link swimmers. Using optimized body-motion coordinates, contour plots of the curvature in shape space give visualization that enables identifying distance-optimal gaits as zero level sets. Combining and comparing results of the two methods enables better understanding of changes in existence, shape and topology of distance-optimal gait trajectories, depending on the swimmers' parameters.Comment: accepted to Automatica, 202

Optimal R&D investment in the management of invasive species

Invasive alien species (IAS) threaten world biodiversity, ecosystem services, and economic welfare. While existing literature has characterized the optimal control of an established IAS, it has not considered how research and development (R&D) into new removal methods or technologies can affect management decisions and costs over time. R&D can lower the costs of control in a management plan and creates an intertemporal trade-off between quick but costly control and gradual but cheaper removal over time. In this paper, we develop and solve a continuous time dynamic optimization model to study how investment in R&D influences the optimal control of an established invasive species. After characterizing the dynamic model solution, we solve the model numerically to study the benefits from R&D in the management of the brown tree snake (Boiga irregularis), and explore how optimal solutions vary across economic and biological conditions. We find that the introduction of R&D significantly reduces overall costs of IAS and management and that the cost reductions substantially outweigh research expenditure. These results imply that policymakers seeking to control IAS should consider R&D as a vital component of cost effective control strategies

Stochastic Analysis: Geometry of Random Processes

A common feature shared by many natural objects arising in probability theory is that they tend to be very “rough”, as opposed to the “smooth” objects usually studied in other branches of mathematics. It is however still desirable to understand their geometric properties, be it from a metric, a topological, or a measure-theoretic perspective. In recent years, our understanding of such “random geometries” has seen spectacular advances on a number of fronts

Park City Lectures on Mechanics, Dynamics, and Symmetry

In these ve lectures, I cover selected items from the following topics: 1. Reduction theory for mechanical systems with symmetry, 2. Stability, bifurcation and underwater vehicle dynamics, 3. Systems with rolling constraints and locomotion, 4. Optimal control and stabilization of balance systems, 5. Variational integrators. Each topic itself could be expanded into several lectures, but I limited myself to what I could reasonably explain in the allotted time. The hope is that the overview is informative enough so that the reader can understand the fundamental ideas and can intelligently choose from the literature for additional details on topics of interest. Compatible with the theme of the PCI graduate school, I assume that the readers are familiar with the elements of geometric mechanics, including the basics of symplectic and Poisson geometry. The reader can find the needed background in, for example, Marsden and Ratiu [1998]

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more