Optimal pilot decisions and flight trajectories in air combat

The thesis concerns the analysis and synthesis of pilot decision-making and the design of optimal flight trajectories. In the synthesis framework, the methodology of influence diagrams is applied for modeling and simulating the maneuvering decision process of the pilot in one-on-one air combat. The influence diagram representations describing the maneuvering decision in a one sided optimization setting and in a game setting are constructed. The synthesis of team decision-making in a multiplayer air combat is tackled by formulating a decision theoretical information prioritization approach based on a value function and interval analysis. It gives the team optimal sequence of tactical data that is transmitted between cooperating air units for improving the situation awareness of the friendly pilots in the best possible way. In the optimal trajectory planning framework, an approach towards the interactive automated solution of deterministic aircraft trajectory optimization problems is presented. It offers design principles for a trajectory optimization software that can be operated automatically by a nonexpert user. In addition, the representation of preferences and uncertainties in trajectory optimization is considered by developing a multistage influence diagram that describes a series of the maneuvering decisions in a one-on-one air combat setting. This influence diagram representation as well as the synthesis elaborations provide seminal ways to treat uncertainties in air combat modeling. The work on influence diagrams can also be seen as the extension of the methodology to dynamically evolving decision situations involving possibly multiple actors with conflicting objectives. From the practical point of view, all the synthesis models can be utilized in decision-making systems of air combat simulators. The information prioritization approach can also be implemented in an onboard data link system.reviewe

Introduction to the functional RG and applications to gauge theories

These lectures contain an introduction to modern renormalization group (RG) methods as well as functional RG approaches to gauge theories. In the first lecture, the functional renormalization group is introduced with a focus on the flow equation for the effective average action. The second lecture is devoted to a discussion of flow equations and symmetries in general, and flow equations and gauge symmetries in particular. The third lecture deals with the flow equation in the background formalism which is particularly convenient for analytical computations of truncated flows. The fourth lecture concentrates on the transition from microscopic to macroscopic degrees of freedom; even though this is discussed here in the language and the context of QCD, the developed formalism is much more general and will be useful also for other systems.Comment: 60 pages, 14 figures, Lectures held at the 2006 ECT* School "Renormalization Group and Effective Field Theory Approaches to Many-Body Systems", Trento, Ital

Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation

Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with Rigid Body Dynamics, these derivatives are difficult to derive analytically and to implement efficiently. To overcome this issue, we extend the modelling tool `RobCoGen' to be compatible with Automatic Differentiation. Additionally, we propose how to automatically obtain the derivatives and generate highly efficient source code. We highlight the flexibility and performance of the approach in two application examples. First, we show a Trajectory Optimization example for the quadrupedal robot HyQ, which employs auto-differentiation on the dynamics including a contact model. Second, we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly moving obstacle in a go-to task by fast, dynamic replanning

Optimal ecosystem management with structural dynamics

We address the problem of optimal management of a self organizing ecosystem along ecological succession. A dynamic carrying capacity is interpreted as depicting the dynamics of habitat creation and occupation along ecological succession. The ecosystem may have three growth modes: pure compensation (concave ecosystem regeneration function), depensation (convex-concave regeneration function) and critical depensation (additionally having negative growth rates for low biomass). We analyse the optimal policies for the management of the ecosystem for the three growth modes. Accordingly, we prove the existence of a Skiba points for certain types of ecosystems. Further, we compare usual golden rule paths with the derived optimal policies near the Skiba points.Ecosystem management; habitat creation; optimal policies; Skiba point

Investigation of Factors Impacting a Helicopter Height-Velocity Diagram

A dynamic helicopter model was incorporated into an optimal control problem to determine minimal landing velocities. The solutions were determined using pseudospectral collocation methods as implemented by the GPOPS-II software. These solutions were then compiled to develop a HV diagram. An HV diagram displays regions of flight based on a helicopter\u27s airspeed and height above the ground in which a safe landing would not be possible following engine failure. The applied methodology for constructing the HV diagram reduced issues involving solution convergence that was encountered in previous research. The influence of ground effect on the dynamic model was also investigated. After analyzing the HV diagrams constructed using five additional ground effect models, the significant impact that a chosen ground effect model has in the overall dynamic model was apparent. Finally, the effect that modifying certain helicopter parameters has on the helicopter\u27s autorotation performance was considered. Optimal control solutions showed a decrease in autorotation capabilities for the case of an increased gross weight as well as for the case of a decreased rotor size

Minimum-lap-time optimisation and simulation

The paper begins with a survey of advances in state-of-the-art minimum-time simulation for road vehicles. The techniques covered include both quasi-steady-state and transient vehicle models, which are combined with trajectories that are either pre-assigned or free to be optimised. The fundamentals of nonlinear optimal control are summarised. These fundamentals are the basis of most of the vehicular optimal control methodologies and solution procedures reported in the literature. The key features of three-dimensional road modelling, vehicle positioning and vehicle modelling are also summarised with a focus on recent developments. Both cars and motorcycles are considered