A Geometrical, Reachable Set Approach for Constrained Pursuit–Evasion Games With Multiple Pursuers and Evaders

This paper presents a solution strategy for deterministic time-optimal pursuit–evasion games with linear state constraints, convex control constraints, and linear dynamics that is consistent with linearized relative orbital motion models such as the Clohessy–Wiltshire equations and relative orbital elements. The strategy first generates polytopic inner approximations of the players’ reachable sets by solving a sequence of convex programs. A bisection method then computes the optimal termination time, which is the least time at which a set containment condition is satisfied. The pursuit–evasion games considered are games with (1) a single pursuer and single evader, (2) multiple pursuers and a single evader, and (3) a single pursuer and multiple evaders. Compared to variational methods, this reachable set strategy leads to a tractable formulation even when there are state and control constraints. The efficacy of the strategy is demonstrated in three numerical simulations for a constellation of satellites in close proximity in low earth orbit

AUTONOMOUS SPACECRAFT RENDEZVOUS WITH A TUMBLING OBJECT: APPLIED REACHABILITY ANALYSIS AND GUIDANCE AND CONTROL STRATEGIES

Rendezvous and proximity operations are an essential component of both military and commercial space missions and are rising in complexity. This dissertation presents an applied reachability analysis and develops a computationally feasible autonomous guidance algorithm for the purpose of spacecraft rendezvous and proximity maneuvers around a tumbling object. Recent advancements enable the use of more sophisticated, computation-based algorithms, instead of traditional control methods. These algorithms are desirable for autonomous applications due to their ability to optimize performance and explicitly handle constraints (e.g., safety, control limits). In an autonomous setting, however, some important questions must be answered before an algorithm implementation can be realized. First, the feasibility of a maneuver is addressed by analyzing the fundamental spacecraft relative dynamics. Particularly, a set of initial relative states is computed and visualized from which the desired rendezvous state can be reached (i.e., backward reachability analysis). Second, with the knowledge that a maneuver is feasible, the Model Predictive Control (MPC) framework is utilized to design a stabilizing feedback control law that optimizes performance and incorporates constraints such as control saturation limits and collision avoidance. The MPC algorithm offers a computationally efficient guidance strategy that could potentially be implemented in real-time on-board a spacecraft.http://archive.org/details/autonomousspacec1094560364Major, United States Air ForceApproved for public release; distribution is unlimited

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

Quantum optimal control, a toolbox for devising and implementing the shapes of external fields that accomplish given tasks in the operation of a quantum device in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The last few years have seen a rapid evolution and expansion of the field. We review here recent progress in our understanding of the controllability of open quantum systems and in the development and application of quantum control techniques to quantum technologies. We also address key challenges and sketch a roadmap for future developments

Hausdorff Distance between Norm Balls and their Linear Maps

We consider the problem of computing the (two-sided) Hausdorff distance between the unit $\ell_{p_{1}}$ and $\ell_{p_{2}}$ norm balls in finite dimensional Euclidean space for $1 < p_1 < p_2 \leq \infty$, and derive a closed-form formula for the same. We also derive a closed-form formula for the Hausdorff distance between the $k_1$ and $k_2$ unit $D$-norm balls, which are certain polyhedral norm balls in $d$ dimensions for $1 \leq k_1 < k_2 \leq d$. When two different $\ell_p$ norm balls are transformed via a common linear map, we obtain several estimates for the Hausdorff distance between the resulting convex sets. These estimates upper bound the Hausdorff distance or its expectation, depending on whether the linear map is arbitrary or random. We then generalize the developments for the Hausdorff distance between two set-valued integrals obtained by applying a parametric family of linear maps to different $\ell_p$ unit norm balls, and then taking the Minkowski sums of the resulting sets in a limiting sense. To illustrate an application, we show that the problem of computing the Hausdorff distance between the reach sets of a linear dynamical system with different unit norm ball-valued input uncertainties, reduces to this set-valued integral setting

Assessing plant design with regards to MPC performance using a novel multi-model prediction method

Model Predictive Control (MPC) is nowadays ubiquitous in the chemical industry and offers significant advantages over standard feedback controllers. Notwithstanding, projects of new plants are still being carried out without assessing how key design decisions, e.g., selection of production route, plant layout and equipment, will affect future MPC performance. The problem addressed in this Thesis is comparing the economic benefits available for different flowsheets through the use of MPC, and thus determining if certain design choices favour or hinder expected profitability. The Economic MPC Optimisation (EMOP) index is presented to measure how disturbances and restrictions affect the MPC’s ability to deliver better control and optimisation. To the author’s knowledge, the EMOP index is the first integrated design and control methodology to address the problem of zone constrained MPC with economic optimisation capabilities (today's standard in the chemical industry). This approach assumes the availability of a set of linear state-space models valid within the desired control zone, which is defined by the upper and lower bounds of each controlled and manipulated variable. Process economics provides the basis for the analysis. The index needs to be minimised in order to find the most profitable steady state within the zone constraints towards which the MPC is expected to direct the process. An analysis of the effects of disturbances on the index illustrates how they may reduce profitability by restricting the ability of an MPC to reach dynamic equilibrium near process constraints, which in turn increases product quality giveaway and costs. Hence the index monetises the required control effort. Since linear models were used to predict the dynamic behaviour of chemical processes, which often exhibit significant nonlinearity, this Thesis also includes a new multi-model prediction method. This new method, called Simultaneous Multi-Linear Prediction (SMLP), presents a more accurate output prediction than the use of single linear models, keeping at the same time much of their numerical advantages and their relative ease of obtainment. Comparing the SMLP to existing multi-model approaches, the main novelty is that it is built by defining and updating multiple states simultaneously, thus eliminating the need for partitioning the state-input space into regions and associating with each region a different state update equation. Each state’s contribution to the overall output is obtained according to the relative distance between their identification point, i.e., the set of operating conditions at which an approximation of the nonlinear model is obtained, and the current operating point, in addition to a set of parameters obtained through regression analysis. Additionally, the SMLP is built upon data obtained from step response models that can be obtained by commercial, black-box dynamic simulators. These state-of-the-art simulators are the industry’s standard for designing large-scale plants, the focus of this Thesis. Building an SMLP system yields an approximation of the nonlinear model, whose full set of equations is not of the user’s knowledge. The resulting system can be used for predictive control schemes or integrated process design and control. Applying the SMLP to optimisation problems with linear restrictions results in convex problems that are easy to solve. The issue of model uncertainty was also addressed for the EMOP index and SMLP systems. Due to the impact of uncertainty, the index may be defined as a numeric interval instead of a single number, within which the true value lies. A case of study consisting of four alternative designs for a realistically sized crude oil atmospheric distillation plant is provided in order to demonstrate the joint use and applicability of both the EMOP index and the SMLP. In addition, a comparison between the EMOP index and a competing methodology is presented that is based on a case study consisting of the activated sludge process of a wastewater treatment plant

Convexity Applications in Single and Multi-Agent Control

The focus of this dissertation is in the application of convexity for control problems; specifically, single-agent problems with linear or nonlinear dynamics and multi-agent problems with linear dynamics. A mixture of convex and non-convex constraints for optimal control problems is also considered. The main contributions of this dissertation include: 1) a convexification of single-agent problems with linear dynamics and annular control constraint, 2) a technique for controlling bounded nonlinear single-agent systems, and 3) a technique for solving multi-agent pursuit-evasion games with linear dynamics and convex control and state constraints. The first result shows that for annularly constrained linear systems, controllability is a sufficient condition for a free or fixed time problem to be solvable as a sequence of convex optimization problems. The second result shows that if a nonlinear system is bounded and “ordered”, it is possible to use a convex combination of bounding linear systems to design a control for the nonlinear system. The third result takes advantage of a convex reachable set computation for each agent in solving games using a geometrical approach. Altogether, the theoretical and computational results demonstrate the significance of convex analysis in solving non-convex control problems

Path and Motion Planning for Autonomous Mobile 3D Printing

Autonomous robotic construction was envisioned as early as the ‘90s, and yet, con- struction sites today look much alike ones half a century ago. Meanwhile, highly automated and efficient fabrication methods like Additive Manufacturing, or 3D Printing, have seen great success in conventional production. However, existing efforts to transfer printing technology to construction applications mainly rely on manufacturing-like machines and fail to utilise the capabilities of modern robotics. This thesis considers using Mobile Manipulator robots to perform large-scale Additive Manufacturing tasks. Comprised of an articulated arm and a mobile base, Mobile Manipulators, are unique in their simultaneous mobility and agility, which enables printing-in-motion, or Mobile 3D Printing. This is a 3D printing modality, where a robot deposits material along larger-than-self trajectories while in motion. Despite profound potential advantages over existing static manufacturing-like large- scale printers, Mobile 3D printing is underexplored. Therefore, this thesis tack- les Mobile 3D printing-specific challenges and proposes path and motion planning methodologies that allow this printing modality to be realised. The work details the development of Task-Consistent Path Planning that solves the problem of find- ing a valid robot-base path needed to print larger-than-self trajectories. A motion planning and control strategy is then proposed, utilising the robot-base paths found to inform an optimisation-based whole-body motion controller. Several Mobile 3D Printing robot prototypes are built throughout this work, and the overall path and motion planning strategy proposed is holistically evaluated in a series of large-scale 3D printing experiments

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

Quantum optimal control, a toolbox for devising and implementing the shapes of external fields that accomplish given tasks in the operation of a quantum device in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The last few years have seen a rapid evolution and expansion of the field. We review here recent progress in our understanding of the controllability of open quantum systems and in the development and application of quantum control techniques to quantum technologies. We also address key challenges and sketch a roadmap for future developments.Comment: this is a living document - we welcome feedback and discussio