Computing Convex Coverage Sets for Faster Multi-objective Coordination

In this article, we propose new algorithms for multi-objective coordination graphs (MO- CoGs). Key to the efficiency of these algorithms is that they compute a convex coverage set (CCS) instead of a Pareto coverage set (PCS). Not only is a CCS a sufficient solution set for a large class of problems, it also has important characteristics that facilitate more efficient solutions. We propose two main algorithms for computing a CCS in MO-CoGs. Convex multi-objective variable elimination (CMOVE) computes a CCS by performing a series of agent eliminations, which can be seen as solving a series of local multi-objective subproblems. Variable elimination linear support (VELS) iteratively identifies the single weight vector w that can lead to the maximal possible improvement on a partial CCS and calls variable elimination to solve a scalarized instance of the problem for w. VELS is faster than CMOVE for small and medium numbers of objectives and can compute an ε-approximate CCS in a fraction of the runtime. In addition, we propose variants of these methods that employ AND/OR tree search instead of variable elimination to achieve memory efficiency. We analyze the runtime and space complexities of these methods, prove their correctness, and compare them empirically against a naive baseline and an existing PCS method, both in terms of memory-usage and runtime. Our results show that, by focusing on the CCS, these methods achieve much better scalability in the number of agents than the current state of the art

Geometry Synthesis and Multi-Configuration Rigidity of Reconfigurable Structures

Reconfigurable structures are structures that can change their shapes to change their functionalities. Origami-inspired folding offers a path to achieving shape changes that enables multi-functional structures in electronics, robotics, architecture and beyond. Folding structures with many kinematic degrees of freedom are appealing because they are capable of achieving drastic shape changes, but are consequently highly flexible and therefore challenging to implement as load-bearing engineering structures. This thesis presents two contributions with the aim of enabling folding structures with many degrees of freedom to be load-bearing engineering structures. The first contribution is the synthesis of kirigami patterns capable of achieving multiple target surfaces. The inverse design problem of generating origami or kirigami patterns to achieve a single target shape has been extensively studied. However, the problem of designing a single fold pattern capable of achieving multiple target surfaces has received little attention. In this work, a constrained optimization framework is presented to generate kirigami fold patterns that can transform between several target surfaces with varying Gaussian curvature. The resulting fold patterns have many kinematic degrees of freedom to achieve these drastic geometric changes, complicating their use in the design of practical load-bearing structures. To address this challenge, the second part of this thesis introduces the concept of multi-configuration rigidity as a means of achieving load-bearing capabilities in structures with multiple degrees of freedom. By embedding springs and unilateral constraints, multiple configurations are rigidly held due to the prestress between the springs and unilateral constraints. This results in a structure capable of rigidly supporting finite loads in multiple configurations so long as the loads do not exceed some threshold magnitude. A theoretical framework for rigidity due to embedded springs and unilateral constraints is developed, followed by a systematic method for designing springs to maximize the load-bearing capacity in a set of target configurations. An experimental study then validates theoretical predictions for a linkage structure. Together, the application of geometry synthesis and multi-configuration rigidity constitute a path towards engineering reconfigurable load-bearing structures.</p

A contribution to the development of assistance systems for serial and parallel robots using the example of mobile concrete pumps and tendon-based rack feeders

Der zunehmende Kostendruck in der Industrie zwingt die Unternehmen, jegliche Art von Prozessen, sei es beispielsweise der Herstellungsprozess eines Produkts oder ein logistischer Lagerverwaltungs-Prozess, effizient zu gestalten. Ein Potential zur Effizienzsteigerung bildet die Prozessautomatisierung. Grenzen der Automatisierung entstehen bei Arbeitsabläufen, die eine gewisse Flexibilität erfordern, wie beispielsweise bei einem Prozess in einer sich ständig ändernden Umgebung mit Personen oder anderen bewegten Hindernissen. Ist ein Prozess vollautomatisiert aufgrund des hohen technischen Aufwands auch wirtschaftlich nicht realisierbar, bieten Assistenzsysteme zumindest die Möglichkeit, Arbeitsabläufe zu optimieren, wobei dem Assistenzsystem, in der Regel also der Maschine, nicht die volle Verantwortung über den Prozessablauf übertragen wird. In diesem Beitrag wird auf Basis eines quadratischen Optimierungsproblems ein echtzeitfähiger Algorithmus entwickelt, mit dem es möglich ist, die inverse Kinematik kinematisch redundanter Manipulatoren und die minimale Seilkraftverteilung seilbasierter Stewart-Gough-Plattformen zu lösen. Diese Lösung bildet die Grundlage für modellbasierte Regelungskonzepte, womit voll- bzw. teilautomatierte Prozesse (Assistenzsysteme) serieller und paralleler Roboter realisiert werden können. Der in diesem Beitrag entwickelte Algorithmus wird auf zwei Beispiele aus dem Bereich der Robotik angewendet: die Autobetonpumpe als ein Beispiel serieller, kinematisch redundanter Manipulatoren und das seilbasierte Regalbediengerät als ein Beispiel für parallele Seilroboter auf Basis der Stewart-Gough-Plattform.The increasing cost pressure in the industry forces the companies to design any kind of process in an efficient manner, for instance the manufacturing process of a product or a logistical warehouse management process. An increase in efficiency can be established by a process automation.However, limitations of automation arise in operations which require a certain flexibility such as a process in a permanently changing environment with persons and other moving obstacles. Once a fully automated process cannot be realised due to its technical complexity and lack of profitability, at least assistance systems can offer the potential to optimize the work flow, whereby the assistance system, so usually the machine, does not bear the full responsibility. In this contribution a real-time capable algorithm is developed based on the quadratic optimization problem which enables the calculation of the inverse kinematics of kinematically redundant manipulators, and of optimal tendon force distributions of tendon-based Stewart-Gough platforms. This solution constitutes the basis for model-based control concepts in order to realise fully and semi-automatic processes (assistance systems) of serial and parallel robots. The algorithm developed in this contribution is applied on two examples from the field of robotics: the mobile concrete pump as an example of a serial, kinematically redundant manipulator, and the tendon-based rack feeder system as an example of a parallel tendon robot based on the Stewart-Gough platform

Estimating The Number Of Vertices Of A Polyhedron

Given a polyhedron P by a list of inequalities we develop unbiased estimates of the number of vertices and bases of P . The estimates are based on applying tree estimation methods to the reverse search technique. The time to generate an unbiased estimate is essentially bounded by the time taken to solve a linear program on P with the simplex method. Computational experience is reported. The method can be applied to estimate the output size of other enumeration problems solvable by reverse search. 2000 Elsevier Science B.V. All rights reserved