@techreport{SchmidtFuegenschuh2023, type = {Working Paper}, author = {Schmidt, Johannes and F{\"u}genschuh, Armin}, title = {Trajectory optimization for arbitrary layered geometries in wire-arc additive manufacturing}, doi = {10.26127/BTUOpen-6267}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-62678}, year = {2023}, abstract = {In wire-arc additive manufacturing, a wire is molten by an electrical or laser arc and deposited droplet-by-droplet to construct the desired workpiece, given as a set of two-dimensional layers. The weld source can move freely over a substrate plate, processing each layer, but there is also the possibility of moving without welding. A primary reason for stress inside the material is the large thermal gradient caused by the weld source, resulting in lower product quality. Thus, it is desirable to control the temperature of the workpiece during the process. One way of its optimization is the trajectory of the weld source. We consider the problem of finding a trajectory of the moving weld source for a single layer of an arbitrary workpiece that maximizes the quality of the part and derive a novel mixed-integer PDE-constrained model, including the calculation of a detailed temperature distribution measuring the overall quality. The resulting optimization problem is linearized and solved using the state-of-the-art numerical solver IBM CPLEX. Its performance is examined by several computational studies.}, subject = {Mixed-integer programming; Trajektorie ; Partielle Differentialgleichung; Finite-Volumen-Methode; W{\"a}rmeleitung; Wire are additive manufacturing; Trajectory planning; Partial differential equations; Finite element method; Heat conduction; Gemischt-ganzzahlige Programmierung; Additive Draht-Lichtbogen-Fertigung,; Trajektorienplanung; Partielle Differenzialgleichungen; Finite-Elemente-Methode; W{\"a}rmeleitung}, language = {en} } @techreport{BeisegelBuhlIsraretal.2021, type = {Working Paper}, author = {Beisegel, Jesse and Buhl, Johannes and Israr, Rameez and Schmidt, Johannes and Bambach, Markus and F{\"u}genschuh, Armin}, title = {Mixed-integer programming for additive manufacturing}, doi = {10.26127/BTUOpen-5731}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-57317}, year = {2021}, abstract = {Since the beginning of its development in the 1950s, mixed integer programming (MIP) has been used for a variety of practical application problems, such as sequence optimization. Exact solution techniques for MIPs, most prominently branch-and-cut techniques, have the advantage (compared to heuristics such as genetic algorithms) that they can generate solutions with optimality certificates. The novel process of additive manufacturing opens up a further perspective for their use. With the two common techniques, Wire Arc Additive Manufacturing (WAAM) and Laser Powder Bed Fusion (LPBD), the sequence in which a given component geometry must be manufactured can be planned. In particular, the heat transfer within the component must be taken into account here, since excessive temperature gradients can lead to internal stresses and warpage after cooling. In order to integrate the temperature, heat transfer models (heat conduction, heat radiation) are integrated into a sequencing model. This leads to the problem class of MIPDECO: MIPs with partial differential equations (PDEs) as further constraints. We present these model approaches for both manufacturing techniques and carry out test calculations for sample geometries in order to demonstrate the feasibility of the approach.}, subject = {Wire arc additive manufacturing; Laser powder bed fusion; Mixed-integer programming; Partial differential equations; Finite element method; Additive Fertigung mit Drahtlichtbogen; Laser-Pulverbett-Schmelzen; Gemischt-ganzzahlige Programmierung; Partielle Differenzialgleichungen; Finite-Elemente-Methode; Rapid Prototyping ; Ganzzahlige Optimierung; Finite-Elemente-Methode; Partielle Differentialgleichung}, language = {en} } @techreport{SchmidtFuegenschuh2021, type = {Working Paper}, author = {Schmidt, Johannes and F{\"u}genschuh, Armin}, title = {Planning inspection flights with an inhomogeneous fleet of micro aerial vehicles}, doi = {10.26127/BTUOpen-5656}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-56569}, year = {2021}, abstract = {We consider the problem of planning an inspection flight to a given set of waypo- ints using an inhomogeneous fleet of multirotor, battery-driven micro aerial vehicles (MAVs). Therein, two subproblems must be solved. On the one side, the detailed trajectories of all MAVs must be planned, taking technical and environmental restrictions into account and on the other side, the MAVs must be assigned to the waypoints considering their installed equipment. The goal is to visit all waypoints in minimal time. The strong interaction of the two subproblems makes it necessary to tackle them simultaneously. Several aspects are taken into account to allow realistic solutions. A two-level time grid approach is applied to achieve smooth trajectories, while the flight dynamics of the MAVs are modeled in great detail. Safety distances must be maintained between them and they can recharge at charging stations located within the mission area. There can be polyhedral restricted air spaces that must be avoided. Furthermore, weather conditions are incorporated by polyhedral wind zones affecting the drones and each waypoint has a time window within it must be visited. We formulate this problem as a mixed-integer linear program and show whether the state-of-the-art numerical solver Gurobi is applicable to solve model instances.}, subject = {Mixed integer linear programming; Inspection path planning; Trajectory planning; Micro aerial vehicles; Gemischt-ganzzahlige Programmierung; Inspektionspfadplanung; Trajektorienplanung; Kleinstdrohnen; Ganzzahlige Optimierung; Tourenplanung; Drohne }, language = {en} } @techreport{SchmidtBuhlFuegenschuh2021, type = {Working Paper}, author = {Schmidt, Johannes and Buhl, Johannes and F{\"u}genschuh, Armin}, title = {A finite element approach for trajectory optimization in Wire-Arc Additive Manufacturing}, editor = {F{\"u}genschuh, Armin}, doi = {10.26127/BTUOpen-5575}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-55753}, year = {2021}, abstract = {In wire-arc additive manufacturing (WAAM), the desired workpiece is built layerwise by a moving heat source depositing droplets of molten wire on a substrate plate. To reduce material accumulations, the trajectory of the weld source should be continuous, but transit moves without welding, called deadheading, are possible. The enormous heat of the weld source causes large temperature gradients, leading to a strain distribution in the welded material which can lead even to cracks. In summary, it can be concluded that the temperature gradient reduce the quality of the workpiece. We consider the problem of finding a trajectory of the weld source with minimal temperature deviation from a given target temperature for one layer of a workpiece with welding segments broader than the width of the weld pool. The temperature distribution is modeled using the finite element method. We formulate this problem as a mixed-integer linear programming model and demonstrate its solvability by a standard mixed-integer solver.}, subject = {Additive manufacturing; Heat equation; Path optimization; Finite element method; Mixed-integer linear programming; Additive Fertigung; Pfadoptimierung; W{\"a}rmeleitungsgleichung; Finite-Elemente-Methode; Gemischt-ganzzahlige lineare Programmierung; Rapid Prototyping ; W{\"a}rmeleitungsgleichung; Bahnplanung; Ganzzahlige lineare Optimierung; Finite-Elemente-Methode}, language = {en} } @techreport{SchmidtFuegenschuh2021, type = {Working Paper}, author = {Schmidt, Johannes and F{\"u}genschuh, Armin}, title = {A two-time-level model for mission and flight planning of an inhomogeneous fleet of unmanned aerial vehicles}, editor = {F{\"u}genschuh, Armin}, doi = {10.26127/BTUOpen-5461}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-54619}, year = {2021}, abstract = {We consider the mission and flight planning problem for an inhomogeneous fleet of unmanned aerial vehicles (UAVs). Therein, the mission planning problem of assigning targets to a fleet of UAVs and the flight planning problem of finding optimal flight trajectories between a given set of waypoints are combined into one model and solved simultaneously. Thus, trajectories of an inhomogeneous fleet of UAVs have to be specified such that the sum of waypoint-related scores is maximized, considering technical and environmental constraints. Several aspects of an existing basic model are expanded to achieve a more detailed solution. A two-level time grid approach is presented to smooth the computed trajectories. The three-dimensional mission area can contain convex-shaped restricted airspaces and convex subareas where wind affects the flight trajectories. Furthermore, the flight dynamics are related to the mass change, due to fuel consumption, and the operating range of every UAV is altitude-dependent. A class of benchmark instances for collision avoidance is adapted and expanded to fit our model and we prove an upper bound on its objective value. Finally, the presented features and results are tested and discussed on several test instances using GUROBI as a state-of-the-art numerical solver.}, subject = {Mixed-integer nonlinear programming; Mission Planning; Inhomogeneous Fleet; Time Windows; Linearization methods; Gemischt-ganzzahlige nichtlineare Programming; Missionsplanung; Inhomogene Flotte; Zeitfenster; Linearisierungsmethoden; Nichtlineare Optimierung; Tourenplanung; Flugk{\"o}rper}, language = {en} } @techreport{BaehrBuhlRadowetal.2019, type = {Working Paper}, author = {B{\"a}hr, Martin and Buhl, Johannes and Radow, Georg and Schmidt, Johannes and Bambach, Markus and Breuß, Michael and F{\"u}genschuh, Armin}, title = {Stable honeycomb structures and temperature based trajectory optimization for wire-arc additive manufacturing}, editor = {F{\"u}genschuh, Armin}, issn = {2627-6100}, doi = {10.26127/BTUOpen-5079}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-50796}, year = {2019}, abstract = {We consider two mathematical problems that are connected and occur in the layer-wise production process of a workpiece using Wire-Arc Additive Manufacturing. As the first task, we consider the automatic construction of a honeycomb structure, given the boundary of a shape of interest. In doing this we employ Lloyd's algorithm in two different realizations. For computing the incorporated Voronoi tesselation we consider the use of a Delaunay triangulation or alternatively, the eikonal equation. We compare and modify these approaches with the aim of combining their respective advantages. Then in the second task, to find an optimal tool path guaranteeing minimal production time and high quality of the workpiece, a mixed-integer linear programming problem is derived. The model takes thermal conduction and radiation during the process into account and aims to minimize temperature gradients inside the material. Its solvability for standard mixed-integer solvers is demonstrated on several test-instances. The results are compared with manufactured workpieces.}, subject = {Eikonal equation; Centroidal Voronoi tessellation; Additive manufacturing; Heat transmission; Mixed-integer linear programming; Geometric optimization; Additive Fertigung; Gemischt-ganzzahlige Programmierung; Geometrische Optimierung; Eikonal-Gleichung; Zentrierte Voronoi-Parkettierung; W{\"a}rmeleitung; Rapid Prototyping ; Eikonal; Ganzzahlige Optimierung; Geometrische Optimierung; W{\"a}rmeleitung}, language = {en} } @techreport{FuegenschuhMuellenstedtSchmidt2019, author = {F{\"u}genschuh, Armin and M{\"u}llenstedt, Daniel and Schmidt, Johannes}, title = {Mission planning for unmanned aerial vehicles}, editor = {F{\"u}genschuh, Armin}, issn = {2627-6100}, doi = {10.26127/BTUOpen-4828}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-48285}, year = {2019}, abstract = {We formulate the mission planning problem for a meet of unmanned aerial vehicles (UAVs) as a mixed-integer nonlinear programming problem (MINLP). The problem asks for a selection of targets from a list to the UAVs, and trajectories that visit the chosen targets. To be feasible, a trajectory must pass each target at a desired maximal distance and within a certain time window, obstacles or regions of high risk must be avoided, and the fuel limitations must be obeyed. An optimal trajectory maximizes the sum of values of all targets that can be visited, and as a secondary goal, conducts the mission in the shortest possible time. In order to obtain numerical solutions to this model, we approximate the MINLP by a mixed-integer linear program (MILP), and apply a state-of-the-art solver (GUROBI) to the latter on a set of test instances.}, subject = {Mixed-integer nonlinear programming; Trajectory planning; Unmanned aerial vehicles; Linear approximation; Flugk{\"o}rper; Tourenplanung; Optimierung}, language = {en} }