Iacopo Gentilini

The travelling salesman problem with neighbourhoods: MINLP solution

The travelling salesman problem (TSP) with neighbourhoods extends the TSP to the case where each vertex of the tour is allowed to move in a given region. This NP-hard optimization problem has recently received increasing attention in several technical fields such as robotics, unmanned aerial vehicles, or utility management. In this paper, the problem is formulated as a non-convex mixed-integer nonlinear programme (MINLP) having the property that fixing all the integer variables to any integer values yield a convex nonlinear programme. This property is used to modify the global MINLP optimizer Couenne, improving by orders of magnitude its performance and allowing the exact solution of instances large enough to be useful in applications. Computational results are presented where neighbourhoods are either polyhedra or ellipsoids in ℝ2 or ℝ3 and with the Euclidean norm as distance metric.

Predicting and evaluating the post-assembly shape of thin-walled components via 3D laser digitization and FEA simulation of the assembly process

Three-dimensional (3D) laser digitization has become a critical research field and a widely used technique for product quality inspection in the manufacturing and medical industries during the last decade. One common application of this technology is to analyze whether the final shape of an assembly component fulfills the designers geometric specifications. This task is currently performed by digitizing the components surface after mounting it into its final assembly or on a special testing frame. In order to speed up this process a new computational method is proposed for inspecting the final shape of an assembly component by virtually mounting it into the assembly, without the physical assembling process taking place. The developed computational method employs laser digitization to measure the initial shape of the assembly component and then finite element analysis (FEA) to predict its post-assembly shape. First, a laser-digitized dense mesh is smoothed and decimated to make it suitable for FEA. Material properties of the component, if not available, are then determined by a calibration process, and specific displacement boundary conditions are applied to reproduce the assembly process. After FEA is executed, the quality of the simulated post-assembly shape is checked using visualization tools such as light-reflection patterns and contour plots of the distance between the computed geometry and the target computer-aided design (CAD) geometry. Moreover, the accuracy of the proposed method is validated by comparing the simulated post-assembly shape with the actual post-assembly shape measured after physically assembling the component. Experiments show that the average distance between simulated shape and actual shape varies from 0.3 mm to 0.6 mm for objects with a characteristic size of a half meter, and that the isophotes and height fields of reflection (HFR) based indices are reduced up to 50%. The proposed method can thus predict the final shape of an assembled component well without assembling it, reducing the time and the cost of product quality inspection.

Multi-goal path planning based on the generalized Traveling Salesman Problem with neighborhoods

Often times in mobile robotics, optimizing a sequence of tasks and the paths between those destinations is an essential factor. In simple cases, this problem can be modeled by the well-researched Traveling Salesman Problem (TSP). In more complex situations however, the TSP is not a suitable model. In redundant robotic systems, a robot can assume infinitely many configurations while performing each given task. In these cases, not only is it necessary to optimize the sequence of tasks, but an optimal configuration must be defined for each task as well. This optimization problem can be better modeled by the Traveling Salesman Problem with Neighborhoods (TSPN) in which nodes can move in given domains called neighborhoods. However, one of the limiting factors to the TSPN is that it cannot efficiently solve realistic instances with non-connected neighborhoods. This research proposes an approach to this problem in which the TSPN is extended into a Generalized Traveling Salesman Problem with Neighborhoods (GTSPN) where each node can be located in multiple regions, called neighborhoodsets. An heuristic procedure is proposed to find a near-optimal tour for GTSPN instances using a genetic algorithm approach. Numerical simulations performed on randomly generated instances with up to 300 neighborhoods show that the proposed procedure determines tours for a given instance within a 1% standard deviation error from the best-known tour.

Loop-shaping controller design for nonlinear systems using the Contoured Robust Controller Bode (CRCBode) plot

In this paper we introduce the Contoured Robust Controller Bode (CRCBode) plot and demonstrate how it can be used for frequency domain controller design for nonlinear systems. The CRCBode plot is based on a standard robust performance criteria which is mapped onto the controller Bode magnitude and phase plots. The contours indicate level sets of a robust performance index and define allowable and forbidden regions for the controller frequency response. We apply an iterative loop-shaping technique to design a compensator which avoids the areas of the CRCBode plot with performance index greater than zero, and we demonstrate the effectiveness of this technique for flow-rate control of a dynamic nonlinear butterfly valve system. Finally we verify the performance of the compensated system via simulation.

Lateral Tape Motion Control With Robust Performance Evaluation Based on RBode Plot

Magnetic tapes are still widely used in data storage facilities. A novel approach is presented for reducing the lateral tape motion (LTM) at the reel and thus for preventing the impacts between tape and reel flanges, which can easily damage the fragile tape edges. To measure the LTM, photonic sensors are employed, which have to be calibrated to compensate for nonlinearities and for the shift of the tape path between sensor probes while the reel winds and unwinds. Moreover, since a sensor cannot be placed as close to the reel as desired, the lateral tape position at the reel is estimated by extrapolating from two sensors. Actuation is provided by a tilted rotary guide. In this paper, first, the identified dynamics at the two sensors are combined to estimate the dynamics at the tape nip, and a complex proportional-integral-lead controller is implemented to compensate for the LTM at the extrapolated location. Then, the robust performance characteristics of the implemented controller is evaluated using the robust Bode plot, which accounts for the uncertainties embedded in the used system identification method based on frequency response data. Finally, the experimental results show a significant reduction above 60% in LTM at the reel.

Subdivision templates for converting a non-conformal hex-dominant mesh to a conformal hex-dominant mesh without pyramid elements

This paper presents a computational method for converting a non-conformal hex-dominant mesh to a conformal hex-dominant mesh without help of pyramid elements. During the conversion, the proposed method subdivides a non-conformal element by applying a subdivision template and conformal elements by a conventional subdivision scheme. Although many finite element solvers accept mixed elements, some of them require a mesh to be conformal without a pyramid element. None of the published automated methods could create a conformal hex-dominant mesh without help of pyramid elements, and therefore the applicability of the hex-dominant mesh has been significantly limited. The proposed method takes a non-conformal hex-dominant mesh as an input and converts it to a conformal hex-dominant mesh that consists only of hex, tet, and prism elements. No pyramid element will be introduced. The conversion thus considerably increases the applicability of the hex-dominant mesh in many finite element solvers.

Cycle time based multi-goal path optimization for redundant robotic systems

Finding an optimal path for a redundant robotic system to visit a sequence of several goal placements poses two technical challenges. First, while searching for an optimal sequence, infinitely many feasible configurations can be used to reach each goal placement. Second, obstacle avoidance has to be considered while optimizing the path from one goal placement to the next. Previous works focused on solving a discrete formulation of this optimization problem where only few configurations are used to represent each goal placement. We instead model it as a Traveling Salesman Problem with Neighborhoods (TSPN), where each neighborhood is defined as the set of the infinitely many configurations corresponding to the same goal placement. A solution procedure based on a Hybrid Random-key Genetic Algorithm (HRKGA) and bidirectional Rapidly-exploring Random Trees (biRRTs) is then proposed. Finally, experimental tests performed on a 7-Degree Of Freedom (DOF) industrial vision inspection system show that the proposed method is able to drastically reduce the cycle time currently required by the system.

Energy-optimal path planning for six-rotors on multi-target missions

Often times in multi-target, Unmanned Aerial System (UAS) applications, minimizing energy consumption is a common goal. In simplified cases, this problem can be solved by minimizing the path length between targets using the Traveling Salesman Problem with Neighborhoods (TSPN). However, this method does not take into account the attitude of the UAS. In addition, minimum path length does not always correlate to minimum energy consumption. This research proposes an approach to both problems. A method is proposed to more accurately model multi-target, six-rotor aircraft missions using the Generalized TSPN (GTSPN), which can account for the non-convex characteristics of the neighborhoods created by accounting for variable attitude. To address the energy consumption problem, a heuristic procedure is proposed to solve GTSPN instances using a genetic algorithm approach that incorporates a fine-tuned, dynamic model of a six-rotor to simulate energy consumption. Numerical simulations are performed on randomly generated instances with up to 50 targets to show that the proposed procedure determines tours for a given instance within a 1% standard deviation error from the best-known tour and on average improves the results obtained with the TSPN formulation up to 11.4%.

Active tape edge position control system

Lateral tape motion (LTM) is a major obstacle to using thinner tapes for greater storage capacity, because impacts between the tape and the flanges of the reel can damage the tape edges. This paper presents an active tape edge position control system employing a tilted rotary guide and photonic sensors. To avoid impacts with the flanges, the tape motion sensor should be placed as close to the reel as possible. Calibration of such a sensors must account for the changing tape path as the reel winds and unwinds. We present the calibration method, the controller design process for a complex proportional integral lead (CPIL) compensator, and the results of experiments, which show promise for reducing damage to tape from LTM at the reel.

Control of lateral tape motion using extrapolated position estimation

Magnetic tapes are still widely used for long term archival storage because of their high capacity, low cost, and high reliability. A major challenge to increasing their storage capacity is lateral tape motion (LTM), which can cause the tape to strike flanges on the tape reel, damaging the fragile tape edge. In this paper we present a method for steering the tape onto the reel to prevent such damage. Since the tape radius is changing, we must estimate the tape position by extrapolating from two photonic sensors. Actuation is provided by a tilted rotary guide. We present a method for calibrating the sensors to compensate for nonlinearities as the tape moves in two dimensions within the gap of the sensor while the reel winds and unwinds. We then show how to combine the identified dynamics at the two sensors to estimate the position at the tape nip and how to implement a complex proportional integral lead controller to compensate for LTM. Experimental results show significant reduction in LTM at the reel.