Many-core Algorithms for Combinatorial Optimization

Combinatorial Optimization is becoming ever more crucial, in these days. From natural sciences to economics, passing through urban centers administration and personnel management, methodologies and algorithms with a strong theoretical background and a consolidated real-word effectiveness is more and more requested, in order to find, quickly, good solutions to complex strategical problems. Resource optimization is, nowadays, a fundamental ground for building the basements of successful projects. From the theoretical point of view, Combinatorial Optimization rests on stable and strong foundations, that allow researchers to face ever more challenging problems. However, from the application point of view, it seems that the rate of theoretical developments cannot cope with that enjoyed by modern hardware technologies, especially with reference to the one of processors industry. In this work we propose new parallel algorithms, designed for exploiting the new parallel architectures available on the market. We found that, exposing the inherent parallelism of some resolution techniques (like Dynamic Programming), the computational benefits are remarkable, lowering the execution times by more than an order of magnitude, and allowing to address instances with dimensions not possible before. We approached four Combinatorial Optimization’s notable problems: Packing Problem, Vehicle Routing Problem, Single Source Shortest Path Problem and a Network Design problem. For each of these problems we propose a collection of effective parallel solution algorithms, either for solving the full problem (Guillotine Cuts and SSSPP) or for enhancing a fundamental part of the solution method (VRP and ND). We endorse our claim by presenting computational results for all problems, either on standard benchmarks from the literature or, when possible, on data from real-world applications, where speed-ups of one order of magnitude are usually attained, not uncommonly scaling up to 40 X factors.

Path planning for image based visual servoing

This thesis deals with Visual Servoing and its strictly connected disciplines like projective geometry, image processing, robotics and non-linear control. More specifically the work addresses the problem to control a robotic manipulator through one of the largely used Visual Servoing techniques: the Image Based Visual Servoing (IBVS). In Image Based Visual Servoing the robot is driven by on-line performing a feedback control loop that is closed directly in the 2D space of the camera sensor. The work considers the case of a monocular system with the only camera mounted on the robot end effector (eye in hand configuration). Through IBVS the system can be positioned with respect to a 3D fixed target by minimizing the differences between its initial view and its goal view, corresponding respectively to the initial and the goal system configurations: the robot Cartesian Motion is thus generated only by means of visual informations. However, the execution of a positioning control task by IBVS is not straightforward because singularity problems may occur and local minima may be reached where the reached image is very close to the target one but the 3D positioning task is far from being fulfilled: this happens in particular for large camera displacements, when the the initial and the goal target views are noticeably different. To overcame singularity and local minima drawbacks, maintaining the good properties of IBVS robustness with respect to modeling and camera calibration errors, an opportune image path planning can be exploited. This work deals with the problem of generating opportune image plane trajectories for tracked points of the servoing control scheme (a trajectory is made of a path plus a time law). The generated image plane paths must be feasible i.e. they must be compliant with rigid body motion of the camera with respect to the object so as to avoid image jacobian singularities and local minima problems. In addition, the image planned trajectories must generate camera velocity screws which are smooth and within the allowed bounds of the robot. We will show that a scaled 3D motion planning algorithm can be devised in order to generate feasible image plane trajectories. Since the paths in the image are off-line generated it is also possible to tune the planning parameters so as to maintain the target inside the camera field of view even if, in some unfortunate cases, the feature target points would leave the camera images due to 3D robot motions. To test the validity of the proposed approach some both experiments and simulations results have been reported taking also into account the influence of noise in the path planning strategy. The experiments have been realized with a 6DOF anthropomorphic manipulator with a fire-wire camera installed on its end effector: the results demonstrate the good performances and the feasibility of the proposed approach.