Real-Time Path Planning Based on Harmonic Functions under a Proper Generalized Decomposition-Based Framework

This paper presents a real-time global path planning method for mobile robots using harmonic functions, such as the Poisson equation, based on the Proper Generalized Decomposition (PGD) of these functions. The main property of the proposed technique is that the computational cost is negligible in real-time, even if the robot is disturbed or the goal is changed. The main idea of the method is the off-line generation, for a given environment, of the whole set of paths from any start and goal configurations of a mobile robot, namely the computational vademecum, derived from a harmonic potential field in order to use it on-line for decision-making purposes. Up until now, the resolution of the Laplace or Poisson equations has been based on traditional numerical techniques unfeasible for real-time calculation. This drawback has prevented the extensive use of harmonic functions in autonomous navigation, despite their powerful properties. The numerical technique that reverses this situation is the Proper Generalized Decomposition. To demonstrate and validate the properties of the PGD-vademecum in a potential-guided path planning framework, both real and simulated implementations have been developed. Simulated scenarios, such as an L-Shaped corridor and a benchmark bug trap, are used, and a real navigation of a LEGO®MINDSTORMS robot running in static environments with variable start and goal configurations is shown. This device has been selected due to its computational and memory-restricted capabilities, and it is a good example of how its properties could help the development of social robots.

Learning the Parametric Transfer Function of Unitary Operations for Real-Time Evaluation of Manufacturing Processes Involving Operations Sequencing

For better designing manufacturing processes, surrogate models were widely considered in the past, where the effect of different material and process parameters was considered from the use of a parametric solution. The last contains the solution of the model describing the system under study, for any choice of the selected parameters. These surrogate models, also known as meta-models, virtual charts or computational vademecum, in the context of model order reduction, were successfully employed in a variety of industrial applications. However, they remain confronted to a major difficulty when the number of parameters grows exponentially. Thus, processes involving trajectories or sequencing entail a combinatorial exposition (curse of dimensionality) not only due to the number of possible combinations, but due to the number of parameters needed to describe the process. The present paper proposes a promising route for circumventing, or at least alleviating that difficulty. The proposed technique consists of a parametric transfer function that, as soon as it is learned, allows for, from a given state, inferring the new state after the application of a unitary operation, defined as a step in the sequenced process. Thus, any sequencing can be evaluated almost in real time by chaining that unitary transfer function, whose output becomes the input of the next operation. The benefits and potential of such a technique are illustrated on a problem of industrial relevance, the one concerning the induced deformation on a structural part when printing on it a series of stiffeners.

Elastic-Plastic Reduced Order Modelling of Sheet and Profiles Bending-under-Tension

The aircrafts fuselage structure is usually composed of an assembly of stringers and frames made of cold-worked aluminium profiles. In particular, frames need of a forming process that shapes the profile into the frame’s curved shape. To do this, both profile ends are clamped, and then the profile is simultaneously stretched and pressed against the mould so that the material is plastically deformed. Industrial experience shows that most of times the resultant frame does not fulfil neither curvature nor planarity tolerances. These defects are mainly due to spring-back, residual stresses, and some technologic restrictions related to the machinery. The lack of understanding has led industry to reduce the automation level, and thus the forming process is frequently interrupted to perform verifications and adjustments that make the process to be time-consuming and very much dependent on the know-how of the machine operator. Aiming to improve the frame’s industrialisation, this work first analyses the influence of several parameters in the final shape. Then, we propose a computer-aided forming process based on the concept of Computational Vademecum (CV), which is also introduced in this work. It allows reducing the dependence on the operator know-how, while reliability and repeatability of the process can be improved.