A Fast and Practical Algorithm for Generalized Penetration Depth Computation

Abstract — We present an efficient algorithm to compute the generalized penetration depth (PD g) between rigid models. Given two overlapping objects, our algorithm attempts to compute the minimal translational and rotational motion that separates the two objects. We formulate the PD g computation based on modeldependent distance metrics using displacement vectors. As a result, our formulation is independent of the choice of inertial and body-fixed reference frames, as well as specific representation of the configuration space. Furthermore, we show that the optimum answer lies on the boundary of the contact space and pose the computation as a constrained optimization problem. We use global approaches to find an initial guess and present efficient techniques to compute a local approximation of the contact space for iterative refinement. We highlight the performance of our algorithm on many complex models. I

Méthode interactive et par l'apprentissage pour la generation de trajectoire en conception du produit

The accessibility is an important factor considered in the validation and verification phase of the product design and usually dominates the time and costs in this phase. Defining the accessibility verification as the motion planning problem, the sampling based motion planners gained success in the past fifteen years. However, the performances of them are usually shackled by the narrow passage problem arising when complex assemblies are composed of large number of parts, which often leads to scenes with high obstacle densities. Unfortunately, humans’ manual manipulations in the narrow passage always show much more difficulties due to the limitations of the interactive devices or the cognitive ability. Meanwhile, the challenges of analyzing the end users’ response in the design process promote the integration with the direct participation of designers.In order to accelerate the path planning in the narrow passage and find the path complying with user’s preferences, a novel interactive motion planning method is proposed. In this method, the integration with a random retraction process helps reduce the difficulty of manual manipulations in the complex assembly/disassembly tasks and provide local guidance to the sampling based planners. Then a hypothesis is proposed about the correlation between the topological structure of the scenario and the motion path in the narrow passage. The topological structure refers to the medial axis (2D) and curve skeleton (3D) with branches pruned. The correlation runs in an opposite manner to the sampling based method and provide a new perspective to solve the narrow passage problem. The curve matching method is used to explore this correlation and an interactive motion planning framework that can learn from experience is constructed in this thesis. We highlight the performance of our framework on a challenging problem in 2D, in which a non-convex object passes through a cluttered environment filled with randomly shaped and located non-convex obstacles.L'accessibilitéest un facteur important pris en compte dans la validation et la vérification en phase de conception du produit et augmente généralement le temps et les coûts de cette phase. Ce domaine de recherche a eu un regain d’intérêt ces quinze dernières années avec notamment de nouveaux planificateurs de mouvement. Cependant, les performances de ces méthodes sont généralement très faibles lorsque le problème se caractérise par des passages étroits des assemblages complexes composées d'un grand nombre de pièces. Cela conduit souvent àdes scènes àforte densitéd'obstacles. Malheureusement, les manipulations manuelles des humains dans le passage étroit montrent toujours beaucoup de difficultés en raison des limitations des dispositifs interactifs ou la capacitécognitive. Pendant ce temps, les défis de l'analyse de la réponse finale des utilisateurs dans le processus de conception promeut l'intégration avec la participation directe des concepteurs.Afin d'accélérer la planification dans le passage étroit et trouver le chemin le plus conforme aux préférences de l'utilisateur, une nouvelle méthode de planification de mouvement interactif est proposée. Nous avons soulignéla performance de notre algorithme dans certains scénarios difficiles en 2D et 3D environnement.Ensuite, une hypothèse est proposésur la corrélation entre la structure topologique du scénario et la trajectoire dans le passage étroit. La méthode basée sur les courbures est utilisée pour explorer cette corrélation et un cadre de planification de mouvement interactif qui peut apprendre de l'expérience est construit dans cette thèse. Nous soulignons la performance de notre cadre sur un problème difficile en 2D, dans lequel un objet non-convexe passe à travers un environnement encombrérempli d'obstacles non-convexes de forme aléatoire et situés

Efficient motion planning using generalized penetration depth computation

Motion planning is a fundamental problem in robotics and also arises in other applications including virtual prototyping, navigation, animation and computational structural biology. It has been extensively studied for more than three decades, though most practical algorithms are based on randomized sampling. In this dissertation, we address two main issues that arise with respect to these algorithms: (1) there are no good practical approaches to check for path non-existence even for low degree-of-freedom (DOF) robots; (2) the performance of sampling-based planners can degrade if the free space of a robot has narrow passages. In order to develop effective algorithms to deal with these problems, we use the concept of penetration depth (PD) computation. By quantifying the extent of the intersection between overlapping models (e.g. a robot and an obstacle), PD can provide a distance measure for the configuration space obstacle (C-obstacle). We extend the prior notion of translational PD to generalized PD, which takes into account translational as well as rotational motion to separate two overlapping models. Moreover, we formulate generalized PD computation based on appropriate model-dependent metrics and present two algorithms based on convex decomposition and local optimization. We highlight the efficiency and robustness of our PD algorithms on many complex 3D models. Based on generalized PD computation, we present the first set of practical algorithms for low DOF complete motion planning. Moreover, we use generalized PD computation to develop a retraction-based planner to effectively generate samples in narrow passages for rigid robots. The effectiveness of the resulting planner is shown by alpha puzzle benchmark and part disassembly benchmarks in virtual prototyping

Efficient configuration space construction and optimization

The configuration space is a fundamental concept that is widely used in algorithmic robotics. Many applications in robotics, computer-aided design, and related areas can be reduced to computational problems in terms of configuration spaces. In this dissertation, we address three main computational challenges related to configuration spaces: 1) how to efficiently compute an approximate representation of high-dimensional configuration spaces; 2) how to efficiently perform geometric, proximity, and motion planning queries in high dimensional configuration spaces; and 3) how to model uncertainty in configuration spaces represented by noisy sensor data. We present new configuration space construction algorithms based on machine learning and geometric approximation techniques. These algorithms perform collision queries on many configuration samples. The collision query results are used to compute an approximate representation for the configuration space, which quickly converges to the exact configuration space. We highlight the efficiency of our algorithms for penetration depth computation and instance-based motion planning. We also present parallel GPU-based algorithms to accelerate the performance of optimization and search computations in configuration spaces. In particular, we design efficient GPU-based parallel k-nearest neighbor and parallel collision detection algorithms and use these algorithms to accelerate motion planning. In order to extend configuration space algorithms to handle noisy sensor data arising from real-world robotics applications, we model the uncertainty in the configuration space by formulating the collision probabilities for noisy data. We use these algorithms to perform reliable motion planning for the PR2 robot.Doctor of Philosoph