14,597 research outputs found
Admissible Velocity Propagation : Beyond Quasi-Static Path Planning for High-Dimensional Robots
Path-velocity decomposition is an intuitive yet powerful approach to address
the complexity of kinodynamic motion planning. The difficult trajectory
planning problem is solved in two separate, simpler, steps: first, find a path
in the configuration space that satisfies the geometric constraints (path
planning), and second, find a time-parameterization of that path satisfying the
kinodynamic constraints. A fundamental requirement is that the path found in
the first step should be time-parameterizable. Most existing works fulfill this
requirement by enforcing quasi-static constraints in the path planning step,
resulting in an important loss in completeness. We propose a method that
enables path-velocity decomposition to discover truly dynamic motions, i.e.
motions that are not quasi-statically executable. At the heart of the proposed
method is a new algorithm -- Admissible Velocity Propagation -- which, given a
path and an interval of reachable velocities at the beginning of that path,
computes exactly and efficiently the interval of all the velocities the system
can reach after traversing the path while respecting the system kinodynamic
constraints. Combining this algorithm with usual sampling-based planners then
gives rise to a family of new trajectory planners that can appropriately handle
kinodynamic constraints while retaining the advantages associated with
path-velocity decomposition. We demonstrate the efficiency of the proposed
method on some difficult kinodynamic planning problems, where, in particular,
quasi-static methods are guaranteed to fail.Comment: 43 pages, 14 figure
Euclidean distance geometry and applications
Euclidean distance geometry is the study of Euclidean geometry based on the
concept of distance. This is useful in several applications where the input
data consists of an incomplete set of distances, and the output is a set of
points in Euclidean space that realizes the given distances. We survey some of
the theory of Euclidean distance geometry and some of the most important
applications: molecular conformation, localization of sensor networks and
statics.Comment: 64 pages, 21 figure
Sampling-Based Methods for Factored Task and Motion Planning
This paper presents a general-purpose formulation of a large class of
discrete-time planning problems, with hybrid state and control-spaces, as
factored transition systems. Factoring allows state transitions to be described
as the intersection of several constraints each affecting a subset of the state
and control variables. Robotic manipulation problems with many movable objects
involve constraints that only affect several variables at a time and therefore
exhibit large amounts of factoring. We develop a theoretical framework for
solving factored transition systems with sampling-based algorithms. The
framework characterizes conditions on the submanifold in which solutions lie,
leading to a characterization of robust feasibility that incorporates
dimensionality-reducing constraints. It then connects those conditions to
corresponding conditional samplers that can be composed to produce values on
this submanifold. We present two domain-independent, probabilistically complete
planning algorithms that take, as input, a set of conditional samplers. We
demonstrate the empirical efficiency of these algorithms on a set of
challenging task and motion planning problems involving picking, placing, and
pushing
A linear relaxation technique for the position analysis of multi-loop linkages
This report presents a new method able to isolate all configurations that a multi-loop linkage can adopt. We tackle the problem by providing formulation and resolution techniques that fit particularly well together. The adopted formulation yields a system of simple equations (only containing linear and bilinear terms, and trivial trigonometric functions for the helical pair exclusively) whose special structure is later exploited by a branch-and-prune method based on linear relaxations. The method is general, as it can be applied to linkages with single or multiple loops with arbitrary topology, involving lower pairs of any kind, and complete, as all possible solutions get accurately bounded, irrespectively of whether the linkage is rigid or mobile
Position analysis based on multi-affine formulations
Aplicat embargament des de la data de defensa fins el 31/5/2022The position analysis problem is a fundamental issue that underlies many problems in Robotics such as the inverse kinematics of serial robots, the forward kinematics of parallel robots, the coordinated manipulation of objects, the generation of valid grasps, the constraint-based object positioning, the simultaneous localization and map building, and the analysis of complex deployable structures. It also arises in other fields, such as in computer aided design, when the location of objects in a design is given in terms of geometric constrains, or in the conformational analysis of biomolecules. The ubiquity of this problem, has motivated an intense quest for methods able of tackling it. Up to now, efficient algorithms for the general problem have remained elusive and they are only available for particular cases. Moreover, the complexity of the problem has typically led to methods difficult to be implemented.
Position analysis can be decomposed into two equally important steps: obtaining a set of closure equations, and solving them. This thesis deals with both of them to obtain a general, simple, and yet efficient solution method that we call the trapezoid method. The first step is addressed relying on dual quaternions. Although it has not been properly highlighted in the past, the use of dual quaternions permits expressing the closure condition of a kinematic loop involving only lower pairs as a system of multi-affine equations. In this thesis, this property is leveraged to introduce an interval-based method specially tailored for solving multi-affine systems. The proposed method is objectively simpler (in the sense that it is easier to understand and to implement) than previous methods based on general techniques such as interval Newton methods, conversions to Bernstein basis, or linear relaxations. Moreover, it relies on two simple operations, namely, linear interpolations and projections on coordinate planes, which can be executed with a high performance. The result is a method that accurately and efficiently bounds the valid solutions of the problem at hand. To further improve the accuracy, we propose the use of redundant, multi affine equations that are derived from the minimal set of equations describing the problem. To improve the efficiency, we introduce a variable elimination methodology that preserves the multi-affinity of the system of equations. The generality and the performance of the proposed trapezoid method are extensively evaluated on different kind of mechanisms, including spherical mechanisms, generic 6R and 7R loops, over-constrained systems, and multi-loop mechanisms. The proposed method is, in all cases, significantly faster than state of the art alternatives.El problema de l'anà lisi de posició és un tema fonamental que subjau a molts problemes de la robòtica, com ara la cinemà tica inversa de robots sèrie, la cinemà tica directa de robots paral·lels, la manipulació coordinada d'objectes, la generació de prensions và lides amb mans robòtiques, el posicionament d'objectes basat en restriccions, la localització i la creació de mapes de forma simultà nia, i l'anà lisi d'estructures desplegables complexes. També sorgeix en altres camps, com ara en el disseny assistit per ordinador, quan la ubicació dels objectes en un disseny es dóna en termes de restriccions geomètriques o en l'anà lisi conformacional de biomolècules. La omnipresència d'aquest problema ha motivat una intensa recerca de mètodes capaços d'afrontar-lo. Fins al moment, els algoritmes eficients per al problema general han estat esquius i només estan disponibles per a casos particulars. A més, la complexitat del problema normalment ha conduït a mètodes difÃcils d'implementar. L'anà lisi de posició es pot descompondre en dos passos igualment importants: l'obtenció d'un sistema d'equacions de tancament i la resolució d'aquest sistema. Aquesta tesi tracta de tots dos passos per tal d'obtenir un mètode de solució general, senzill i alhora eficient que anomenem el mètode del trapezoide. El primer pas s'aborda utilitzant quaternions duals. Tot i que no ha estat suficientment destacat en el passat, l'ús de quaternions duals permet expressar la condició de tancament d'un bucle cinemà tic que impliqui només parells inferiors com a un sistema d'equacions multi-afins. En aquesta tesi s'aprofita aquesta propietat per introduir un mètode especialment dissenyat per resoldre sistemes multi-afins. El mètode proposat és objectivament més senzill (en el sentit que és més fà cil d'entendre i d'implementar) que els mètodes anteriors que utilitzen tècniques generals com ara els mètodes de Newton basats en intervals, les conversions a la base de Bernstein o les relaxacions lineals. A més, el mètode es basa en dues operacions simples, a saber, les interpolacions lineals i les projeccions en plans de coordenades, que es poden executar de forma molt eficient. El resultat és un mètode que acota amb precisió i eficiència les solucions và lides del problema. Per millorar encara més la precisió, proposem l'ús d'equacions multi-afins redundants derivades del conjunt mÃnim d'equacions que descriuen el problema. Per altra banda, per millorar l'eficiència, introduïm un metodologia d'eliminació de variables que preserva la multi-afinitat del sistema d'equacions. La generalitat i el rendiment del mètode del trapezoide s'avalua extensivament en diferents tipus de mecanismes, inclosos els mecanismes esfèrics, bucles 6R i 7R genèrics, sistemes sobre-restringits i mecanismes de múltiples bucles. El mètode proposat és, en tots els casos, significativament més rà pid que els mètodes alternatius descrits en la literatura fins al moment.Postprint (published version
A Certified-Complete Bimanual Manipulation Planner
Planning motions for two robot arms to move an object collaboratively is a
difficult problem, mainly because of the closed-chain constraint, which arises
whenever two robot hands simultaneously grasp a single rigid object. In this
paper, we propose a manipulation planning algorithm to bring an object from an
initial stable placement (position and orientation of the object on the support
surface) towards a goal stable placement. The key specificity of our algorithm
is that it is certified-complete: for a given object and a given environment,
we provide a certificate that the algorithm will find a solution to any
bimanual manipulation query in that environment whenever one exists. Moreover,
the certificate is constructive: at run-time, it can be used to quickly find a
solution to a given query. The algorithm is tested in software and hardware on
a number of large pieces of furniture.Comment: 12 pages, 7 figures, 1 tabl
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