How to design, and tune, a computed torque controller: An introduction and a Matlab example

This note briefly introduces the computed torque control method for trajectory tracking. The method is applicable to fully actuated robots, i.e, those whose inverse dynamics can be solved for any feasible acceleration. This includes many systems, like robot arms or hands, or any tree-like mechanism with all its joints actuated. Using simple explanations, we see how such a controller can be obtained using feedback linearization, and how its gains can be tuned to satisfy a desired settling time for the error signal. We end up discussing the advantages and shortcomings of the controller. A companion Matlab script can be downloaded from https://bit.ly/3QShxYi that implements and tests the controller on a simple actuated pendulum

Revisiting trilateration for robot localization

Locating a robot from its distances, or range measurements, to three other known points or stations is a common operation, known as trilateration. This problem has been traditionally solved either by algebraic or numerical methods. An approach that avoids the direct algebrization of the problem is proposed here. Using constructive geometric arguments, a coordinate-free formula containing a small number of Cayley-Menger determinants is derived. This formulation accommodates a more thorough investigation of the effects caused by all possible sources of error, including round-off errors, for the first time in this context. New formulas for the variance and bias of the unknown robot location estimation, due to station location and range measurements errors, are derived and analyzed. They are proved to be more tractable compared with previous ones, because all their terms have geometric meaning, allowing a simple analysis of their asymptotic behavior near singularities.This work was supported by the project 'Design and implementation of efficient parallelizable algorithms with applications to robotics and proteomics' (J-00869).Peer Reviewe

A randomized kinodynamic planner for closed-chain robotic systems

Kinodynamic RRT planners are effective tools for finding feasible trajectories in many classes of robotic systems. However, they are hard to apply to systems with closed-kinematic chains, like parallel robots, cooperating arms manipulating an object, or legged robots keeping their feet in contact with the environ- ment. The state space of such systems is an implicitly-defined manifold, which complicates the design of the sampling and steering procedures, and leads to trajectories that drift away from the manifold when standard integration methods are used. To address these issues, this report presents a kinodynamic RRT planner that constructs an atlas of the state space incrementally, and uses this atlas to both generate ran- dom states, and to dynamically steer the system towards such states. The steering method is based on computing linear quadratic regulators from the atlas charts, which greatly increases the planner efficiency in comparison to the standard method that simulates random actions. The atlas also allows the integration of the equations of motion as a differential equation on the state space manifold, which eliminates any drift from such manifold and thus results in accurate trajectories. To the best of our knowledge, this is the first kinodynamic planner that explicitly takes closed kinematic chains into account. We illustrate the performance of the approach in significantly complex tasks, including planar and spatial robots that have to lift or throw a load at a given velocity using torque-limited actuators.Peer ReviewedPreprin

Shape-from-image via cross-sections

International Conference on Pattern Recognition (ICPR), 2000, Barcelona (España)Using structural geometry, Whiteley (1991) showed that a line drawing is a correct projection of a spherical polyhedron if and only if it has a cross-section compatible with it. We extend the class of drawings to which this test applies, including those of polyhedral disks. Our proof is constructive, showing how to derive all spatial interpretations; it relies on elementary synthetic geometric arguments, and, as a by-product, it yields a simpler and shorter proof of Whiteley's result. Moreover, important properties of line drawings are visually derived as corollaries: realizability is independent of the adopted projection, it is an invariant projective property, and for trihedral drawings it can be checked with a pencil and an unmarked ruler alone.Peer Reviewe

La difusión de la prensa diaria en los Paises Catalanes entre 1976-1996

Esta investigación analiza la evolución de la difusión de la prensa diaria en relación a la vertebración política de los territorios de Cataluña, Islas Baleares y País Valenciano con el conjunto del estado, desde el principio de la transición a la democracia en 1976 hasta 1996. Las principales conclusiones apuntan a un incremento de la vertebración estatal de estos territorios, especialmente en cuanto a su dependencia informativa provocada por el incremento muy significativo de la prensa central de penetración en cuanto a ventas totales, tasas de difusión y ocupación del mercado. El estado de las Autonomías se revela, pues, no como un factor de mayor autonomía informativa territorial, sino de integración y homogeneización.This study analyses generic processes affecting the various tiers of the daily press in relation to the evolution of the political structuring of the Catalanspeaking areas (Catalonia, Balearic Islands and Valencian Community) within the Spanish State, from the beginning of the transition to democracy in 1976 through to 1996. The major movements to be detected in press diffusion are the increase in the "vertebration" of the Spanish state as a whole, evident as much in the increased weight of the centralised statewide press penetrating the Catalanspeaking market as in the process of homogenisation revealed by key data referring to total sales, circulation density and market shares

Multi-loop position analysis via iterated linear programming

Robotics: Science and Systems Conference (RSS), 2006, Filadelfia (EE.UU.)This paper presents a numerical method able to isolate all configurations that an arbitrary loop linkage can adopt, within given ranges for its degrees of freedom. The procedure is general, in the sense that it can be applied to single or multiple intermingled loops of arbitrary topology, and complete, in the sense that all possible solutions get accurately bounded, irrespectively of whether the analyzed linkage is rigid or mobile. The problem is tackled by formulating a system of linear, parabolic, and hyperbolic equations, which is here solved by a new strategy exploiting its structure. The method is conceptually simple, geometric in nature, and easy to implement, yet it provides solutions at the desired accuracy in short computation times.This work was supported by the project 'Planificador de trayectorias para sistemas robotizados de arquitectura arbitraria' (J-00930).Peer Reviewe

Inverse kinematics by distance matrix completion

International Workshop on Computational Kinematics (CK), 2005, Cassino (Italia)This paper characterizes a family of serial robots whose inverse kinematics can be translated into a system of distance constraints that can be solved using a sequence of constructive operations taking as fixed reference either a triangle or a tetrahedron. The relevance of the obtained family of robots is established when it is shown to contain the best-known commercial serial robots.This work was supported by the project 'Design and implementation of efficient parallelizable algorithms with applications to robotics and proteomics' (J-00869).Peer Reviewe

Computing wrench-feasible paths for cable-driven hexapods

Motion paths of cable-driven hexapods must carefully be planned to ensure that the lengths and tensions of all cables remain within acceptable limits, for a given wrench applied to the platform. The cables cannot go slack -to keep the control of the robot- nor excessively tight -to prevent cable breakage- even in the presence of bounded perturbations of the wrench. This paper proposes a path planning method that accommodates such constraints simultaneously. Given two configurations of the robot, the method attempts to connect them through a path that, at any point, allows the cables to counteract any wrench lying in a predefined uncertainty region. The feasible C-space is placed in correspondence with a smooth manifold, which facilitates the definition of a continuation strategy to search this space systematically from one configuration, until the second configuration is found, or path non-existence is proved at the resolution of the search. The force Jacobian is full rank everywhere on the C-space, which implies that the computed paths will naturally avoid crossing the forward singularity locus of the robot. The adjustment of tension limits, moreover, allows to maintain a meaningful clearance relative to such locus. The approach is applicable to compute paths subject to geometric constraints on the platform pose, or to synthesize free-flying motions in the full six-dimensional C-space. Experiments are included that illustrate the performance of the method in a real prototype.Postprint (published version

A motion planning approach to 6-D manipulation with aerial towed-cable systems

Presentado al International Micro Air Vehicle Conference and Flight Competition celebrado en Toulouse (Francia) del 17 al 20 de septiembre de 2013.We propose a new approach for the reliable 6-dimensional quasi-static manipulation with aerial towed- cable systems. The novelty of this approach lies in the combination of results deriving from the static analysis of cable-driven manipulators with a cost-based motion-planning algorithm to solve manipulation queries. Such a combination of methods is able to produce feasible paths that do not approach dangerous/uncontrollable configurations of the system. As part of our approach, we also propose an original system that we name the FlyCrane. It consists of a platform attached to three flying robots using six fixed-length cables. Results of simulations on 6-D quasi-static manipulation problems show the interest of the method.This work has been partially supported by the Spanish Ministry of Economy and Competitiveness under contract DPI2010-18449, by the European Community under contract ICT 287617 “ARCAS”, and by a Juan de la Cierva contract supporting the first author.Peer Reviewe