Dynamic whole-body motion generation under rigid contacts and other unilateral constraints

The most widely used technique for generating wholebody motions on a humanoid robot accounting for various tasks and constraints is inverse kinematics. Based on the task-function approach, this class of methods enables the coordination of robot movements to execute several tasks in parallel and account for the sensor feedback in real time, thanks to the low computation cost. To some extent, it also enables us to deal with some of the robot constraints (e.g., joint limits or visibility) and manage the quasi-static balance of the robot. In order to fully use the whole range of possible motions, this paper proposes extending the task-function approach to handle the full dynamics of the robot multibody along with any constraint written as equality or inequality of the state and control variables. The definition of multiple objectives is made possible by ordering them inside a strict hierarchy. Several models of contact with the environment can be implemented in the framework. We propose a reduced formulation of the multiple rigid planar contact that keeps a low computation cost. The efficiency of this approach is illustrated by presenting several multicontact dynamic motions in simulation and on the real HRP-2 robot

Inverse Kinematics without matrix inversion

This paper presents a new singularity robust and computationally efficient method for solving the inverse kinematics (IK) problem. In this method, the transformation from Cartesian space to joint space is performed in a feedback loop and as a result the new feedback inverse kinematics (FIK) law operates as a filter and does not require matrix manipulations (inversion, singular value decomposition or a computation of a damping factor). While the computational demand is greatly reduced, the performance is comparable to the one delivered by the damped least squares (DLS) law. The new algorithm is capable of escaping and avoiding kinematic singularities and in this respect it outperforms pseudo-inverse based formulations

Kinematics and Robot Design II (KaRD2019) and III (KaRD2020)

This volume collects papers published in two Special Issues “Kinematics and Robot Design II, KaRD2019” (https://www.mdpi.com/journal/robotics/special_issues/KRD2019) and “Kinematics and Robot Design III, KaRD2020” (https://www.mdpi.com/journal/robotics/special_issues/KaRD2020), which are the second and third issues of the KaRD Special Issue series hosted by the open access journal robotics.The KaRD series is an open environment where researchers present their works and discuss all topics focused on the many aspects that involve kinematics in the design of robotic/automatic systems. It aims at being an established reference for researchers in the field as other serial international conferences/publications are. Even though the KaRD series publishes one Special Issue per year, all the received papers are peer-reviewed as soon as they are submitted and, if accepted, they are immediately published in MDPI Robotics. Kinematics is so intimately related to the design of robotic/automatic systems that the admitted topics of the KaRD series practically cover all the subjects normally present in well-established international conferences on “mechanisms and robotics”.KaRD2019 together with KaRD2020 received 22 papers and, after the peer-review process, accepted only 17 papers. The accepted papers cover problems related to theoretical/computational kinematics, to biomedical engineering and to other design/applicative aspects

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

Minimal Representation for the Control of the Adept Quattro with Rigid Platform via Leg Observation Considering a Hidden Robot Model

International audiencePrevious works on the Gough-Stewart (GS) platform have shown that its visual servoing using the observation of its leg directions was possible by observing only three of its six legs but that the convergence to the desired pose was not guarantied. This can be explained by considering that the visual servoing of the leg direction of the GS platform was equivalent to controlling another robot, the 3-UPS that has assembly modes and singular configurations different from those of the GS platform. Considering this hidden robot model allowed the simplification of the singularity analysis of the mapping between the leg direction space and the Cartesian space. In this paper, the work on the definition of the hidden robot models involved in the visual servoing using the observation of the robot leg directions is extended to another robot, the Adept Quattro. It will be shown that the hidden robot model is completely different from the model involved in the control of the GS platform. Therefore, the results obtained for the GS platform are not valuable for this robot. The hidden robot has assembly modes and singular configurations different from those of the Quattro. An accuracy analysis is performed to show the importance of the leg selection. All these results are validated on a Quattro simulator created using ADAMS/Controls and interfaced with Matlab/Simulink

Kinematic and dynamic analysis of spatial six degree of freedom parallel structure manipulator

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2003Includes bibliographical references (leaves: 63-69)Text in English; Abstract: Turkish and Englishviii, 86 leavesThis thesis covers a study on kinematic and dynamic analysis of a new type of spatial six degree of freedom parallel manipulator. The background for structural synthesis of parallel manipulators is also given. The structure of the said manipulator is especially designed to cover a larger workspace then well-known Stewart Platform and its derivates. The main point of interest for this manipulator is its hybrid actuating system, consisting of three revolute and three linear actuators.Kinematic analysis comprises forward and inverse displacement analysis. Screw Theory and geometric constraint considerations were the main tools used. While it was possible to derive a closed-form solution for the inverse displacement analysis, a numerical approach was used to solve the problem of forward displacement analysis. Based on the results of the kinematic analysis, a rough workspace study of the manipulator is also accomplished. On the dynamics part, attention has been given on inverse dynamics problem using Lagrange-Euler approach.Both high and lower level software were heavily utilized. Also computer software called .CASSoM. and .iMIDAS. are developed to be used for structural synthesis and inverse displacement analysis. The major contribution of the study to the scientific community is the proposal of a new type of parallel manipulator, which has to be studied extensively regarding its other interesting properties

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'anàlisi de posició és un tema fonamental que subjau a molts problemes de la robòtica, com ara la cinemàtica inversa de robots sèrie, la cinemàtica directa de robots paral·lels, la manipulació coordinada d'objectes, la generació de prensions vàlides amb mans robòtiques, el posicionament d'objectes basat en restriccions, la localització i la creació de mapes de forma simultània, i l'anàlisi 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'anàlisi 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 difícils d'implementar. L'anàlisi 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 cinemàtic 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 fàcil 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 vàlides del problema. Per millorar encara més la precisió, proposem l'ús d'equacions multi-afins redundants derivades del conjunt mínim 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 ràpid que els mètodes alternatius descrits en la literatura fins al moment.Postprint (published version