Configuration-based compliance control of kinematically redundant robot arm Part I: Theoretical framework

Kada je popustljivost vrha robota dominantno određena popustljivošću njegovih zglobova, generalizovana matrica krutosti robota može se preslikati iz prostora radnog zadatka u prostor unutrašnjih koordinata robota primenom kongruentne transformacije. Generisana na ovaj način, matrica krutosti u unutrašnjim koordinatama je u opštem slučaju nedijagonalna. Nedijagonalni elementi se mogu generisati samo redundantnom aktuacijom (poliartikulacioni aktuatori). Mada je ova vrsta aktuatora široko rasprostranjena kod bioloških sistema, njena praktična primena kod robota i sličnih veštačkih sistema je ekstremno problematična. Da bi se prevazišao ovaj problem, predlaže se rešenje bazirano na kinematskoj redundansi. U okviru ovog rada koji se sastoji iz dva dela, prikazuje se novi pristup upravljanja popustljivošću vrha robota, odnosno elastomehaničkom interakcijom vrha robota i njegovog okruženja, primenom kinematske redundanse umesto aktuacione. U prvom delu ovaj pristup je prikazan kroz koncipiranje metode upravljanja krutošću promenom konfiguracije (CSC) za slučaj kinetosatičke konzistentnosti, primenom projekcije gradijenta optimizacione funkcije koja minimizira Euklidovu normu nedijagonalnih elemenata matrice krutosti robota izražene u unutrašnjim koordinatama.When the robot endpoint compliance is dominantly influenced by the flexibility of its joints, the robot taskspace generalized stiffness matrix can be mapped onto jointspace using appropriate congruence transformation. Thus produced, the jointspace stiffness matrix is generally nondiagonal. Off-diagonal elements can be generated by redundant actuation only (polyarticular actuators). Although this kind of actuation is widely present in biological systems, its practical implementation in engineering systems is very difficult. To overcome this problem, use of kinematic redundancy is proposed. This two-part paper presents an approach to the control of robot endpoint compliance, i.e., elasto-mechanical interaction between a robot and its environment using kinematic redundancy instead of actuation redundancy. In Part I this approach is developed by proposing the Configuration-based Stiffness Control (CSC) method for kinetostatically consistent control of robot compliant behaviour, based on the gradient projection of the cost function which minimizes the norm of off-diagonal elements of the jointspace matrix

Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings

International audienceThe paper presents an advanced stiffness modeling technique for perfect and non-perfect parallel manipulators under internal and external loadings. Particular attention is paid to the manipulators composed of non-perfect serial chains, whose geometrical parameters differ from the nominal ones and do not allow to assemble manipulator without internal stresses that considerably affect the stiffness properties and also change the end-effector location. In contrast to other works, several types of loadings are considered simultaneously: an external force applied to the end-effector, internal loadings generated by the assembling of non-perfect serial chains and external loadings applied to the intermediate points (auxiliary loading due to the gravity forces and relevant compensator mechanisms, etc.). For this type of manipulators, a non-linear stiffness modeling technique is proposed that allows to take into account inaccuracy in the chains and to aggregate their stiffness models for the case of both small and large deflections. Advantages of the developed technique and its ability to compute and compensate the compliance errors caused by the considered factors are illustrated by an example that deals with parallel manipulators of the Orthoglide family

CAD-based approach for identification of elasto-static parameters of robotic manipulators

The paper presents an approach for the identification of elasto-static parameters of a robotic manipulator using the virtual experiments in a CAD environment. It is based on the numerical processing of the data extracted from the finite element analysis results, which are obtained for isolated manipulator links. This approach allows to obtain the desired stiffness matrices taking into account the complex shape of the links, couplings between rotational/translational deflections and particularities of the joints connecting adjacent links. These matrices are integral parts of the manipulator lumped stiffness model that are widely used in robotics due to its high computational efficiency. To improve the identification accuracy, recommendations for optimal settings of the virtual experiments are given, as well as relevant statistical processing techniques are proposed. Efficiency of the developed approach is confirmed by a simulation study that shows that the accuracy in evaluating the stiffness matrix elements is about 0.1%.Comment: arXiv admin note: substantial text overlap with arXiv:0909.146

On the role of robot configuration in Cartesian stiffness control

The stiffness ellipsoid, i.e. the locus of task-space forces obtained corresponding to a deformation of unit norm in different directions, has been extensively used as a powerful representation of robot interaction capabilities. The size and shape of the stiffness ellipsoid at a given end-effector posture are influenced by both joint control parameters and - for redundant manipulators - by the chosen redundancy resolution configuration. As is well known, impedance control techniques ideally provide control parameters which realize any desired shape of the Cartesian stiffness ellipsoid at the end-effector in an arbitrary non-singular configuration, so that arm geometry selection could appear secondary. This definitely contrasts with observations on how humans control their arm stiffness, who in fact appear to predominantly use arm configurations to shape the stiffness ellipsoid. To understand this discrepancy, we provide a more complete analysis of the task-space force/deformation behavior of redundant arms, which explains why arm geometry also plays a fundamental role in interaction capabilities of a torque controlled robot. We show that stiffness control of realistic robot models with bounds on joint torques can't indeed achieve arbitrary stiffness ellipsoids at any given arm configuration. We first introduce the notion of maximum allowable Cartesian force/displacement (“stiffness feasibility”) regions for a compliant robot. We show that different robot configurations modify such regions, and explore the role of different configurations in defining the performance limits of Cartesian stiffness controllers. On these bases, we design a stiffness control method that suitably exploits both joint control parameters and redundancy resolution to achieve desired task-space interaction behavior

Outils pour l’identification des paramètres de raideur des robots à l’aide d’un logiciel de CAO

This report proposes a CAD-based approach for identification of the elasto-static parameters of the robotic manipulators. The main contributions are in the areas of virtual experiment planning and algorithmic data processing, which allows to obtain the stiffness matrix with required accuracy. In contrast to previous works, the developed technique operates with the deflection field produced by virtual experiments in a CAD environment. The proposed approach provides high identification accuracy (about 0.1% for the stiffness matrix element) and is able to take into account the real shape of the link, coupling between rotational/translational deflections and joint particularities. To compute the stiffness matrix, the numerical technique has been developed, and some recommendations for optimal settings of the virtual experiments are given. In order to minimize the identification errors, the statistical data processing technique was applied. The advantages of the developed approach have been confirmed by case studies dealing with the links of parallel manipulator of the Orthoglide family, for which the identification errors have been reduced to 0.1%ANR COROUSS

Enhanced stiffness modeling of manipulators with passive joints

The paper presents a methodology to enhance the stiffness analysis of serial and parallel manipulators with passive joints. It directly takes into account the loading influence on the manipulator configuration and, consequently, on its Jacobians and Hessians. The main contributions of this paper are the introduction of a non-linear stiffness model for the manipulators with passive joints, a relevant numerical technique for its linearization and computing of the Cartesian stiffness matrix which allows rank-deficiency. Within the developed technique, the manipulator elements are presented as pseudo-rigid bodies separated by multidimensional virtual springs and perfect passive joints. Simulation examples are presented that deal with parallel manipulators of the Ortholide family and demonstrate the ability of the developed methodology to describe non-linear behavior of the manipulator structure such as a sudden change of the elastic instability properties (buckling)

Stiffness modeling of parallel mechanisms at limb and joint/link levels

Drawing on screw theory and the virtual joint method, this paper presents a general and hierarchical approach for semianalytical stiffness modeling of parallel mechanisms. The stiffness model is built by two essential steps: 1) formulating the map between the stiffness matrices of platform and limbs using the duality of wrench and twist of the platform; and 2) formulating the map between stiffness matrices of a limb and a number of elastic elements in that limb using the duality of the wrench attributed to the limb and the twist of the endlink of that limb. By merging these two threads, the Cartesian stiffness matrix can be explicitly expressed in terms of the compliance matrices of joints and links. The proposed approach bridges the gap between two currently available approaches and is thereby very useful for evaluating stiffness over the entire workspace and investigating the influences of joint/link compliances on those of the platform in a quick and precise manner. A stiffness analysis for a 3-PRS parallel mechanism is presented as an example to illustrate the effectiveness of the proposed approach

STABILITY OF MANIPULATOR CONFIGURATION UNDER EXTERNAL LOADING

International audienceThe paper is devoted to the analysis of robotic manipulator behavior under internal and external loadings. The main contributions are in the area of stability analysis of manipulator configurations corresponding to the loaded static equilibrium. In contrast to other works, in addition to usually studied the end-platform behavior with respect to the disturbance forces, the problem of configuration stability for each kinematic chain is considered. The proposed approach extends the classical notion of the stability for the static equilibrium configuration that is completely defined the properties of the Cartesian stiffness matrix only. The advantages and practical significance of the proposed approach are illustrated by several examples that deal with serial kinematic chains and parallel manipulators. It is shown that under the loading the manipulator workspace may include some specific points that are referred to as elastostatic singularities where the chain configurations become unstable