International audience

A cuspidal serial robot can travel from one inverse kinematic solution to another without crossing a singularity. Cuspidal robots ask for extra care and caution in trajectory planning, as identifying an aspect related to one unique inverse kinematic solution is not possible. The issues related to motion planning with cuspidal robots are related to the inherent property arising from the geometric design of the robot. The cuspidality property has not been considered in recent industrial 6R robots with a non-spherical wrist. In this work, cuspidality is illustrated with the JACO robot (gen 2, non-spherical wrist), a serial arm by Kinova Robotics which is deployed in various applications and is cuspidal in nature. A nonsingular change of solutions for the robot is provided to highlight the effect of cuspidal robots on the interference with the environment. The pose with multiple inverse kinematic solutions in an aspect is presented. Problems in choosing the initial solution of the path in cuspidal robots, and its consequence, is illustrated with an example path in the workspace of the JACO robot. The paper presents the importance of cuspidality analysis of 6R robots and the implications of neglecting it.

The kinematics of cuspidal 3R regional robots was studied extensively in the past. Moreover, certain industrial 6R robots were found to be cuspidal (e.g. Fanuc CRX series, Kinova GEN2), which makes cuspidal robots finally interesting for practical applications. This necessitates optimal trajectory planning, respecting the dynamics and technical limits of the particular robot. In this paper, a method for singularity-free time-optimal point-to-point trajectory (PtP) trajectory planning is proposed. As a special case, this method is applicable to time-optimal singularity-free assembly mode changing. Results are shown for 3R robots and a 6R Fanuc CRX10iA/L.

Cuspidal robots are robots with at least two inverse kinematic solutions that can be connected by a singularity-free path. Deciding the cuspidality of generic 3R robots has been studied in the past, but extending the study to six-degree-of-freedom robots can be a challenging problem. Many robots can be modeled as a polynomial map together with a real algebraic set so that the notion of cuspidality can be extended to these data.

International audience

International audience

This paper proposes a new kind of light-weight manipulators suitable for safe interactions. The proposed manipulators use anti-parallelogram joints in series, referred to as X-joints. Each X-joint is remotely actuated with cables and springs in parallel, thus realizing a tensegrity one-degree-of-freedom mechanism. As compared to manipulators built with simple revolute joints in series, manipulators with tensegrity X-joint offer a number of advantages, such as an intrinsic stability, variable stiffness and lower inertia. This new design was inspired by the musculosleketon architecture of the bird neck that is known to have remarkable features such as a high dexterity. The paper analyzes in detail the kinetostatics of a X-joint and proposes a 3-degree-of-freedom manipulator made of three such joints in series. Both simulation results and experiment results conducted on a test-bed prototype are presented and discussed.

There have been several research works on reconfigurable parallel manipulators in the last few years. Some robots are reconfigurable in the sense that the position of the anchor points on the moving platform or the actuated joints can be changed. Some problems may arise when one intends to make a prototype and develop its control scheme. A reconfigurable planar parallel robot, named NaVARo, is a 3-DOF planar parallel manipulator with eight actuation modes. The subject of this paper is about a control scheme of NaVARo while taking advantage of multiple sensors such as motor encoders, additional absolute encoders and magnetic sensors used to determine the current assembly mode of the manipulator. Finally, a methodology is presented to determine the home configuration of NaVARo.

This paper presents a novel design of a compact and light-weight robotic hand for a social humanoid robot. The proposed system is able to perform common hand gestures and self-adaptable grasps by mixing under-actuated and self-adaptable hand kinematics in a unique design. The hand answers the need for precise finger postures and sensor-less force feedback during gestures and for finger adaptation and autonomous force distribution during grasps. These are provided by a dual actuation system embodied within the palm and the fingers. Coexistence is ensured by compliant transmissions based on elastomer bars rather than classical tension springs, thanks to their high elastic coefficient at reduced sizes and strains. The proposed solution significantly reduces the weight and the size of the hand by using a reduced number of small actuators for gesturing and a single motor for grasping. The hand prototype (ALPHA) is realized to confirm the design feasibility and functional capabilities. It is controlled to provide safe human-robot interaction and preserve mechanical integrity in order to be embodied on a humanoid robot.

This paper presents a numerical method to conceive and design the kinematic model of an anthropomorphic robotic hand used for gesturing and grasping. In literature, there are few numerical methods for the finger placement of human-inspired robotic hands. In particular, there are no numerical methods, for the thumb placement, that aim to improve the hand dexterity and grasping capabilities by keeping the hand design close to the human one. While existing models are usually the result of successive parameter adjustments, the proposed method determines the fingers placements by mean of empirical tests. Moreover, a surgery test and the workspace analysis of the whole hand are used to find the best thumb position and orientation according to the hand kinematics and structure. The result is validated through simulation where it is checked that the hand looks well balanced and that it meets our constraints and needs. The presented method provides a numerical tool which allows the easy computation of finger and thumb geometries and base placements for a human-like dexterous robotic hand.

This paper presents a methodology to analyze the assembly conditions of parallel manipulators and compute the maximum pose errors of their moving platform, while considering geometric errors, joint clearances, link flexibility and joint elasticity. First, the proposed methodology consists in determining the zone(s) of the manipulator workspace in which the manipulator can be assembled assuming that its links and joints are rigid, while taking into account geometric errors and joint clearances. Then, the minimum energy required to assemble the manipulator in the non-assembly zone(s) is computed, while considering link flexibility and joint elasticity. The maximum pose errors of the moving-platform are also computed throughout the manipulator workspace. Finally, a two-dof spatial parallel manipulator, named IRSbot-2, is used as an illustrative example.

The paper focuses on the stiffness modeling of parallel manipulators composed of non-perfect serial chains, whose geometrical parameters differ from the nominal ones. In these manipulators, there usually exist essential internal forces/torques that considerably affect the stiffness properties and also change the end-effector location. These internal loadings are caused by elastic deformations of the manipulator elements during assembling, while the geometrical errors in the chains are compensated for by applying appropriate forces. For this type of manipulators, a non-linear stiffness modeling technique is proposed that allows us 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 for the compliance errors caused by different factors are illustrated by an example that deals with parallel manipulators of the Orthoglide family.

This paper focuses on stiffness matrix computation for manipulators with passive joints, compliant actuators, and flexible links. It proposes both explicit analytical expressions and an efficient recursive procedure that are applicable in the general case and allow us to obtain the desired matrix either in analytical or numerical form. Advantages of the developed technique and its ability to produce both singular and nonsingular stiffness matrices are illustrated by application examples that deal with stiffness modeling of two Stewart-Gough platforms.

Parallel robots admit generally several solutions to the direct kinematics problem. The aspects are associated with the maximal singularity free domains without any singular configurations. Inside these regions, some trajectories are possible between two solutions of the direct kinematic problem without meeting any type of singularity: non-singular assembly mode trajectories. An established condition for such trajectories is to have cusp points inside the joint space that must be encircled. This paper presents an approach based on the notion of uniqueness domains to explain this behaviour.

We study in this paper a class of 3-RPR manipulators for which the direct kinematic problem (DKP) is split into a cubic problem followed by a quadratic one. These manipulators are geometrically characterized by the fact that the moving triangle is the image of the base triangle by an indirect isometry. We introduce a specific coordinate system adapted to this geometric feature and which is also well adapted to the splitting of the DKP. This allows us to obtain easily precise descriptions of the singularities and of the cusp edges. These latter second order singularities are important for nonsingular assembly mode changing. We show how to sort assembly modes and use this sorting for motion planning in the joint space.

The paper focuses on stiffness matrix computation for manipulators with passive joints. It proposes both explicit analytical expressions and an efficient recursive procedure that are applicable in general case and allow obtaining the desired matrix either in analytical or numerical form. Advantages of the developed technique and its ability to produce both singular and non-singular stiffness matrices are illustrated by application examples that deal with stiffness modeling of two Stewart-Gough platforms.

In this paper, a new methodology for the optimal design of parallel kinematic machine tools is proposed. This approach is based on the concept of the maximal inscribed parallelepiped and uses technology-oriented constraints that are motivated by particular applications. This methodology is applied on two translational parallel robots with three degrees-of-freedom (DOF): the Y-STAR and the UraneSX. An analysis of the size of their workspace as a function of the design constraints is made. It is shown that, for identical workspaces with similar properties, the size of the legs of the UraneSX are greater than for the Y-STAR, thus leading to larger deformations. However, the footprint surface needed in order to install the Y-STAR is about two times bigger than for the UraneSX. Therefore, it may be interested to use the UraneSX in order to save some place on ground in manufacturing centres.

This paper introduces a methodology to analyze geometrically the singularities of manipulators, of which legs apply both actuation forces and constraint moments to their moving platform. Lower mobility parallel manipulators and parallel manipulators, of which some legs have no spherical joint, are such manipulators. The geometric conditions associated with the dependency of six PlUumlcker vectors of finite lines or lines at infinity constituting the rows of the inverse Jacobian matrix are formulated using Grassmann-Cayley algebra (GCA). Accordingly, the singularity conditions are obtained in vector form. This study is illustrated with the singularity analysis of four manipulators.

In this paper, a novel approach for parallel kinematic machine control relying on a fast exteroceptive measure is implemented and validated on the Orthoglide robot. This approach begins with rewriting the robot models as a function of the only end-effector pose. It is shown that such an operation reduces the model complexity. Then, this approach uses a classical Cartesian space computed torque control with a fast exteroceptive measure, reducing the control schemes complexity. Simulation results are given to show the expected performance improvements and experiments prove the practical feasibility of the approach.

The paper presents a new stiffness modelling method for overconstrained parallel manipulators, which is applied to 3-d.o.f. translational mechanisms. It is based on a multidimensional lumped-parameter model that replaces the link flexibility by localized 6-d.o.f. virtual springs. In contrast to other works, the method includes a FEA-based link stiffness evaluation and employs a new solution strategy of the kinetostatic equations, which allows computing the stiffness matrix for the overconstrained architectures and for the singular manipulator postures. The advantages of the developed technique are confirmed by application examples, which deal with comparative stiffness analysis of two translational parallel manipulators.

The Orthoglide is a Delta-type PKM dedicated to 3-axis rapid machining applications that was originally developed at IRCCyN in 2000-2001 to meet the advantages of both serial 3-axis machines (regular workspace and homogeneous performances) and parallel kinematic architectures (good dynamic performances and stiffness). This machine has three fixed parallel linear joints that are mounted orthogonally. The geometric parameters of the Orthoglide were defined as function of the size of a prescribed cubic Cartesian workspace that is free of singularities and internal collision. The interesting features of the Orthoglide are a regular Cartesian workspace shape, uniform performances in all directions and good compactness. In this paper, a new method is proposed to analyze the stiffness of overconstrained Delta-type manipulators, such as the Orthoglide. The Orthoglide is then benchmarked according to geometric, kinematic and stiffness criteria: workspace to footprint ratio, velocity and force transmission factors, sensitivity to geometric errors, torsional stiffness and translational stiffness.

This paper deals with the in-depth kinematic analysis of a special parallel wrist, called the agile eye. The agile eye is a three-legged spherical parallel robot with revolute joints, in which all pairs of adjacent joint axes are orthogonal. Its most peculiar feature, demonstrated in this paper for the first time, is that its workspace is unlimited and flawed only by six singularity curves (instead of surfaces). These curves correspond to self-motions of the mobile platform and of the legs, or to a lockup configuration. This paper also demonstrates that the four solutions to the direct kinematics of the agile eye (assembly modes) have a simple direct relationship with the eight solutions to the inverse kinematics (working modes)

This paper investigates the singular curves in two-dimensional slices of the joint space of a family of planar parallel manipulators. It focuses on special points, referred to as cusp points, which may appear on these curves. Cusp points play an important role in the kinematic behavior of parallel manipulators since they make possible a nonsingular change of assembly mode. The purpose of this study is twofold. First, it reviews an important previous work, which, to the authors' knowledge, has never been exploited yet. Second, it determines the cusp points in any two-dimensional slice of the joint space. First results show that the number of cusp points may vary from zero to eight. This work finds applications in both design and trajectory planning

The design of a spherical wrist with parallel architecture is the object of this article. This study is part of a larger project, which aims to design and to build an eel robot for inspection of immersed piping. The kinematic analysis of the mechanism is presented first to characterize the singular configurations as well as the isotropic configurations. We add the design constraints related to the application, such as (i) the compactness of the mechanism, (ii) the symmetry of the elements in order to ensure static and dynamic balance and (iii) the possibility of the mechanism to fill the elliptic form of the ell sections.

In the present paper, we introduce a new control architecture aimed at driving virtual humans in interaction with virtual environments, by motion capture. It brings decoupling of functionalities, and also of stability thanks to passivity. We show projections can break passivity, and thus must be used carefully. Our control scheme enables task space and internal control, contact, and joint limits management. Thanks to passivity, it can be easily extended. Besides, we introduce a new tool as for manikin's control, which makes it able to build passive projections, so as to guide the virtual manikin when sharp movements are needed.

A classification of a family of 3-revolute (3R) positioning manipulators is established. This classification is based on the topology of their workspace. The workspace is characterized in a half-cross section by the singular curves. The workspace topology is defined by the number of cusps and nodes that appear on these singular curves. The design parameters space is shown to be divided into nine domains of distinct workspace topologies, in which all manipulators have similar global kinematic properties. Each separating surface is given as an explicit expression in the DH-parameters.

The subject of this paper is the design of a new concept of modular parallel mechanisms for three, four or five-axis machining applications. Most parallel mechanisms are designed for three- or six-axis machining applications. In the last case, the position and the orientation of the tool are coupled and the shape of the workspace is complex. The aim of this paper is to use a simple parallel mechanism with two-degree-of-freedom (dof) for translation motions and to add one or two legs to add one or two-dofs for rotation motions. The kinematics and singular configurations are studied for each mechanism.

This paper addresses the architecture optimization of a three-degree-of-freedom translational parallel mechanism designed for machining applications. The design optimization is conducted on the basis of a prescribed Cartesian workspace with prescribed kinetostatic performances. The resulting machine, the Orthoglide, features three fixed parallel linear joints which are mounted orthogonally, and a mobile platform which moves in the Cartesian x-y-z space with fixed orientation. The interesting features of the Orthoglide are a regular Cartesian workspace shape, uniform performances in all directions, and good compactness. A small-scale prototype of the Orthoglide under development is presented at the end of this paper.

The aim of this paper is to characterize the notion of aspects in the workspace and in the joint space for parallel manipulators. In opposite to the serial manipulators, the parallel manipulators can admit not only multiple inverse kinematic solutions, but also multiple direct kinematic solutions. Two Jacobian matrices appear in the kinematic relations between the joint-rate and the Cartesian-velocity vectors, which are called the "inverse kinematics" and the "direct kinematics" matrices. The study of these matrices allow one to define the parallel and the serial singularities respectively. The notion of working modes is introduced to separate inverse kinematic solutions. Thus we can find out the domains of the workspace and the joint space which exempt of singularity. An application of this study is the movability analysis in the workspace of the manipulator as well as the path-planning and control. This study is illustrated with a RR-RRR planar parallel manipulator.

The subject of this paper is a special class of closed chain manipulators. First, we analyze a family of two-degree-of-freedom (DOF) five-bar planar linkages. Two Jacobian matrices appear in the kinematic relations between the joint-rate and the Cartesian-velocity vectors, which are called the "inverse kinematics" and the "direct kinematics" matrices. It is shown that the loci of points of the workspace where the condition number of the direct-kinematics matrix remains constant, i.e., the isoconditioning loci, are the coupler points of the four-bar linkage obtained upon locking the middle joint of the linkage. Furthermore, if the line of centers of the two activated revolutes is used as the axis of a third actuated revolute, then a 3-DOF hybrid manipulator is obtained. The isoconditioning loci of this manipulator are surfaces of revolution generated by the isoconditioning curves of the 2-DOF manipulator, whose axis of symmetry is that of the third actuated revolute.