Damien Chablat

Doina Pisla, Ionut Zima, Calin Vaida et al.

Minimally invasive surgery (MIS) reduces patient trauma and shortens recovery time; however, conventional laparoscopic instruments remain constrained by limited range of movements. This work presents the control architecture of a 4-DOF flexible laparoscopic instrument integrating distal bending, independent distal head rotation, shaft rotation, and a gripper, while maintaining a 10 mm diameter compatible with standard trocars. The actuation unit and SpaceMouse teleoperation are implemented on Raspberry Pi 5 with Motoron controllers. An analytical scissor-linkage model is derived and parameterized. The predicted jaw opening corresponds to CAD measurements (MAE 0.13{\textdegree}) and OptiTrack motion capture (MAE 1.43{\textdegree}). Integration with the ATHENA parallel robot is validated through a simulated pancreatic surgery procedure.

Stanley Mugisha, Vamsi Krishna Guda, Christine Chevallereau et al.

Humans use collaborative robots as tools for accomplishing various tasks. The interaction between humans and robots happens in tight shared workspaces. However, these machines must be safe to operate alongside humans to minimize the risk of accidental collisions. Ensuring safety imposes many constraints, such as reduced torque and velocity limits during operation, thus increasing the time to accomplish many tasks. However, for applications such as using collaborative robots as haptic interfaces with intermittent contacts for virtual reality applications, speed limitations result in poor user experiences. This research aims to improve the efficiency of a collaborative robot while improving the safety of the human user. We used Gaussian process models to predict human hand motion and developed strategies for human intention detection based on hand motion and gaze to improve the time for the robot and human security in a virtual environment. We then studied the effect of prediction. Results from comparisons show that the prediction models improved the robot time by 3\% and safety by 17\%. When used alongside gaze, prediction with Gaussian process models resulted in an improvement of the robot time by 2\% and the safety by 13\%.

Haribhau Durgesh, Guillaume Michel, Shivesh Kumar et al.

The optimization of parallel kinematic manipulators (PKM) involve several constraints that are difficult to formalize, thus making optimal synthesis problem highly challenging. The presence of passive joint limits as well as the singularities and self-collisions lead to a complicated relation between the input and output parameters. In this article, a novel optimization methodology is proposed by combining a local search, Nelder-Mead algorithm, with global search methodologies such as low discrepancy distribution for faster and more efficient exploration of the optimization space. The effect of the dimension of the optimization problem and the different constraints are discussed to highlight the complexities of closed-loop kinematic chain optimization. The work also presents the approaches used to consider constraints for passive joint boundaries as well as singularities to avoid internal collisions in such mechanisms. The proposed algorithm can also optimize the length of the prismatic actuators and the constraints can be added in modular fashion, allowing to understand the impact of given criteria on the final result. The application of the presented approach is used to optimize two PKMs of different degrees of freedom.

A Gutierrez, V Guda, S Mugisha et al.

In a human-robot interaction system, the most important thing to consider is the safety of the user. This must be guaranteed in order to implement a reliable system. The main objective of this paper is to generate a safe motion scheme that takes into account the obstacles present in a virtual reality (VR) environment. The work is developed using the MoveIt software in ROS to control an industrial robot UR5. Thanks to this, we will be able to set up the planning group, which is realized by the UR5 robot with a 6-sided prop and the base of the manipulator, in order to plan feasible trajectories that it will be able to execute in the environment. The latter is based on the interior of a vehicle, containing a person (which would be the user in this case) for which the configuration will also be made to be taken into account in the system. To do this, we first investigated the software's capabilities and options for path planning, as well as the different ways to execute the movements. We also compared the different trajectory planning algorithms that the software is capable of using in order to determine which one is best suited for the task. Finally, we proposed different mobility schemes to be executed by the robot depending on the situation it is facing. The first one is used when the robot has to plan trajectories in a safe space, where the only obstacle to avoid is the user's workspace. The second one is used when the robot has to interact with the user, where a dummy model represents the user's position as a function of time, which is the one to be avoided.

Wanda Zhao, Alexandr Klimchik, Anatol Pashkevich et al.

The paper focuses on the stiffness analysis of multi-link serial planar manipulators, which may demonstrate nonlinear stiffness behavior under the compressive loading. Two important cases are considered, where the manipulator has either a straight or non-straight initial configuration. It was proved that in the first case the loading may cause the buckling if it exceeds some critical value, and the manipulator suddenly changes its straight shape and stiffness properties. For computing this critical force, a general eigenvalue-based technique was proposed that can be applied to any multi-link serial manipulator. For the second case dealing with non-straight initial configurations, a universal energy-based technique was applied that allowed to detect quasi-buckling phenomenon when it is observed very fast but not instant change of the manipulator shape and its stiffness coefficient under the loading. These results are illustrated by numerous examples of non-linear stiffness behavior of three-and four-link manipulators that are subjected to compressive force.

Durgesh Haribhau Salunkhe, Christoforos Spartalis, Jose Capco et al.

Cuspidal robots can travel from one inverse kinematic solution to another without meeting a singularity. The name cuspidal was coined based on the existence of a cusp point in the workspace of 3R serial robots. The existence of a cusp point was proved to be a necessary and sufficient condition for orthogonal robots to be cuspidal, but it was not possible to extend this condition to non-orthogonal robots. The goal of this paper is to prove that this condition stands for any generic 3R robot. This result would give the designer more flexibility. In the presented work, the geometrical interpretation of the inverse kinematics of 3R robots is revisited and important observations on the nonsingular change of posture are noted. The paper presents a theorem regarding the existence of reduced aspects in any generic 3R serial robot. Based on these observations and on this theorem, we prove that the existence of a cusp point is a necessary and sufficient condition for any 3R generic robot to be cuspidal.

Liang Ma, Damien Chablat, Fouad Bennis et al.

Musculoskeletal disorder (MSD) is one of the major health problems in physical work especially in manual handling jobs. In several literatures, muscle fatigue is considered to be closely related to MSD, especially for muscle related disorders. In addition to many existing analysis techniques for muscle fatigue assessment and MSD risk analysis, in this paper, a new muscle fatigue model was proposed. The new proposed model reflects the influence of external load, workload history, and individual differences. This model is simple in mathematics and can be easily applied in realtime calculation, such as the application in realtime virtual work simulation and evaluation. The new model was mathematically validated with 24 existing static models by comparing the calculated METs, and qualitatively or quantitatively validated with 3 existing dynamic models. The proposed model shows high or moderate similarities in predicting the METs with all the 24 static models. Validation results with the three dynamic models were also promising. The main limitation of the model is that it still lacks experimental validation for more dynamic situations. Relevance to industry Muscle fatigue is one of the main reasons causing MSDs in industry, especially for physical work. Correct evaluation of muscle fatigue is necessary to determine work-rest regimens and reduce the risks of MSD.

Guillaume Michel, Durgesh Salunkhe, Philippe Bordure et al.

In otolaryngologic surgery, more and more robots are being studied to meet the clinical needs of operating rooms. However, to help design and optimize these robots, the workspace must be precisely defined taking into account patient variability. The aim of this work is to define a geometric atlas of the middle ear and paranasal sinuses for endoscopic robotic applications. Scans of several patients of different ages and sexes were used to determine the average size of these workspaces, which are linked by the similar use of endoscopes in surgery.

Guillaume Michel, Durgesh Haribhau Salunkhe, Philippe Bordure et al.

In otolaryngologic surgery, endoscopy is increasingly used to provide a better view of hard-to-reach areas and to promote minimally invasive surgery. However, the need to manipulate the endoscope limits the surgeon's ability to operate with only one instrument at a time. Currently, several robotic systems are being developed, demonstrating the value of robotic assistance in microsurgery. The aim of this literature review is to present and classify current robotic systems that are used for otological and endonasal applications. For these solutions, an analysis of the functionalities in relation to the surgeon's needs will be carried out in order to produce a set of specifications for the creation of new robots.

Wanda Zhao, Anatol Pashkevich, Damien Chablat

The paper focuses on the redundancy resolution in kinematic control of a new type of serial manipulator composed of multiple tensegrity segments, which are moving in a multi-obstacle environment. The general problem is decomposed into two sub-problems, which deal with collision-free path planning for the robot end-effector and collision-free motion planning for the robot body. The first of them is solved via discrete dynamic programming, the second one is worked out using quadratic programming with mixed linear equality/nonequality constraints. Efficiency of the proposed technique is confirmed by simulation.

Wanda Zhao, Anatol Pashkevich, Damien Chablat

The paper focuses on the stiffness modeling of a new type of compliant manipulator and its non-linear behavior while interacting with the environment. The manipulator under study is a serial mechanical structure composed of dualtriangle segments. The main attention is paid to the initial straight configuration which may suddenly change its shape under the loading. It was discovered that under the external loading such manipulator may have six equilibrium configurations but only two of them are stable. In the neighborhood of these configurations, the manipulator behavior was analyzed using the Virtual Joint Method (VJM). This approach allowed us to propose an analytical technique for computing a critical force causing the buckling and evaluate the manipulator shape under the loading. A relevant simulation study confirmed the validity of the developed technique and its advantages in non-linear stiffness analysis.

Pol Hamon, Damien Chablat, Franck Plestan

This article presents a new hand architecture with three under-actuated fingers. Each finger performs spatial movements to achieve more complex and varied grasping than the existing planar-movement fingers. The purpose of this hand is to grasp complex-shaped workpieces as they leave the machining centres. Among the taxonomy of grips, cylindrical and spherical grips are often used to grasp heavy objects. A combination of these two modes makes it possible to capture most of the workpieces machined with 5-axis machines. However, the change in grasping mode requires the fingers to reconfigure themselves to perform spatial movements. This solution requires the addition of two or three actuators to change the position of the fingers and requires sensors to recognize the shape of the workpiece and determine the type of grasp to be used. This article proposes to extend the notion of under-actuated fingers to spatial movements. After a presentation of the kinematics of the fingers, the problem of stability is discussed as well as the transmission of forces in this mechanism. The complete approach for calculating the stability conditions is presented from the study of Jacobian force transmission matrices. CAD representations of the hand and its behavior in spherical and cylindrical grips are presented.

Huiping Shen, Yinan Zhao, Ju Li et al.

This paper presents a novel three-degree-of-freedom (3-DOF) translational parallel manipulator (TPM) by using a topological design method of parallel mechanism (PM) based on position and orientation characteristic (POC) equations. The proposed PM is only composed of lower-mobility joints and actuated prismatic joints, together with the investigations on three kinematic issues of importance. The first aspect pertains to geometric modeling of the TPM in connection with its topological characteristics, such as the POC, degree of freedom and coupling degree, from which its symbolic direct kinematic solutions are readily obtained. Moreover, the decoupled properties of input-output motions are directly evaluated without Jacobian analysis. Sequentially, based upon the inverse kinematics, the singular configurations of the TPM are identified, wherein the singular surfaces are visualized by means of a Gr{ö}bner based elimination operation. Finally, the workspace of the TPM is evaluated with a geometric approach. This 3-DOF TPM features less joints and links compared with the well-known Delta robot, which reduces the structural complexity. Its symbolic direct kinematics and partially-decoupled property will ease path planning and dynamic analysis. The TPM can be used for manufacturing large work pieces.

Wanda Zhao, Anatol Pashkevich, Alexandr Klimchik et al.

The paper focuses on the kinematics control of a compliant serial manipulator composed of a new type of dualtriangle elastic segments. Some useful optimization techniques were applied to solve the geometric redundancy problem, ensure the stability of the manipulator configurations with respect to the external forces/torques applied to the endeffector. The efficiency of the developed control algorisms is confirmed by simulation.

Jing Geng, Vigen Arakelian, Damien Chablat

The shaking force balancing is a well-known problem in the design of high-speed robotic systems because the variable dynamic loads cause noises, wear and fatigue of mechanical structures. Different solutions, for full or partial shaking force balancing, via internal mass redistribution or by adding auxiliary links were developed. The paper deals with the shaking force balancing of the Orthoglide. The suggested solution based on the optimal acceleration control of the manipulator's common center of mass allows a significant reduction of the shaking force. Compared with the balancing method via adding counterweights or auxiliary substructures, the proposed method can avoid some drawbacks: the increase of the total mass, the overall size and the complexity of the mechanism, which become especially challenging for special parallel manipulators. Using the proposed motion control method, the maximal value of the total mass center acceleration is reduced, as a consequence, the shaking force of the manipulator decreases. The efficiency of the suggested method via numerical simulations carried out with ADAMS is demonstrated.

Damien Chablat, Wanda Zhao, Anatol Pashkevich et al.

The paper focuses on the mechanics of a compliant serial manipulator composed of new type of dual-triangle elastic segments. Both the analytical and numerical methods were used to find the manipulator stable and unstable equilibrium configurations, as well as to predict corresponding manipulator shapes. The stiffness analysis was carried on for both loaded and unloaded modes, the stiffness matrices were computed using the Virtual Joint Method (VJM). The results demonstrate that either buckling or quasi-buckling phenomenon may occur under the loading, if the manipulator corresponding initial configuration is straight or non-straight one. Relevant simulation results are presented that confirm the theoretical study.

Jing Chang, Wenrui Wang, Damien Chablat et al.

As a traditional tool of external assistance, crutches play an important role in society. They have a wide range of applications to help either the elderly and disabled to walk or to treat certain illnesses or for post-operative rehabilitation. But there are many different types of crutches, including shoulder crutches and elbow crutches. How to choose has become an issue that deserves to be debated. Because while crutches help people walk, they also have an impact on the body. Inappropriate choice of crutches or long-term misuse can lead to problems such as scoliosis. Previous studies were mainly experimental measurements or the construction of dynamic models to calculate the load on joints with crutches. These studies focus only on the level of the joints, ignoring the role that muscles play in this process. Although some also take into account the degree of muscle activation, there is still a lack of quantitative analysis. The traditional dynamic model can be used to calculate the load on each joint. However, due to the activation of the muscle, this situation only causes part of the load transmitted to the joint, and the work of the chair will compensate the other part of the load. Analysis at the muscle level allows a better understanding of the impact of crutches on the body. By comparing the levels of activation of the trunk muscles, it was found that the use of crutches for walking, especially a single crutch, can cause a large difference in the activation of the back muscles on the left and right sides, and this difference will cause muscle degeneration for a long time, leading to scoliosis. In this article taking scoliosis as an example, by analyzing the muscles around the spine, we can better understand the pathology and can better prevent diseases. The objective of this article is to analyze normal walking compared to walking with one or two crutches using OpenSim software to obtain the degree of activation of different muscles in order to analyze the impact of crutches on the body.

Guillaume Michel, Durgesh Salunkhe, Damien Chablat et al.

Since the insertion area in the middle ear or in the sinus cavity is very narrow, the mobility of the endoscope is reduced to a rotation around a virtual point and a translation for the insertion of the camera. This article first presents the anatomy of these regions obtained from 3D scanning and then a mechanism based on the architecture of the agile eye coupled to a double parallelogram to create an RCM. This mechanism coupled with a positioning mechanism is used to handle an endoscope. This tool is used in parallel to the surgeon to allow him to have better rendering of the medium ear than the use of Binocular scope. The mechanism offers a wide working space without singularity whose borders are fixed by joint limits. This feature allows ergonomic positioning of the patient's head on the bed as well as for the surgeon and allows other applications such as sinus surgery.

Yann Briheche, Frédéric Barbaresco, Fouad Bennis et al.

Electronic phased-array radars offer new possibilities for radar search pattern optimization by using bi-dimensional beam-forming and beam-steering. Radar search pattern optimization can be approximated as a set cover problem and solved using integer programming, while accounting for localized clutter and terrain masks in detection constraints. We present a set cover problem approximation for time-budget minimization of radar search patterns, under constraints of range, detection probability and direction-specific scan update rates. Branch\&Bound is a classical optimization procedure for solving combinatorial problems. It is known mainly as an exact algorithm, but features interesting characteristics, making it particularly fit for solving optimization problems in real-time applications and producing just-in-time solutions.

Huiping Shen, Damien Chablat, Boxiong Zeng et al.

According to the topological design theory and method of parallel mechanism (PM) based on position and orientation characteristic (POC) equations, this paper studied a 3-DOF translational PM that has three advantages, i.e., (i) it consists of three fixed actuated prismatic joints, (ii) the PM has analytic solutions to the direct and inverse kinematic problems, and (iii) the PM is of partial motion decoupling property. Firstly, the main topological characteristics, such as the POC, degree of freedom and coupling degree were calculated for kinematic modeling. Thanks to these properties, the direct and inverse kinematic problems can be readily solved. Further, the conditions of the singular configurations of the PM were analyzed which corresponds to its partial motion decoupling property.

Yang Zhang, Vigen Arakelian, Baptiste Veron et al.

The paper deals with coupled systems including hand-operated balanced manipulators and lightweight robots. The aim of such a cooperation is to displace heavy payloads with less powerful robots. In other term, in the coupled system for handling of heavy payloads by a HOBM an operator is replaced by a LWR. The advantages of the coupled HOBM and LWR are disclosed and the optimal design of the cooperative workspace is discussed. Behavior of the coupled system in a static mode when the velocities the HOBM are limited does not present any special problems. In this mode, the inertial forces are significantly lower than the gravitational one. The payload is completely balanced by the HOBM and the LWR assumes the prescribed displacements with low load. However, in a dynamic mode, the HOBM with massive links creates additional loads on the LWR, which can be significant. The present study considers a method for determination of inertia effects of the HOBM on the LWR. The given numerical simulations show the significant increasing of the input torques due to the inertia forces of the HOBM. Behavior of the HOBM with cable lift and the LWR is also examined.

Damien Chablat, Luc Rolland

This article presents a new variable actuation mechanism based on the 3-RPR parallel robot. This mechanismis an evolution of the NaVARo robot, a 3-RRR parallel robot, for which the second revolute joint of the threelegs is replaced by a scissor to obtain a larger working space and avoid the use of parallelograms to operate thesecond revolute joint. To obtain better spatial rigidity, the leg mechanism is constructed by placing the scissorsin an orthogonal plane to the plane of the manipulator displacement (3-RRR or even the 3-RPR). This geometricproperty brings the significant consequence of allowing the scissors to directly substitute the prismatic chains in the3-RPR and enjoy the same kinematics advantages for the overall robots as only one solution to the inverse kinematicmodel. From the Jacobian expression, surfaces of singularity can be calculated and presented in a compact form.The singularity equations are presented for a robot with a similar base and mobile platform. The properties of thescissors are then determined to have a prescribed regular workspace.

Boxiong Zeng, Ting-Li Yang, Huiping Shen et al.

According to the topological design theory and method of parallel mechanism (PM) based on position and orientation characteristic (POC) equations, this paper design a novel 3-translation (3T) PM that has three advantages, i.e., 1) it consists on three actuated prismatic joints, 2) the PM has analytical direct position solutions, and 3) the PM is of partial motion decoupling property. Firstly, the main topological characteristics such as the POC, degree of freedom and coupling degree are calculated for kinematics modelling. Due to the special constraint feature of the 3-translation, the analytical direct position solutions of the PM can be directly obtained without needing to use one-dimensional search method. Further, the conditions of the singular configuration of the PM, as well as the singularity location inside the workspace are analyzed according to the inverse kinematics.

Xiaorong Zhu, Huiping Shen, Chengqi Wu et al.

The determination of the mobility of parallel mechanisms (PM) is a fundamental problem. An automatic and intelligent analysis platform will be a significant tool for the design and optimization of mechanical systems. Based on the theory of position and orientation characteristics (POC) equations, a systematic approach to computer-aided mobility analysis of PMs is presented in this paper. First, a digital model for topological structures which has a mapping relationship with position and orientation characteristics of mechanism is proposed. It describes not only the dimension of the motion output, but also gives the mapping relationship between the output characteristic and the axis of the kinematic joints. Secondly, algorithmic rules are established that convert the union and intersection operations of POC into the binary logical operations and the automatic analysis of POC are realized. Then, the algorithm of the automatic mobility analysis of PMs and its implementation with VC++ are written .The mobility and its properties (POC) will also be analyzed and displayed automatically after introducing by users of the data of topological structures representation. Finally, typical examples are provided to show the effectiveness of the software platform.

Alexandr Klimchik, Damien Chablat, Anatol Pashkevich

The paper presents advancement of the matrix structural analysis technique (MSA) for stiffness modeling of robotic manipulators. In contrast to the classical MSA, it can be applied to both parallel and serial manipulators composed of flexible and rigid links connected by rigid, passive or elastic joints with multiple external loadings. The manipulator stiffness model is presented as a set of basic equations describing the link elasticities that are supplemented by a set of constraints describing connections between links. These equations are aggregated straightforwardly in a common linear system without traditional merging of the matrix rows and columns, which allows avoiding conventional manual transformations at the expense of numerical inversion of the sparse matrix of higher dimension.

Huiping Shen, Chengqi Wu, Damien Chablat et al.

In this paper a new asymmetric 3-translational (3T) parallel manipulator, i.e., RPa(3R) 2R+RPa, with zero coupling degree and decoupled motion is firstly proposed according to topology design theory of parallel mechanism (PM) based on position and orientation characteristics (POC) equations. The main topological characteristics such as POC, degree of freedom and coupling degree are calculated. Then, the analytical formula for the direct and inverse kinematic are directly derived since coupling degree of the PM is zero. The study of singular configurations is simple because of the independence of the kinematic chains.

P Wenger, Damien Chablat

Tensegrity mechanisms have several interesting properties that make them suitable for a number of applications. Their analysis is generally challenging because the static equilibrium conditions often result in complex equations. A class of planar one-degree-of-freedom (dof) tensegrity mechanisms with three linear springs is analyzed in detail in this paper. The kinetostatic equations are derived and solved under several loading and geometric conditions. It is shown that these mechanisms exhibit up to six equilibrium configurations, of which one or two are stable. Discriminant varieties and cylindrical algebraic decomposition combined with Groebner base elimination are used to classify solutions as function of the input parameters.

Damien Chablat, Luc Baron, Ranjan Jha

This paper presents the kinematic analysis of the 3-PPPS parallel robot with an equilateral mobile platform and a U-shape base. The proposed design and appropriate selection of parameters allow to formulate simpler direct and inverse kinematics for the manipulator under study. The parallel singularities associated with the manipulator depend only on the orientation of the end-effector, and thus depend only on the orientation of the end effector. The quaternion parameters are used to represent the aspects, i.e. the singularity free regions of the workspace. A cylindrical algebraic decomposition is used to characterize the workspace and joint space with a low number of cells. The dis-criminant variety is obtained to describe the boundaries of each cell. With these simplifications, the 3-PPPS parallel robot with proposed design can be claimed as the simplest 6 DOF robot, which further makes it useful for the industrial applications.

Damien Chablat, Xianwen Kong, Chengwei Zhang

A family of reconfigurable parallel robots can change motion modes by passing through constraint singularities by locking and releasing some passive joints of the robot. This paper is about the kinematics, the workspace and singularity analysis of a 3-PRPiR parallel robot involving lockable Pi and R (revolute) joints. Here a Pi joint may act as a 1-DOF planar parallelogram if its lock-able P (prismatic) joint is locked or a 2-DOF RR serial chain if its lockable P joint is released. The operation modes of the robot include a 3T operation modes to three 2T1R operation modes with two different directions of the rotation axis of the moving platform. The inverse kinematics and forward kinematics of the robot in each operation modes are dealt with in detail. The workspace analysis of the robot allow us to know the regions of the workspace that the robot can reach in each operation mode. A prototype built at Heriot-Watt University is used to illustrate the results of this work.

Natalia Varminska, Damien Chablat

In this article, a theoretical justification of one type of skew-symmetric optimal translational motion (moving in the minimal acceptable time) of a flexible object carried by a robot from its initial to its final position of absolute quiescence with the exception of the oscillations at the end of the motion is presented. The Hamilton-Ostrogradsky principle is used as a criterion for searching an optimal control. The data of experimental verification of the control are presented using the Orthoglide robot for translational motions and several masses were attached to a flexible beam.

Michel Coste, Philippe Wenger, Damien Chablat

This paper investigates a situation pointed out in a recent paper, in which a non-singular change of assembly mode of a planar 2-RPR-PR parallel manipulator was realized by encircling a point of multiplicity 4. It is shown that this situation is, in fact, a non-generic one and gives rise to cusps under a small perturbation. Furthermore , we show that, for a large class of singularities of multiplicity 4, there are only two types of stable singularities occurring in a small perturbation: these two types are given by the complex square mapping and the quarto mapping. Incidentally , this paper confirms the fact that, generically, a local non-singular change of solution must be accomplished by encircling a cusp point.

S Caro, Damien Chablat, P Lemoine et al.

The subject of this paper is about the kinematic analysis and the trajectory planning of the Orthoglide 5-axis. The Orthoglide 5-axis a five degrees of freedom parallel kinematic machine developed at IRCCyN and is made up of a hybrid architecture, namely, a three degrees of freedom translational parallel manip-ulator mounted in series with a two degrees of freedom parallel spherical wrist. The simpler the kinematic modeling of the Or-thoglide 5-axis, the higher the maximum frequency of its control loop. Indeed, the control loop of a parallel kinematic machine should be computed with a high frequency, i.e., higher than 1.5 MHz, in order the manipulator to be able to reach high speed motions with a good accuracy. Accordingly, the direct and inverse kinematic models of the Orthoglide 5-axis, its inverse kine-matic Jacobian matrix and the first derivative of the latter with respect to time are expressed in this paper. It appears that the kinematic model of the manipulator under study can be written in a quadratic form due to the hybrid architecture of the Orthoglide 5-axis. As illustrative examples, the profiles of the actuated joint angles (lengths), velocities and accelerations that are used in the control loop of the robot are traced for two test trajectories.

Ranjan Jha, Damien Chablat, Fabrice Rouillier et al.

Trajectory planning is a critical step while programming the parallel manipulators in a robotic cell. The main problem arises when there exists a singular configuration between the two poses of the end-effectors while discretizing the path with a classical approach. This paper presents an algebraic method to check the feasibility of any given trajectories in the workspace. The solutions of the polynomial equations associated with the tra-jectories are projected in the joint space using Gr{ö}bner based elimination methods and the remaining equations are expressed in a parametric form where the articular variables are functions of time t unlike any numerical or discretization method. These formal computations allow to write the Jacobian of the manip-ulator as a function of time and to check if its determinant can vanish between two poses. Another benefit of this approach is to use a largest workspace with a more complex shape than a cube, cylinder or sphere. For the Orthoglide, a three degrees of freedom parallel robot, three different trajectories are used to illustrate this method.

R. Jha, Damien Chablat, Fabrice Rouillier et al.

Workspace and joint space analysis are essential steps in describing the task and designing the control loop of the robot, respectively. This paper presents the descriptive analysis of a family of delta-like parallel robots by using algebraic tools to induce an estimation about the complexity in representing the singularities in the workspace and the joint space. A Gr{ö}bner based elimination is used to compute the singularities of the manipulator and a Cylindrical Algebraic Decomposition algorithm is used to study the workspace and the joint space. From these algebraic objects, we propose some certified three dimensional plotting describing the the shape of workspace and of the joint space which will help the engineers or researchers to decide the most suited configuration of the manipulator they should use for a given task. Also, the different parameters associated with the complexity of the serial and parallel singularities are tabulated, which further enhance the selection of the different configuration of the manipulator by comparing the complexity of the singularity equations.

Giulio Cerruti, Damien Chablat, David Gouaillier et al.

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.

Sophie Sakka, Damien Chablat, Ruina Ma et al.

Repetitive tasks in industrial works may contribute to health problems among operators, such as musculo-skeletal disorders, in part due to insufficient control of muscle fatigue. In this paper, a predictive model of fatigue is proposed for repetitive push/pull operations. Assumptions generally accepted in the literature are first explicitly set in this framework. Then, an earlier static fatigue model is recalled and extended to quasi-static situations. Specifically, the maximal torque that can be generated at a joint is not considered as constant, but instead varies over time accordingly to the operator's changing posture. The fatigue model is implemented with this new consideration and evaluated in a simulation of push/pull operation. Reference to this paper should be made as follows: Sakka, S., Chablat, D., Ma, R. and Bennis, F. (2015) 'Predictive model of the human muscle fatigue: application to repetitive push-pull tasks with light external load', Int.

Renaud Henry, Damien Chablat, Mathieu Porez et al.

This paper addresses the dimensional synthesis of an adaptive mechanism of contact points ie a leg mechanism of a piping inspection robot operating in an irradiated area as a nuclear power plant. This studied mechanism is the leading part of the robot sub-system responsible of the locomotion. Firstly, three architectures are chosen from the literature and their properties are described. Then, a method using a multi-objective optimization is proposed to determine the best architecture and the optimal geometric parameters of a leg taking into account environmental and design constraints. In this context, the objective functions are the minimization of the mechanism size and the maximization of the transmission force factor. Representations of the Pareto front versus the objective functions and the design parameters are given. Finally, the CAD model of several solutions located on the Pareto front are presented and discussed.

Damien Chablat, Ranjan Jha, Fabrice Rouillier et al.

Having non-singular assembly modes changing trajectories for the 3-RPS parallel robot is a well-known feature. The only known solution for defining such trajectory is to encircle a cusp point in the joint space. In this paper, the aspects and the characteristic surfaces are computed for each operation mode to define the uniqueness of the domains. Thus, we can easily see in the workspace that at least three assembly modes can be reached for each operation mode. To validate this property, the mathematical analysis of the determinant of the Jacobian is done. The image of these trajectories in the joint space is depicted with the curves associated with the cusp points.

Liang Ma, Wei Zhang, Bo Hu et al.

Cumulative local muscle fatigue may lead to potential musculoskeletal disorder (MSD) risks {\color{red}, and subject-specific muscle fatigability needs to be considered to reduce potential MSD risks.} This study was conducted to determine local muscle fatigue rate at shoulder joint level based on an exponential function derived from a muscle fatigue model. Forty male subjects participated in a fatiguing operation under a static posture with a range of relative force levels (14% - 33%). Remaining maximum muscle strengths were measured after different fatiguing sessions. The time course of strength decline was fitted to the exponential function. Subject-specific fatigue rates of shoulder joint moment strength were determined. Good correspondence ($R^2>0.8$) was found in the regression of the majority (35 out of 40 subjects). Substantial inter-individual variability in fatigue rate was found and discussed.

Alexandr Klimchik, Stéphane Caro, Yier Wu et al.

The paper focuses on the stiffness modeling of robotic manipulators with gravity compensators. The main attention is paid to the development of the stiffness model of a spring-based compensator located between sequential links of a serial structure. The derived model allows us to describe the compensator as an equivalent non-linear virtual spring integrated in the corresponding actuated joint. The obtained results have been efficiently applied to the stiffness modeling of a heavy industrial robot of the Kuka family.

Alexandr Klimchik, Anatol Pashkevich, Damien Chablat

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%.

Stefan Staicu, Damien Chablat

Recursive matrix relations for the complete dynamics of a 3-PRP planar parallel robot are established in this paper. Three identical planar legs connecting to the moving platform are located in the same vertical plane. Knowing the motion of the platform, we develop first the inverse kinematical problem and determine the positions, velocities and accelerations of the robot. Further, the inverse dynamic problem is solved using an approach based on the principle of virtual work. Finally, some graphs of simulation for the input powers of three actuators and the internal joint forces are obtained.

Ruina Ma, Damien Chablat, Fouad Bennis

Pushing/Pulling tasks is an important part of work in many industries. Usually, most researchers study the Push/Pull tasks by analyzing different posture conditions, force requirements, velocity factors, etc. However few studies have reported the effects of fatigue. Fatigue caused by physical loading is one of the main reasons responsible for MusculoSkeletal Disorders (MSD). In this paper, muscle groups of articulation is considered and from joint level a new approach is proposed for muscle fatigue evaluation in the arms Push/Pull operations. The objective of this work is to predict the muscle fatigue situation in the Push/Pull tasks in order to reduce the probability of MSD problems for workers. A case study is presented to use this new approach for analyzing arm fatigue in Pushing/Pulling.

Liang Ma, Ruina Ma, Damien Chablat et al.

During the conceptual and prototype design stage of an industrial product, it is crucial to take assembly/disassembly and maintenance operations in advance. A well-designed system should enable relatively easy access of operating manipulators in the constrained environment and reduce musculoskeletal disorder risks for those manual handling operations. Trajectory planning comes up as an important issue for those assembly and maintenance operations under a constrained environment, since it determines the accessibility and the other ergonomics issues, such as muscle effort and its related fatigue. In this paper, a customer-oriented interactive approach is proposed to partially solve ergonomic related issues encountered during the design stage under a constrained system for the operator's convenience. Based on a single objective optimization method, trajectory planning for different operators could be generated automatically. Meanwhile, a motion capture based method assists the operator to guide the trajectory planning interactively when either a local minimum is encountered within the single objective optimization or the operator prefers guiding the virtual human manually. Besides that, a physical engine is integrated into this approach to provide physically realistic simulation in real time manner, so that collision free path and related dynamic information could be computed to determine further muscle fatigue and accessibility of a product design

Montserrat Manubens, Guillaume Moroz, Damien Chablat et al.

This paper investigates the conditions in the design parameter space for the existence and distribution of the cusp locus for planar parallel manipulators. Cusp points make possible non-singular assembly-mode changing motion, which increases the maximum singularity-free workspace. An accurate algorithm for the determination is proposed amending some imprecisions done by previous existing algorithms. This is combined with methods of Cylindric Algebraic Decomposition, Gröbner bases and Discriminant Varieties in order to partition the parameter space into cells with constant number of cusp points. These algorithms will allow us to classify a family of degenerate 3-RPR manipulators.

Damien Chablat, Guillaume Moroz, Vigen Arakelian et al.

This paper proposes a new design method to determine the feasible set of parameters of translational or position/orientation decoupled parallel robots for a prescribed singularity-free workspace of regular shape. The suggested method uses Groebner bases to define the singularities and the cylindrical algebraic decomposition to characterize the set of parameters. It makes it possible to generate all the robot designs. A 3-RRR decoupled robot is used to validate the proposed design method.

Alexandr Klimchik, Anatoly Pashkevich, Damien Chablat et al.

The paper is devoted to the compliance errors compensation for parallel manipulators under external loading. Proposed approach is based on the non-linear stiffness modeling and reduces to a proper adjusting of a target trajectory. In contrast to previous works, in addition to compliance errors caused by machining forces, the problem of assembling errors caused by inaccuracy in the kinematic chains is considered. The advantages and practical significance of the proposed approach are illustrated by examples that deal with groove milling with Orthoglide manipulator.

Ruina Ma, Damien Chablat, Fouad Bennis et al.

Human muscle fatigue is considered to be one of the main reasons for Musculoskeletal Disorder (MSD). Recent models have been introduced to define muscle fatigue for static postures. However, the main drawbacks of these models are that the dynamic effect of the human and the external load are not taken into account. In this paper, each human joint is assumed to be controlled by two muscle groups to generate motions such as push/pull. The joint torques are computed using Lagrange's formulation to evaluate the dynamic factors of the muscle fatigue model. An experiment is defined to validate this assumption and the result for one person confirms its feasibility. The evaluation of this model can predict the fatigue and MSD risk in industry production quickly.

Alexandr Klimchik, Anatoly Pashkevich, Stéphane Caro et al.

The 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 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.