Anatol Pashkevich

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.

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.

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.

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.

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.

Alexandr Klimchik, Yier Wu, Stéphane Caro et al.

The paper is devoted to the accuracy improvement of robot-based milling by using an enhanced manipulator model that takes into account both geometric and elastostatic factors. Particular attention is paid to the model parameters identification accuracy. In contrast to other works, the proposed approach takes into account impact of the gravity compensator and link weights on the manipulator elastostatic properties. In order to improve the identification accuracy, the industry oriented performance measure is used to define optimal measurement configurations and an enhanced partial pose measurement method is applied for the identification of the model parameters. The advantages of the developed approach are confirmed by experimental results that deal with the elastostatic calibration of a heavy industrial robot used for milling. The achieved accuracy improvement factor is about 2.4.

Alexandr Klimchik, Dmitry Bondarenko, Anatol Pashkevich et al.

The paper deals with the problem of compliance errors compensation in robotic-based milling. Contrary to previous works that assume that the forces/torques generated by the manufacturing process are constant, the interaction between the milling tool and the workpiece is modeled in details. It takes into account the tool geometry, the number of teeth, the feed rate, the spindle rotation speed and the properties of the material to be processed. Due to high level of the disturbing forces/torques, the developed compensation technique is based on the non-linear stiffness model that allows us to modify the target trajectory taking into account nonlinearities and to avoid the chattering effect. Illustrative example is presented that deals with robotic-based milling of aluminum alloy.

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%.

Alexandr Klimchik, Yier Wu, Claire Dumas et al.

The paper focuses on the stiffness modeling of heavy industrial robots with gravity compensators. The main attention is paid to the identification of geometrical and elastostatic parameters and calibration accuracy. To reduce impact of the measurement errors, the set of manipulator configurations for calibration experiments is optimized with respect to the proposed performance measure related to the end-effector position accuracy. Experimental results are presented that illustrate the advantages of the developed technique.

Alexandr Klimchik, Yier Wu, Stéphane Caro et al.

The paper focuses on the calibration of serial industrial robots using partial pose measurements. In contrast to other works, the developed advanced robot calibration technique is suitable for geometrical and elastostatic calibration. The main attention is paid to the model parameters identification accuracy. To reduce the impact of measurement errors, it is proposed to use directly position measurements of several points instead of computing orientation of the end-effector. The proposed approach allows us to avoid the problem of non-homogeneity of the least-square objective, which arises in the classical identification technique with the full-pose information. The developed technique does not require any normalization and can be efficiently applied both for geometric and elastostatic identification. The advantages of a new approach are confirmed by comparison analysis that deals with the efficiency evaluation of different identification strategies. The obtained results have been successfully applied to the elastostatic parameters identification of the industrial robot employed in a machining work-cell for aerospace industry.

Alexandr Klimchik, Yier Wu, Gabriel ABBA et al.

The paper focuses on the robust identification of geometrical and elastostatic parameters of robotic manipulator. The main attention is paid to the efficiency improvement of the identification algorithm. To increase the identification accuracy, it is proposed to apply the weighted least square technique that employs a new algorithm for assigning of the weighting coefficients. The latter allows taking into account variation of the measurement system precision in different directions and throughout the robot workspace. The advantages of the proposed approach are illustrated by an application example that deals with the elasto-static calibration of industrial robot.

Alexandr Klimchik, Yier Wu, Stéphane Caro et al.

The paper deals with the modeling and identification of the gravity compensators used in heavy industrial robots. The main attention is paid to the geometrical parameters identification and calibration accuracy. To reduce impact of the measurement errors, the design of calibration experiments is used. The advantages of the developed technique are illustrated by experimental results

Yier Wu, Alexandr Klimchik, Anatol Pashkevich et al.

The paper deals with the design of experiments for manipulator geometric and elastostatic calibration based on the test-pose approach. The main attention is paid to the efficiency improvement of numerical techniques employed in the selection of optimal measurement poses for calibration experiments. The advantages of the developed technique are illustrated by simulation examples that deal with the geometric calibration of the industrial robot of serial architecture.