Computer algebra for solving dynamics problems of piezoelectric robots with large number of joints

The application of general control theory to complex mechanical systems represents an extremely difficult problem. If industrial piezoelectric robots have large number of joints, development of new control algorithms is unavoidable in order to achieve high positioning accuracy. The efficiency of computer algebra application was compared with the most popular methods of forming the dynamic equations of robots in real time. To this end, a computer algebra system VIBRAN was used. Expressions for the generalized inertia matrix of the robots have been derived by means of the computer algebra technique with the following automatic program code generation. As shown in the paper, such application could drastically reduce the number of floating point product operations that are required for efficient numerical simulation of piezoelectric robots

Recursive and Symbolic Calculation of the Elastodynamic Model of Flexible Parallel Robots

International audienceThis paper presents a symbolic and recursive calculation of the elastodynamic model of flexible parallel robots. In order to reduce the computational time required for simulating the elastodynamic behavior of robots, it is necessary to minimize the number of operators in the symbolic expression of the model. Some algorithms have been proposed for the rigid case, for parallel robots with lumped springs or for serial robots with distributed flexibilities. In this paper, we extend the previous works to parallel robots with distributed flexibilities. The generalized Newton-Euler model is used and combined with the principle of virtual powers to minimize the number of operators and intermediate variables. Recursive calculations are proposed for the computation of the Jacobian matrices defining the kinematic constraints in order to decrease the number of operators. The proposed algorithm is used to compute the elastodynamic model of a prototype of a planar parallel robot developed at IRCCyN: the DualEMPS. The computed model is compared both with simulations done on Adams and with experiments. The validity of the approach in terms of result accuracy and computational time is demonstrated

Recursive Symbolic Calculation of the Dynamic Model of Flexible Parallel Robots

International audienceThis paper presents a symbolic and recursive calculation of the dynamic model of flexible parallel robots. In order to reduce the computational time, it is necessary to minimize the number of operators in the symbolic expression of the model. Some algorithms have been proposed for the rigid case, for parallel robots with lumped springs or for serial robots with distributed flexibilities, but to the best of our knowledge, nothing has been developed for parallel robots with distributed flexibilities. This paper aims at filling this gap. In order to minimize the number of operations, the Newton-Euler principle is used and combined with the principle of virtual powers. The Jacobian matrices defining the kinematic constraints are computed using recursive calculations that decrease the number of operators. The proposed algorithm is used to compute the elastodynamic model of a planar parallel robot. The obtained results, compared with those obtained with commercial softwares, show the validity of the proposed algorithm

An efficient finite element formulation of dynamics for a flexible robot with different type of joints

If two adjacent links of a flexible robot are connected via a revolute joint or a fixed prismatic joint, the relative motion of the next link will depend on both the joint motion and the elastic displacement of the distal end of the previous link. However, if the two adjacent links are connected via a sliding prismatic joint, the relative motion of the next link will depend additionally on the elastic deformation distributed along the previous link. Therefore, formulation of the motion equations for a multi-link flexible robot consisting of the revolute joints, the fixed prismatic joints and the sliding prismatic joints is challenging. In this study, the finite element kinematic and dynamic formulation was successfully developed and validated for the flexible robot, in which a transformation matrix is proposed to describe the kinematics of both the joint motion and the link deformation. Additionally, a new recursive formulation of the dynamic equations is introduced. As compared with the previous methods, the time complexity of the formulation is reduced by O(2η), where η is the number of finite elements on all links. The numerical examples and experiments were implemented to validate the proposed kinematic and dynamic modelling method

New Method for Global Identification of the Joint Drive Gains of Robots using a Known Inertial Payload

International audienceOff-line robot dynamic identification methods are mostly based on the use of the Inverse Dynamic Identification Model (IDIM), which calculates the joint force/torque that is linear in relation to the dynamic parameters, and on the use of linear least squares technique to calculate the parameters (IDIM-LS technique). The joint forces/torques are calculated as the product of the known control signal (the current reference) by the joint drive gains. Then it is essential to get accurate values of joint drive gains to get accurate identification of inertial parameters. In this paper it is proposed a new method for the identification of the total joint drive gains in one step, using available joint sampled data given by the standard controller of the moving robot and using CAD or measured values of the inertial parameters of a known payload. A new inverse dynamic model calculates the current reference signal of each joint j that is linear in relation to the dynamic parameters of the robot, to the inertial parameters of a known payload fixed to the end-effector, and to the inverse of the joint j drive gain. This model is calculated with current reference and position sampled data while the robot is tracking one reference trajectory without load on the robot and one trajectory with the known payload fixed on the robot. Each joint j drive gain is calculated independently by the weighted LS solution of an over-determined linear systems obtained with the equations of the joint j. The method is experimentally validated on an industrial Stäubli RX-90 robot

Chapitre d'équation 1 Section 1

International audienceOff-line robot dynamic identification methods are mostly based on the use of the Inverse Dynamic Identification Model (IDIM), which calculates the joint force/torque that is linear in relation to the dynamic parameters, and on the use of linear least squares technique to calculate the parameters (IDIM-LS technique). The joint forces/torques are calculated as the product of the known control signal (the current reference) by the joint drive gains. Then it is essential to get accurate values of joint drive gains to get accurate identification of inertial parameters. In this paper it is proposed a new method for the identification of the total joint drive gains in one step using available joint sampled data given by the standard controller of the moving robot and using only the weighted mass of a payload, without any CAD values of its inertial parameters. A new inverse dynamic model calculates the current reference signal of each joint j that is linear in relation to the dynamic parameters of the robot, to the inertial parameters of a known mass fixed to the end-effector, and to the inverse of the joint j drive gain. This model is calculated with current reference and position sampled data while the robot is tracking one reference trajectory without load on the robot and one trajectory with the known mass fixed on the robot. Each joint j drive gain is calculated independently by the weighted LS solution of an over-determined linear systems obtained with the equations of the joint j. The method is experimentally validated on an industrial Stäubli RX-90 robot