The contribution of this paper comes from a modeling which allows simplify equations compared to the previous study. Depending on the number of channels, we calculate the teleoperation transparency at steady states and discuss conditions to achieve ideal transparency. New experimental results are proposed with the four channel teleoperation system to validate again our simulator. Then results of the calculations are checked by simulation for each type of control laws.

A classical frequency approach in order to tune the closed-loop of each robot for bilateral teleoperation system is studied. The originality of the tuning is done through closed loop of velocity, position and force. Where the resulting equation of the dynamic gives coefficients that can be assimilate to the apparent impedance of each robot. The apparent impedance feel by the operator depending on the number of control channel is studied with the Hannaford method.

A cascaded force and position control is implemented on each of two robots of a bilateral teleoperation system. The aim is to propose a classical frequency approach in order to tune the closed-loop of each robot for different operating modes. Thus an efficient four channel bilateral teleoperation controller is proposed. It can be decomposed into four different two channel controller variations that can introduce inner virtual flexibility. This virtual flexibility is calculated for each case and can be tuned with the gains of the position control of the robots. An original way to calculate the apparent impedance is provided.

Knowledge of the mass and inertial parameters of a humanoid robot is crucial for the development of model-based controller and motion planning in dynamics situation. Parameters are usually provided from Computer Aided Design (CAD) data and thus inaccurate specially if the robot is modified over time. In this paper, a practical method consisting of hanging a humanoid robot to a fix force sensor to perform its dynamic identification is proposed. This allows, contrary to the literature, to generate very exciting and dynamic motions to identify most of the elements of the inertia tensors in a reduced amount of time. This procedure transforms an instable floating base legged humanoid robot to a safe fix base tree structure robot which makes easier to generate optimal exciting motions. Because of a better excitation the overall trajectory lasts for less than a minute. The method was experimentally validated with a HOAP3 humanoid robot and using a 6-axis force sensor. A reduction of 3 times in average of the RMS difference between measured external reaction forces and moments and their estimates from CAD data was obtained with a single minute of optimal exciting motions.

This paper presents a novel optimization method for generating persistently exciting trajectories for inertial parameters identification of a robot. The exciting performance of the trajectories is usually evaluated by the condition number of the regressor matrix, which appears in the linear regression model for identification. In this paper, the efficient formulation is presented to directly compute the gradient of the condition number with respect to joint trajectory parameters, by deriving the derivative of the singular values and regressor matrices. Direct gradient computation can enhance computational performance of optimization, which is essential for large DOF systems under many physical consistent conditions such as humanoid robots. The proposed method is validated by generating several trajectories for the humanoid robot HRP-4.

Knowledge of the mass and inertial parameters of a humanoid robot or a human being is crucial for the development of model-based control, as well as for monitoring the rehabilitation process. These parameters are also important for obtaining realistic simulations in the field of motion planning and human motor control. For robots, they are often provided by computer-aided design data, while averaged anthropometric table values are often used for human subjects. The unit/subject-specific inertial parameters can be identified by using the external wrench caused by the ground reaction. However, the identification accuracy intrinsically depends on the excitation properties of the recorded motion. In this paper, a new method for obtaining optimal excitation motions is proposed. This method is based on the identification model of legged systems and on optimization processes to generate excitation motions while handling mechanical constraints. A pragmatic decomposition of this problem, the use of a new excitation criterion, and a quadratic program to identify inertial parameters are proposed. The method has been experimentally validated onto an HOAP-3 humanoid robot and with one human subject.

International audience

The Kuka LWR is equipped with torque sensors mounted into the actuated joints. Each torque sensor is calibrated separately before it is mounted on the robot. This needs a second calibration at the last stage of the assembling of the robot in order to take into account the effect of the robot structure through it's jacobian matrix. This final calibration is necessary to improve the accuracy of the estimation of the interaction wrench of the robot with its environment. However, the proposed calibration techniques are usually complicated, time-consuming, and must be carried out before assembling the sensors on the robot. In this paper, a simple and fast method for calibrating the sensors once they are assembled on the robot is presented. The method is based on the least squares solution of an over-determined linear system obtained with the robot inverse dynamic identification model in which are included the sensor gains. This model is calculated with available sensor measurement and joint position sampled data while the robot is tracking some reference trajectories without load on the robot and some trajectories with a known payload fixed on the robot. The method is experimentally validated on the Kuka LWR4+ but can be applied to any similar kind of robot equipped with joint torque sensors.

Modeling and simulation are fundamental tools to develop new urban vehicles. The aim of this work is to model and simulate a narrow urban tilting car, which should significantly decrease traffic congestion, pollution, and parking problems. The structure of the vehicle contains closed kinematic chains. The modeling approach is based on the modified Denavit and Hartenberg description, which is commonly used in robotics, by considering the vehicle as a mobile robot composed of a multibody poly-articulated system in which the terminal links are the wheels. This description allows automatic calculating of the symbolic expressions of the geometric, kinematic, and dynamic models. A simulator is developed with MATLAB/Simulink, and the simulation of different scenarios is performed and analyzed.

Off-line dynamic identification requires the use of a model linear in relation to the robot dynamic parameters and the use of linear least squares technique to calculate the parameters. Most of time, the used model is the Inverse Dynamic Identification Model (IDIM). However, the computation of its symbolic expressions is extremely tedious. In order to simplify the procedure, the use of the Power Identification Model (PIM), which is dramatically simpler to obtain and that contains exactly the same dynamic parameters as the IDIM, was previously proposed. However, even if the identification of the PIM parameters for a 2 degrees-of-freedom (DOF) planar serial robot was successful, its fails to work for 6 DOF industrial robots. This paper discloses the reasons of this failure and presents a methodology for the identification of the robot dynamic parameters using the PIM. The method is experimentally validated on an industrial 6 DOF Stäubli TX-40 robot.

This paper deals with joint stiffness off-line identification with new closed loop output error method which minimizes the quadratic error between the actual motor force/torque and the simulated one. The measurement of the joint position and its derivatives are not necessary. This method called DIDIM (Direct and Inverse Dynamic Identification Models) was previously validated on rigid robots and is now extended to a flexible joint manipulator. DIDIM method for flexible joint manipulators is derived into a three-step procedure: first, a rigid low frequency dynamic model is identified with DIDIM method; second, approximate values of the inertia ratio and stiffness are identified using the total inertia and friction values of step 1 and classical non linear programming algorithm; third, all the dynamic parameters (inertia, friction, stiffness) of the flexible robot are more accurately identified all together, starting from the values identified in step 1 and 2 and using the DIDIM method. An experimental setup exhibits results and shows the effectiveness of our approach compared with a classical output error methods.

This paper deals with the topic of industrial robots identification. The usual identification method is based on the use of the inverse dynamic model (IDM) and least squares (LS) technique. Good results can be obtained provided that a well-tuned bandpass filtering is used. However, we are always in doubt if regressors are exogenous i.e. statistically uncorrelated with error terms. Surprisingly, in papers dealing with identification of real-world systems, exogeneity assumption is never verified whereas it is a fundamental condition to obtain unbiased estimates. In Econometrics, the Durbin-Wu-Hausman test (DWH-test) is a theoretical method for investigating whether regressors are exogenous or not. The DWH-test makes of the Two Stage Lesat Squares estimator (2SLS) and an augmented LS regression. However, this test cannot be used as is for robots identification: instruments set is supposed to be valid and restrictive statistical assumptions are made while they are quite implausible in practice. In this paper, we aim at bridging the gap between Econometrics and Control engineering practices by introducing a revisited version relevant for robots identification. An experimental validation performed on a 2 degrees of freedom (DOF) robot shows the effectiveness and the usefulness of this revisited DWH-test.

Off-line robot dynamic identification methods are generally based on the use of the Inverse Dynamic Identification Model (IDIM), which calculates the joint forces/torques (estimated as the product of the known control signal - the input reference of the motor current loop - by the joint drive gains) that are linear in relation to the dynamic parameters, and on the use of linear least squares technique to calculate the parameters (IDIM-LS technique). However, as actuation redundant parallel robot are overconstrained, their IDIM has infinity of solutions for the force/torque prediction, depending of the value of the desired overconstraint that is a priori unknown in the identification process. As a result, the IDIM cannot be used for the identification procedure. On the contrary the Power Identification Model (PIM) of any types of robot manipulator has a unique formulation and contains the same dynamic parameters as the IDIM. This paper proposes to use the PIM of actuation redundant robots for identification purpose. The identification of the inertial parameters of a planar parallel robot with actuation redundancy, the DualV, is then carried out using its PIM. Experimental results show the validity of the method.

This paper deals with a new iterative learning dynamic identification and control method of robot. The robot is closed-loop controlled with a Computed Torque Control (CTC). The parameters of the Inverse Dynamic Model (IDM), which calculates the CTC are calculated to minimize the quadratic error between the actual joint force/torque and a joint force/torque calculated with the Inverse Dynamic Identification Model (IDIM), linear in relation to the parameters. Usually the parameters are off-line linear least squares estimated (IDIM-LS) where the IDIM is calculated with the joint position and its noisy derivatives, which cannot take into account variations of the parameters. The new method called IDIM-ILIC (IDIM with Iterative Learning Identification and Control) overcomes these 2 drawbacks. The parameters are periodically calculated over a moving time window to update the IDM of the CTC, and the IDIM is calculated with the noise-free data of the trajectory generator, which avoids using the noisy derivatives of the actual joint position. A study of convergence of the method is performed in simulation and an experimental setup with stationary parameters and with a variation of the payload on a prismatic joint validates the procedure.

For any rigid robot, a set of 14 standard parameters characterises the dynamics of each of its links and joints. Only a subset of these standard parameters: the base parameters have unique values identified with the Inverse Dynamic Identification Model and linear least squares techniques (IDIM-LS). Moreover, some of the base parameters are poorly identified when their effect on the joint torques is too small. They can be eliminated, leading to a new subset of essential (base) parameters. However, the consistency of the identified values of the base or the essential parameters cannot be guaranteed, regarding to the loss of the positive definiteness of the robot inertia matrix. The past methods proposed to verify the physical consistency of the identified parameters, relies on complicated, time consuming computations and even leads to non-optimal LS parameters. We propose a method that overcomes these drawbacks, calculating the set of optimal LS standard parameters closest to a set of a priori consistent dynamic parameters obtained through CAD data given by the robot manufacturers. This is a straightforward method, which relies on the use of the Singular Value Decomposition (SVD), the Cholesky factorization and the linear least squares techniques. The method is experimentally validated on a Stäubli TX-40, which is a 6 Degrees of Freedom (DoF) industrial robot. This example enlighten a strong result: the essential base parameters, which have significant identified values with respect to their small relative standard deviation, are consistent.

In this paper, the global identification of spring balancer, dynamic parameters and joint drive gains of a 6 Degrees Of Freedom (DOF) robot is performed. Off-line identification method is based on the use of the Inverse Dynamic Identification Model (IDIM) which takes into account a spring balancer for gravity compensation and linear Least Squares (LS) technique to estimate the parameters from the positions and joint torques. It is key to get accurate values of joint drive gains to get accurate identification because the joint torques are calculated as the product of the current reference by the joint drive gains. Recently a new method validated on small payload robots (less than 10 Kg) allows to identify simultaneously all joint drive gains and dynamic parameters. This method is based on the Total Least Squares (TLS) solution of an over-determined linear system obtained with the inverse dynamic model calculated while the robot is tracking reference trajectories without load and trajectories with a known payload fixed on the robot. This method is used to identify accurately the heavy industrial robot Kuka KR270 (270Kg payload) with its spring balancer. This is a new step to promote a practical and easy to use method for global dynamic identification of any small or heavy gravity compensated industrial robots that does not need any a priori data, which are too often missing from manufacturer's data sheet.

Off-line robot dynamic identification methods are based on the use of the Inverse Dynamic Identification Model (IDIM), which calculates the joint forces/torques that are 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 the previous works, it was proposed to identify each gain separately. This does not allow taking into account the dynamic coupling between the robot axes. In this paper the global joint drive gains parameters of all joints are calculated simultaneously. The method is based on the total least squares solution of an over-determined linear system obtained with the inverse dynamic model calculated with available current reference and position sampled data while the robot is tracking one reference trajectory without load on the robot and one trajectory with a known payload fixed on the robot. The method is experimentally validated on an industrial Stäubli TX-40 robot.

Off-line robot dynamic identification methods are mostly based on the use of the inverse dynamic model, which is linear with respect to the dynamic parameters. This model is calculated with torque and position sampled data while the robot is tracking reference trajectories that excite the system dynamics. This allows using linear least-squares techniques to estimate the parameters. This method requires the joint force/torque and position measurements and the estimate of the joint velocity and acceleration, through the bandpass filtering of the joint position at high sampling rates. A new method called DIDIM (Direct and Inverse Dynamic Identification Models) has been proposed and validated on a 2 degree-of freedom robot [1]. DIDIM method requires only the joint force/torque measurement. It is based on a closed-loop simulation of the robot using the direct dynamic model, the same structure of the control law, and the same reference trajectory for both the actual and the simulated robot. The optimal parameters minimize the 2-norm of the error between the actual force/torque and the simulated force/torque. A validation experiment on a 6 dof Staubli TX40 robot shows that DIDIM method is very efficient on industrial robots.

Usually, the joint transmission friction model for robots is composed of a viscous friction force and of a constant dry sliding friction force. However, according to the Coulomb law, the dry friction force depends linearly on the load driven by the transmission, which has to be taken into account for robots working with large variation of the payload or inertial and gravity forces. Moreover, for robots actuating at low velocity, the Stribeck effect must be taken into account. This paper proposes a new inverse dynamic identification model for n degrees of freedom (dof) serial robot, where the dry sliding friction force is a linear function of both the dynamic and the external forces, with a velocity-dependent coefficient. A new sequential identification procedure is carried out. At a first step, the friction model parameters are identified for each joint (1 dof), moving one joint at a time (this step has been validated in). At a second step, these values are fixed in the n dof dynamic model for the identification of all robot inertial and gravity parameters. For the two steps, the identification concatenates all the joint data collected while the robot is tracking planned trajectories with different payloads to get a global least squares estimation of inertial and new friction parameters. An experimental validation is carried out with an industrial 3 dof robot.

Off-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. 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 Sta¿ubli RX-90 robot.

Usually, the joint transmission friction model for robots is composed of a viscous friction force and of a constant dry sliding friction force. However, according to the Coulomb law, the dry friction force depends linearly on the load driven by the transmission. It follows that this effect must be taken into account for robots working with large variation of the payload or inertial and gravity forces, and actuated with transmissions as speed reducer, screw-nut or worm gear. This paper proposes a new inverse dynamic identification model for n degrees of freedom (dof) serial robot, where the dry sliding friction force is a linear function of both the dynamic and the external forces, with a velocity-dependent coefficient. A new identification procedure groups all the joint data collected while the robot is tracking planned trajectories with different payloads to get a global least squares estimation of inertial and new friction parameters. An experimental validation is carried out with a joint of an industrial robot.

The identification of the dynamic parameters of robot is based on the use of the inverse dynamic model which is linear with respect to the parameters. This model is sampled while the robot is tracking ldquoexcitingrdquo trajectories, in order to get an over determined linear system. The linear least squares solution of this system calculates the estimated parameters. The efficiency of this method has been proved through the experimental identification of a lot of prototypes and industrial robots. However, this method needs joint torque and position measurements and the estimation of the joint velocities and accelerations through the pass band filtering of the joint position at high sample rate. So, the observation matrix is noisy. Moreover identification process takes place when the robot is controlled by feedback. These violations of assumption imply that the LS solution is biased. The Simple Refined Instrumental Variable (SRIV) approach deals with this problem of noisy observation matrix and can be statistically optimal. This paper focuses on this technique which will be applied to a 2 degrees of freedom (DOF) prototype developed by the IRCCyN Robotic team.

Usually, the identification of the dynamic parameters of robot makes use of the inverse dynamic model which is linear with respect to the parameters. This model is sampled while the robot is tracking exciting trajectories. This allows using linear least squares (LS) techniques to estimate the parameters. The efficiency of this method has been proved through experimental identifications of a lot of prototypes and industrial robots. However, it is known that LS estimators are sensitive to outliers and leverage points. Thus, it may be helpful to verify their reliability. This is possible by using robust regressions and residual analysis. Then, we compare the results with those obtained with classical LS regression. This paper deals with this issue and introduces the experimental identification and residual analysis of an one degree of freedom (DOF) haptic interface using the Huber's estimator. To verify the pertinence of our analyses, this comparison is also performed on a medical interface consisting of a complex mechanical structure.

The identification of the dynamic parameters of robot is based on the use of the inverse dynamic model which is linear with respect to the parameters. This model is sampled while the robot is tracking trajectories which excite the system dynamics in order to get an over determined linear system. The linear least squares solution of this system calculates the estimated parameters. The efficiency of this method has been proved through the experimental identification of many prototype and industrial robots. However, this method needs joint torque and position measurements and the estimation of the joint velocities and accelerations through the pass band filtering of the joint position at high sample rate. The new method bypasses the need to measure or estimate joint position, velocity and acceleration by using both Direct and Inverse Dynamic Identification Models (DIDIM). It needs only torque data at a low sample rate. It is based on a closed loop simulation which integrates the direct dynamic model. The optimal parameters minimize the 2 norm of the error between the actual torque and the simulated torque assuming the same control law and the same tracking trajectory. This non linear least squares problem is dramatically simplified using the inverse model to calculate the derivatives of the cost function.

The aim of haptic interfaces is to enhance the user's immersion in virtual environments through the stimulation of the haptic sense (motion capture and force feedback). Most devices make use of an articulated mechanical structure introducing distortions between the operator and the explored world. To assess the quality of the interface, this distortion must be identified. This paper deals with this issue and introduces the modeling and the identification of a 3 degrees of freedom haptic interface using inverse model and least squares method used in robotics.

In this paper we present four methods for the identification of the inertial parameters of the load of a manipulator. The knowledge of the values of these parameters can be used to tune the control law parameters in order to improve the dynamic accuracy of the robot. They can also be exploited to verify the load transported by the robot. The methods presented have been validated using Staubli RX 90 robot. The experimentation has been carried out using data collected from the industrial control system (version CS8) of the manufacturer. This version allows to have access to joint positions, velocities and torques. The methods presented are based on solving linear system of equations using weighted least squares solution.

The haptic interfaces aim at the user's immersion in virtual environments through the stimulation of the haptic sense. Most devices consist of an articulated mechanical structure introducing distortions between the operator and the explored world. This distortion must be identified in order to assess the quality of the interface. The least-squares (LS) regressions are often used because of their simplicity. However, if the identification process takes place when the device is controlled by feedback, then the LS estimator is biased. To verify the reliability of the results, the bias of the estimator must be evaluated. This paper deals with this issue and introduces the design and the application of a derivate of the CESTAC method.

Parametric identification consists in estimating the values of physical parameters of robotic systems. The most popular methods consist in using the least squares regression because of their simplicity. However, we don't know how much they are dependent on the measurement accuracy and so on we ignore the necessary resolution they require to produce good quality results. This paper focuses on this issue and introduces a derivation of the CESTAC method, which will be applied to an industrial 6 degrees of freedom (DOF) serial robot, to estimate the minimal resolution indispensable for an accurate parametric identification.

This paper deals with the problem of dynamic modeling and identification of passenger cars. It presents a new method that is based on robotics techniques for modeling and description of tree-structured multibody systems. This method enables us to systematically obtain the dynamic identification model, which is linear with respect to the dynamic parameters. The estimation of the parameters is carried out using a weighted least squares method. The identification is tested using vehicle dynamics simulation software used by the car manufacturer PSA Peugeot-CitroËn in order to define a set of trajectories with good excitation properties and to determine the number of degrees of freedom of the model. The method has then been used to estimate the dynamic parameters of an experimental Peugeot 406, which is equipped with different position, velocity, and force sensors.

This paper deals with the experimental identification of the dynamic parameters of parallel machines. The dynamic parameters are estimated by using the weighted least squares solution of an over determined linear system obtained from the sampling of the dynamic model along a closed loop exciting trajectory. Experimental results are exhibited for the H4 robot, a fully parallel structure providing 3 degrees of freedom (DOF) in translation and 1 DOF in rotation. A comparative study is performed depending on the available measurements, i.e., different sensor locations (motor, end effector).

Deals with a comparison of sensor location and nature in the identification of physical parameters for mechanical systems with lumped elasticities. The identification model is a linear model in relation to a minimal set of parameters. The dynamic parameters are estimated by using the solution of weighted least squares of an over determined linear system obtained from the sampling of the dynamic model along a closed loop tracking trajectory. An experimental study exhibits the identification results depending on two types of sensors (position, acceleration) and different locations (motor, load).

Proposes a method to identify the joint stiffness of a robot using a bandpass filter. It is based on moving one axis at a time. The dynamic model reduces to a model which is linear in relation to a minimum set of dynamical parameters which have to be identified. These parameters are estimated using the least squares solution of an over determined linear system obtained from the sampling of the dynamic model along a closed loop tracking trajectory. Conditions for a good data processing before identification are exhibited through practical aspects concerning data sampling and data filtering. An experimental study shows the efficiency of the method with two sets of data depending on motor joint position measurements.

This paper deals with the design and the identification of the dynamic model of a compactor, an articulated frame steering mobile engine for use in road construction. The theoretical development is based on an extended classical robot description and takes the contact strengths between rigid wheels and unprepared terrain into account. This formulation allows the automatic symbolic calculation on the dynamic model. The achieved model is linear in relation to a set of dynamic parameters which can be identified using a weighted least squares method. A survey of these techniques is given and applied to the experimental identification of the dynamic parameters of the compactor.

Presents a method for the modeling of mechanical systems with lumped elasticity. The main applications of the method concern high speed machine tools and robots with elastic joints. The method can provide the kinematic and dynamic models of such systems. To achieve this goal we adapted some well known tools and notations which are widely used for rigid robots. The inverse dynamic model has to be redefined and developed.

This paper presents a comparison of two methods for robot dynamic identification which include the weighted least squares estimation and the extended Kalman filtering. Comparative experimental results and discussion are presented for a SCARA robot.

This paper presents a new approach to identify the minimum dynamic parameters of robots using least squares techniques (LS) and a power model. Theoretical analysis is carried out from a filtering point of view and clearly shows the superiority of the power model over the energy one and over the dynamic identification model which has been used to carry out a classical ordinary LS estimation and a new weighted LS estimation. These results are checked from comparing experimental identification of the dynamic parameters of a planar SCARA prototype robot.

This paper presents the experimental results of the identification of the dynamic parameters of the 6 degree of freedom SR400 robot. This industrial robot is characterized by having a parallelogram closed loop and a mechanical coupling between the joints of the hand. The different steps starting from the modelling up to the validation of the results are given. Practical issues are addressed.

A common way to identify the inertial parameters of robots is to use a linear model as function of a minimal set of base parameters and standard least squares techniques. In experimental applications, noise on position and torque measurements, friction modeling error and bad excitation restrict dramatically the identification. This paper presents a methodology to overcome these difficulties. The proposed identification method is based on experiments which are designed by means of physical interpretation and spectrum analysis of the robot dynamic model in order to reduce sensitivity to noise. These experiments are planned in order to ensure optimal condition number of the observation matrix. The proposed algorithms have been integrated in a software package called Robot Identification Software Tool (RIST). The successful application of this new method to a 3 degrees of freedom robot proves the efficiency of the algorithms.

The authors present two methods for determining the base inertial parameters of robots containing closed loops. This set of parameters is the minimum set which can be identified using the dynamic or energy model. The first method is symbolic; the solution is obtained by first determining the quasi base parameters of a corresponding tree structure robot; the closed-loops are then taken into account to get the quasi base parameters of the robot. Direct general relations are given for the two steps. The second method is numerical; the multiple solutions of the relations expressing the passive variables as a function of active variables are taken into account; the number of the base parameters is seen to be a function of each solution.>

The authors present a Bayesian approach using an energy model to identify the base (identifiable) inertial parameters of a robot, given a prior statistical information (expected value and covariance matrix) about the solution vector. An application of a three-degree-of-freedom robot is simulated to show the efficiency of the method.>

An approach to the problem of determining the minimum set of inertial parameters of robots is presented. The calculation is based on numerical QR and singular value decomposition factorizations and on scaling of matrices. It proceeds in two steps: the number of base parameters is determined, and a set of base parameters is determined by eliminating some standard parameters which are regrouped with some others in linear relations. Different models, linear in the inertial parameters, are used: a complete dynamic model, a simplified dynamic model, and an energy model. The method is general. It can be applied to open-loop or graph-structured robots. The algorithms are easy to implement. An application for the PUMA 560 robot is given.>

The determination of the minimum set of inertial parameters of robots contributes to the reduction of the computational cost of the dynamic models and simplifies the identification of the inertial parameters. These parameters can be obtained from the classical inertial parameters by eliminating those that have no effect on the dynamic model and by regrouping some others. A direct method is presented for determining the minimum set of inertial parameters of serial robots. The method permits determination of most of the regrouped parameters by means of closed-form relations.>

A direct method is developed to determine the minimum set of inertial parameters of tree-structure robots giving complete information. The method makes it possible to classify most of the regrouped parameters by closed-form relations. A linear model for the identification of the minimum inertial parameters is also presented. The identification model is computationally simple; it is a function of the joint positions and velocities and does not need to calculate the joint accelerations. The identification model is based on the energy theorem, providing a model which is linear in the link parameters.>

A direct method is presented to determine the minimum set of inertial parameters of robots. The set consists of the classical parameters that affect the dynamic model and the regrouped parameters. The method permits to most of the regrouped parameters to be determined by means of a closed-form function of the geometric parameters of the robot. It is proved that the minimum number of inertial parameters is less than 7n-4, where n is the number of joints. The method is general whatever the values of the geometric parameters. The method can be extended to tree structure robots and will be integrated into the software package SYMORO.>

This paper presents an efficient method for the calculation of the inverse dynamic model of robots. The given method reduces significantly the computational burden such that the inverse dynamics can be computed on real time at servo rate. The method leads almost directly to models with minimum number of arithmetic operations. The method is based on Newton-Euler formulation, on an iterative symbolic procedure and on an analysis of the links inertial parameters which leads to condensate their number by eliminating and regrouping some of them. A FORTRAN program has been developed to generate automatically the dynamic models of open chain robots.