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Base parameters of manipulator dynamics
Abstract
A base parameter set as a minimum set of inertial parameters whose
values can determine a dynamic model uniquely is investigated for a
general parallel and perpendicular manipulator with rotational joints
only. The notion of a base parameter is useful for an efficient and
accurate identification of the manipulator dynamic model. A set of
inertial parameters described in linear combinations of link parameters
directly and completely in closed form is given and proved to constitute
a base parameter set. It can be derived from this that the minimum
number of inertial parameters whose values can determine the dynamic
model is 7 N -4β1
(7 N -4β2-2 if the first joint axis parallel to
the gravity vector), where N is the number of links in the
manipulator, and β1 is the number of links connected by
joints whose axes are always parallel to the first joint axis. After
defining the base parameter, it is also shown that any base parameter
set can be obtained from one base parameter set by a nonsingular linear
transformation. The method adopted has the potential advantage of
determining the relations between base parameters and manipulator
motions
... The factor that truly affects robot dynamics is only part of the inertial parameters and can be estimated through identification procedures. The set of a minimum number of inertial parameters, that is, the base parameter set, can be selected on the basis of a numerical method with respect to the QR decomposition [28] or by regrouping the standard parameters through linear relations [29,30]. The dynamic equation (3) can then be regrouped into another form with N b identifiable base parameters. ...
... and Σ is the diagonal covariance matrix of the measured actuator torques such that [30]. The covariance matrix of MLE p ml is equal to ...
... In addition, the covariance matrix Σ in the optimization process was derived from a random trajectory, and the parameter was estimated through the traditional linear LS method (refer to [30] (p. 294)), as plotted in Figure 4. ...
As the foundation of model control, robot dynamics is crucial. However, a robot is a complex multi-input–multi-output system. System noise seriously affects parameter identification results, thereby inevitably requiring us to conduct signal processing to extract useful signals from chaotic noise. In this research, the dynamic parameters were identified on the basis of the proposed multi-criteria embedded optimization design method, to obtain the optimal excitation signal and then use maximum likelihood estimation for parameter identification. Considering the movement coupling characteristics of the multi-axis, experiments were based on a two degrees-of-freedom manipulator with joint torque sensors. Simulation and experimental results showed that the proposed method can reasonably resolve the problem of mutual opposition within a single criterion and improve the identification robustness in comparison with other optimization criteria. The mean relative standard deviation was 0.04 and 0.3 lower in the identified parameters than in F1 and F3, respectively, thus signifying that noise is effectively alleviated. In addition, validation experimental curves were close to the estimation model, and the average of root mean square (RMS) is 0.038, thereby confirming the accuracy of the proposed method.
... The definition of those parameters will be given, according to Gautier and Kahlil [7,8,9] and Mayeda [17], in the next section. ...
... Mayeda [17] states: "the link inertial parameters are redundant in the sense that the same dynamic equations might be determined even if some link inertial parameters take different values. Therefore, it is unfortunately impossible to estimate all the link inertial parameter values from link motion and joint torque data". ...
... In [17] are formalized some definitions and properties of the base parameters set. Those considerations are reported in Appendix A. ...
In this work, a complete and systematic identification procedure of the dynamic
parameters of robot manipulators is presented. A new method, based
on the Frisch Scheme, has been developed to face up the estimation problem.
Starting from the results present in the literature, the dynamic model
of the robot has been firstly derived and properly reduced. Then the optimal
joint exciting trajectories are determined both with evolutionary and
direct search optimization techniques. Meanwhile, the issues related to the
acquisition and reconstruction of data from sensors are treated. Thereafter,
the dynamic parameters of the robot (masses, centers of gravity, moments of
inertia, friction coefficients, etc.) are estimated using an innovative approach
exploiting the Frisch scheme, which, under certain hypothesis, may increase
the accuracy of the estimation, compared to least squares methods usually
adopted in the literature. The whole procedure has been tested in a practical
case of study to identify the dynamic parameters of a six-degree-of-freedom
robot manipulator.
... In this work, we focus on identifying the minimal parameters of a space robot based on the momentum model while on orbit. The minimal parameters define the dynamic model uniquely [12,13]. They are a linear combination of the link parameters, which are the mass (m i ), the product of mass and position of CoM (m i i a i ) components, and the inertia tensor i I i components of multiple links. ...
... They are a linear combination of the link parameters, which are the mass (m i ), the product of mass and position of CoM (m i i a i ) components, and the inertia tensor i I i components of multiple links. Such a linear combination is due to constraining the relative motion of an adjacent pair of links with a joint [12], referred as kinematic constraints. The inertial parameters are redundant in defining the dynamic model; consequently, only the minimal parameters can be identified [14]. ...
... Hence, the momentum model stays intact, and it is in the minimal form. More properties of minimal parameters are discussed in [12,13]. ...
Accurate information of inertial parameters is critical to motion planning and control of space robots. Before the launch, only a rudimentary estimate of the inertial parameters is available from experiments and computer-aided design (CAD) models. After the launch, on-orbit operations substantially alter the value of inertial parameters. In this work, we propose a new momentum model-based method for identifying the minimal parameters of a space robot while on orbit. Minimal parameters are combinations of the inertial parameters of the links and uniquely define the momentum and dynamic models. Consequently, they are sufficient for motion planning and control of both the satellite and robotic arms mounted on it. The key to the proposed framework is the unique formulation of momentum model in the linear form of minimal parameters. Further, to estimate the minimal parameters, we propose a novel joint trajectory planning and optimization technique based on direction combinations of joints' velocity. The efficacy of the identification framework is demonstrated on a 12 degrees-of-freedom, spatial, dual-arm space robot. The methodology is developed for tree-type space robots, requires just the pose and twist data, and scalable with increasing number of joints.
... In accordance with [21] and [22], we can utilize the column linear dependency of H s to regroup the standard parameters and therefore (13) can be rewritten as ...
... Here, we can construct the same Lyapunov function shown in (21). Then, the derivative of V (e) along system (22) can be writteṅ ...
This paper proposes a novel interaction force estimation scheme capable of estimating the interaction forces for industrial robots with high precision in the absence of force sensors. Specifically, we first establish the dynamic model of a class of industrial robots via model identification methods. Furthermore, a high-order finite-time observer (HOFTO) is established to estimate the interaction forces, where HOFTO serves as an interaction force observer and is designed to accurately estimate external time-varying interaction forces. In addition, we strictly analyze the stability of our approach in two different cases, endowing HOFTO with reliable estimation abilities in broader applications. Subsequently, we integrate the estimated force information into the applications of force control frameworks (e.g., collision detection and impedance control). Several evaluations on a real 6-axes robot demonstrate the effectiveness of the proposed approach.
... To solve this issue, it is necessary to perform a set of column rearrangements within Y χ , eventually leading to the set of b ≤ p base parameters that are actually linear combinations of the standard parameters χ. Base inertial parameters are defined by [39,40] as the set of dynamic parameters which is sufficient to completely describe the -intrinsically constrained -dynamics of a robot mechanism. As exposed in [37], the base parameter vector β ∈ R b can be obtained by performing a set of rearrangements in the symbolic expressions of (4) (note that in this context, some of the performed symbolic simplifications are only made possible using proximal DH convention). ...
... where ∆y(q) ∈ R r is the vector built from the sampling of e CLOE (t, β); Φ i CLOE ∈ R (r×b) is the matrix built from the sampling of G q s = ∂q s /∂β| β=β i CLOE ∈ R (n×b) , the Jacobian matrix of q s evaluated atβ i CLOE ; and the term ε i CLOE ∈ R r is the vector built from the sampling of the residuals of the Taylor series expansion. Then, ∆β i , the LS estimate of ∆β i CLOE at iteration i is calculated with (40). Please note that numerically computing the Jacobian G q s with finite differences requires b + 1 model simulations. ...
This work aims at reviewing, analyzing and comparing a range of state-of-the-art approaches to inertial parameter identification in the context of robotics. We introduce “BIRDy (Benchmark for Identification of Robot Dynamics)”, an open-source Matlab toolbox, allowing a systematic and formal performance assessment of the considered identification algorithms on either simulated or real serial robot manipulators. Seventeen of the most widely used approaches found in the scientific literature are implemented and compared to each other, namely: the Inverse Dynamic Identification Model with Ordinary, Weighted, Iteratively Reweighted and Total Least-Squares (IDIM-OLS, -WLS, -IRLS, -TLS); the Instrumental Variables method (IDIM-IV), the Maximum Likelihood (ML) method; the Direct and Inverse Dynamic Identification Model approach (DIDIM); the Closed-Loop Output Error (CLOE) method; the Closed-Loop Input Error (CLIE) method; the Direct Dynamic Identification Model with Nonlinear Kalman Filtering (DDIM-NKF), the Adaline Neural Network (AdaNN), the Hopfield-Tank Recurrent Neural Network (HTRNN) and eventually a set of Physically Consistent (PC-) methods allowing the enforcement of parameter physicality using Semi-Definite Programming, namely the PC-IDIM-OLS, -WLS, -IRLS, PC-IDIM-IV, and PC-DIDIM. BIRDy is robot-agnostic and features a complete inertial parameter identification pipeline, from the generation of symbolic kinematic and dynamic models to the identification process itself. This includes functionalities for excitation trajectory computation as well as the collection and pre-processing of experiment data. In this work, the proposed methods are first evaluated in simulation, following a Monte Carlo scheme on models of the 6-DoF TX40 and RV2SQ industrial manipulators, before being tested on the real robot platforms. The robustness, precision, computational efficiency and context of application the different methods are investigated and discussed.
... Identifiable non-redundant dynamic parameters may be expressed as a minimum set of dynamic parameters whose values may determine a model. Such parameter sets are called base or minimum dynamic parameters, and are sufficient to describe the dynamic behavior of the mechanic system [14] . There are methodologies that allow for determining the parameters affecting the dynamic, as well as the set of minimum parameters to identify the model [7,14] . ...
... Such parameter sets are called base or minimum dynamic parameters, and are sufficient to describe the dynamic behavior of the mechanic system [14] . There are methodologies that allow for determining the parameters affecting the dynamic, as well as the set of minimum parameters to identify the model [7,14] . Once the parameters are identified, it is necessary to validate such results by applying them to the model. ...
This study discusses the design and assessment of different parameter identification meth- ods applied to robot systems, such as least squares, extended Kalman filter, Adaptive Lin- ear Neuron (Adaline) neural networks, Hopfield recurrent neural networks and genetic al- gorithms. First, the characteristics of the methods above mentioned are described. Second, using the software MatLab/Simulink, a simulation of a Selective Compliant Assembly Robot Arm (SCARA) robot with 3 Degrees of Freedom (DOF) is carried out by applying these pa- rameter identification methods, thereby obtaining the performance indicators of the algo- rithms that allow for parameter identification. Therefore, this study enables the adequate selection of identification methods to obtain parameters that characterize the dynamics of industrial robots, particularly of the SCARA type. Hence, having the values of the base parameters of a robot contributes to the design of new control methods, since the robot characteristic dynamic model is known.
... Only a few parameters can actually be estimated, because of linear dependencies in the set of dynamic parameters [9]. This minimal set of linearly independent dynamic parameters can be determined analytically for the classical model of a manipulator [10]. However, when the dynamics of unusual actuators is considered, the minimal set of identifiable parameters is yet to be determined. ...
... It is well-known ( [13], [10]) that the dynamic identification model of a manipulator arm is expressed by Φ (q,q,q) θ = τ , where θ is the stack vector of the dynamic parameters of the model to be identified, and Φ is the associated regressor. In order to derive this model for the manipulator arm including its actuators' dynamics, we replace τ by its expression given in (8): ...
This paper deals with the dynamic modeling and identification of an electrically driven underwater robot ma-nipulator. The proposed study includes the dynamic modeling of the actuators of the arm as well as the identification of the parameters of the model. The proposed method deals with the specific case of heterogeneously actuated arms, namely arms with actuators behaving differently for each joint, being considered at the kinematic level. Indeed, we show how to estimate the arms parameters when some of their revolute joints are directly actuated by geared motors, while the others are actuated by linear actuators. A minimum set of identifiable parameters is determined, and adequate excitation trajectories are generated and used in the identification procedure. Real-time experimental validation on the manipulator arms of Ifremer's HROV (Hybrid Remotely Operated Vehicle) Ariane underwater vehicle demonstrates that the proposed method improves the estimation of the dynamic model.
... The base parameters are the minimal set of identifiable parameters to parametrize the dynamic equation. They are obtained by regrouping some of the standard parameters by means of linear relations [11,28] or a numerical method with respect to the QR decomposition [29]. Then the dynamics equation with N b identifiable base parameters can be addressed as ...
... J. Jin, N. Gans / Robotics and Computer-Integrated Manufacturing 31 (2015)[21][22][23][24][25][26][27][28][29] ...
This paper proposes a novel, hybrid and decentralized, switched-system approach for formation and heading consensus control of mobile robots under switching communication topology, including collision avoidance capability. The set of robots consists of nonholonomic wheeled mobile robots and can include a teleoperated UAV. The key feature of this approach is a virtual graph, which is derived by adding a set of relative translation vectors to the real graph of the multiple robots. Our approach results in the robots in the real graph moving to the desired formation and achieving heading consensus while the virtual robots on the virtual graph reach pose consensus. If any robot detects a nearby obstacle or other robot, the robot will temporarily move along an avoidance vector, which is perpendicular and positively projected onto the attractive vector, such that collision is avoided while minimally deviating from its formation control path. Experimental results are provided by two different research groups to demonstrate the effectiveness of our approach. These experiments extend the theoretical development by introducing a teleoperated quadrotor as a leader robot of the multi-robot systems. The same control law works for the extended system, with no modifications.
... These dynamic parameters are obtained by combining the geometric parameters and inertial properties of the counterpart elements, which are called the minimal set of inertial parameters (MSIP). Numerical and analytical methods for calculating the MSIP have been established [5][6][7][8], and various experimental identification methods have been developed. ...
Background/Objectives: This study aimed to examine how uncertainties in inertial properties and minimal sets of inertial parameters (MSIP) affect inverse-dynamics simulations of high-acceleration sport movements and to demonstrate that applying MSIP identified through the free vibration measurement method improves simulation accuracy. Methods: Monte Carlo simulations were performed for running, side-cutting, vertical jumping, arm swings, and leg swings by introducing uncertainties in inertial properties and MSIP. Results: These uncertainties significantly affect the joint torques and ground reaction forces and moments (GRFs&Ms), especially during large angular acceleration. The mass and longitudinal position of the center of gravity had strong effects. Subsequently, MSIP identified by our methods with free vibration measurement were applied to the same tasks, improving the accuracy of the predicted ground reaction forces compared with the standard regression-based estimates. The root mean square error decreased by up to 148 N. Conclusions: These results highlight that uncertainties in inertial properties and MSIP affected the calculated joint torques and GRFs&Ms, and combining experimentally identified MSIP with dynamics simulations enhances precision. These findings demonstrate that utilizing the MSIP from free vibration measurement in inverse dynamics simulations improves the accuracy of dynamic models in sports biomechanics, thereby providing a robust framework for precise biomechanical analyses.
... Numerical and analytical methods for calculating MSIP have been established (Mayeda et al., 1990;Gautier, 1990;Kawasaki et al., 1991), and various experimental identification techniques have been developed. Conventional identification methods utilize measured link motions and joint torques (Mayeda, 1989;Tafazoli et al., 1999;Wang et al., 2020) or measured link motions and ground reaction forces (Bonnet and Venture, 2015;Xiu et al., 2016;Ayusawa et al., 2014;Timotej and Marko, 2006;Chenut et al., 2002;Bonnet et al., 2016). ...
The inertial properties (mass, center of gravity, and inertia tensor) of an object are fundamental and important input values. They have a significant effect on the accuracy of human motion simulation. Thus, an accurate identification method of inertial properties is crucial. All inertial properties of individual links modeled with multiple links cannot be identified from the link motion, interjoint torque, or external force data because they are redundant to the multibody dynamics model. Minimum dynamic parameters needed to represent the multibody dynamics model have been defined and identified. These dynamic parameters are obtained by combining the geometric parameters and inertial properties of the counterpart elements and are called the minimum set of inertial parameters (MSIP). A set of measured link motions and ground reaction forces are utilized in conventional identification methods. The MSIP for a sagittal plane can be identified from motions such as the walking motion of human bodies. However, it is difficult to perform three-dimensional identification, including planes beyond the sagittal plane. Therefore, a new method for identifying MSIP by expanding and applying free vibration measurements has been developed. With this method, highly accurate three-dimensional identification has been demonstrated using a mock-up model of the human body consisting of two links made of iron. However, the human body is complex and possesses flexibility due to muscles and organs, making it uncertain whether the developed method, which assumes a rigid body model, can be applied. In this study, appropriate identification procedures and conditions were examined to apply the developed method to the complex and multi-degree-of-freedom human body. The results demonstrated that valid identification of the MSIP can be obtained without exciting the body’s flexibility.
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... Numerical and analytical methods for calculating MSIP have been established [13][14][15], and various experimental identification methods have been developed. Conventional identification methods employ a set of measured link motions and interjoint torques [16][17][18] or a set of measured link motions and floor reaction forces [2,[19][20][21][22][23][24]. ...
The inertial properties of an object (mass, center of gravity, and inertia tensor) are fundamental parameters that considerably affect the accuracy of motion control and simulation results. Therefore, an accurate identification of inertial properties is crucial. All inertial properties of individual links modeled with multiple links cannot be identified via link motion, interjoint torque, or external force data because they are redundant to the multibody dynamics model. The minimum dynamic parameters necessary to represent the multibody dynamics model have been defined and identified. These dynamic parameters are obtained by combining the geometric parameters and inertial properties of the counterpart elements and are called the minimal set of inertial parameters (MSIP). Conventional identification methods use a set of measured link motions and ground reaction forces. MSIP for a sagittal plane can be identified from motions such as the walking motion of human bodies. However, applying these methods to three-dimensional identification is challenging. The primary difficulty lies in the large number of parameters involved, making it challenging to find motions that appropriately excite all MSIP in three dimensions to be identified. In this study, a new method for identifying the MSIP of a multibody system is developed by expanding and applying the identification method based on free vibration measurements, which is the identification method for the inertial properties of a single body. This method shows that MSIP for three dimensions can be identified theoretically and experimentally with high accuracy via considerably simple motion measurements.
... To address these challenges, it's often beneficial to decompose the tree-type manipulator into multiple serial chains [10]. Several studies, including those by Mayeda et al. [11], Khalil et al. [12], and Khosla [13], have developed formulas to determine the minimum set of serial link robots. However, these methods have limitations in identifying the minimum set of dynamics parameters for serial robots. ...
In this work, the branch of the tree robot has been controlled for crack sealing of concrete pipe. This tree robot is used for repair and maintenance purposes. It can maneuvers inside vertical pipes, horizontal pipes and surfaces. A CAD model of the pipe is modelled in Solidworks, and a mimic of the existing crack is simulated inside the pipes. Furthermore, the crack repair has been assured for the branch of the tree robot. However, due to the presence of uncertainty and disturbances, the end-effector of the tree robot doesn't follow the desired crack trajectory. Sliding mode control (SMC) is a well-known method to address such types of problems. But, conventional SMC solved one aspect of the problem. Therefore, The Non-singular fast terminal sliding mode control (NFTSMC) is proposed for this work since it ensures fast convergence in finite time. After performing the simulation and numerous iterations, it is found that the NFTSMC gives a more promising result compared to SMC with constant plus proportional reaching law (CPPRL). Furthermore, the work exploits the Lyapunov candidate function to ensure the asymptotic stability of the crack trajectory.
... To address these challenges, it's often beneficial to decompose the tree-type manipulator into multiple serial chains [10]. Several studies, including those by Mayeda et al. [11], Khalil et al. [12], and Khosla [13], have developed formulas to determine the minimum set of serial link robots. However, these methods have limitations in identifying the minimum set of dynamics parameters for serial robots. ...
In this work, the branch of the tree robot is controlled for crack sealing of concrete pipe. This tree robot has been used for repair and maintenance purposes. It can maneuver inside vertical pipe, horizontal pipes and surfaces. A CAD model of the pipe has been modelled in Solidworks, and a mimic of the existing crack is simulated inside the pipes. Furthermore, the crack repair has been assured for the branch of the tree robot. However, due to the presence of uncertainty and disturbances, the end-effector of the tree robot doesn't follow the desired crack trajectory. Sliding mode control (SMC) is a well-known method to address such types of problems. But, conventional SMC solved one aspect of the problem. Therefore, Nonsingular terminal sliding mode control (NTSMC) is proposed for this work since it guarantees convergence in finite time. After performing the simulation and numerous iterations, it is found that the NTSMC gives a more promising result than SMC with constant plus proportional reaching law (CPPRL). Furthermore, the work exploits the Lyapunov candidate function to ensure the asymptotic stability of the crack trajectory.
... One of the better methods to solve the kinematic and dynamic problems is to break the tree-type manipulator into multiple serial chains. Mayeda et al. [14], Khalil et al. [15], and Khosla [16] have derived a formula for determining the minimum set of serial link robots. However, these methods are insufficient for a minimum set of dynamics parameters for the serial robot. ...
In this work, the branch (three links) of the tree robot has been controlled for crack sealing. This tree robot dealt with the tree robot for repair and maintenance purposes. This tree robot maneuvers inside the vertical pipe, horizontal pipes and surfaces. A CAD model of the pipe has been modelled in Solid-works, and a mimic of the existing crack has been simulated inside the pipes. Furthermore, the crack repair has been assured for the branch of the tree robot. However, due to the presence of uncertainty and disturbances, the end-effector of the tree robot doesn't follow the desired crack trajectory. The control of crack trajectory in the presence of parametric perturbation and external disturbance is a challenging task. Sliding mode control is a well-known method to address such types of problems. Therefore, The sliding mode control (SMC) is proposed with different reaching laws for this work. The four-reaching laws of SMC, Constant rate reaching law (CRL), Constant plus proportional rate reaching law (CPPRL), Power rate reaching law (PRRL), and General reaching law (GRL) have been designed and compared. After performing the simulation and numerous iterations , it has been found that the CPPRL reaching law gives a more promising result in comparison to other mentioned laws. However, the Constant rate reaching has to be less chattering than other reaching laws. Furthermore, the work exploits the Lyapunov candidate function to ensure the asymptotic stability of the crack trajectory.
... To address these challenges, it's often beneficial to decompose the tree-type manipulator into multiple serial chains [10]. Several studies, including those by Mayeda et al. [11], Khalil et al. [12], and Khosla [13], have developed formulas to determine the minimum set of serial link robots. However, these methods have limitations in identifying the minimum set of dynamics parameters for serial robots. ...
... One of the better methods to solve the kinematic and dynamic problems is to break the tree-type manipulator into multiple serial chains. Mayeda et al. [14], Khalil et al. [15], and Khosla [16] have derived a formula for determining the minimum set of serial link robots. However, these methods are insufficient for a minimum set of dynamics parameters for the serial robot. ...
In this work, the branch (three links) of the tree robot has been controlled for crack sealing. This tree robot dealt with the tree robot for repair and maintenance purposes. This tree robot maneuvers inside the vertical pipe, horizontal pipes and surfaces. A CAD model of the pipe has been modelled in Solid-works, and a mimic of the existing crack has been simulated inside the pipes. Furthermore, the crack repair has been assured for the branch of the tree robot. However, due to the presence of uncertainty and disturbances, the end-effector of the tree robot doesn't follow the desired crack trajectory. The control of crack trajectory in the presence of parametric perturbation and external disturbance is a challenging task. Sliding mode control is a well-known method to address such types of problems. Therefore, The sliding mode control (SMC) is proposed with different reaching laws for this work. The four-reaching laws of SMC, Constant rate reaching law (CRL), Constant plus proportional rate reaching law (CPPRL), Power rate reaching law (PRRL), and General reaching law (GRL) have been designed and compared. After performing the simulation and numerous iterations , it has been found that the CPPRL reaching law gives a more promising result in comparison to other mentioned laws. However, the Constant rate reaching has to be less chattering than other reaching laws. Furthermore, the work exploits the Lyapunov candidate function to ensure the asymptotic stability of the crack trajectory.
... One of the better methods to solve the kinematic and dynamic problems is to break the tree-type manipulator into multiple serial chains. Mayeda et al. [14], Khalil et al. [15], and Khosla [16] have derived a formula for determining the minimum set of serial link robots. However, these methods are insufficient for a minimum set of dynamics parameters for the serial robot. ...
... To address these challenges, it's often beneficial to decompose the tree-type manipulator into multiple serial chains [10]. Several studies, including those by Mayeda et al. [11], Khalil et al. [12], and Khosla [13], have developed formulas to determine the minimum set of serial link robots. However, these methods have limitations in identifying the minimum set of dynamics parameters for serial robots. ...
... As mentioned in (Atkeson and Hollerbach, 1986) in the case of interconnected bodies for example serial industrial robots not all inertial parameters are required. This is because some of the inertial parameters appear as a linear combination of other parameters (Mayeda et al., 1990). The minimum set of inertial parameters can be obtained by Gautier and Khalil (Gautier and Khalil, 1988) or by numerical QR decomposition of the observation matrix (Gautier, 1990). ...
... Mayeda et. al. [7] investigates the base parameters of dynamic models for parallel and perpendicular manipulators with only rotational joints. This study focuses on non-redundant parameters of the dynamic model for these manipulators. ...
Robot dynamics is required for simulation, control, analysis of robot motion planners and controllers. There are a number of dynamic modelling investigations of robots with the different approaches and these investigations mostly focus on the link flexibility, joint friction or actuator dynamics. In addition to that these studies present dynamic model without any attached linear or torsion springs. In this study, the dynamic modelling of a two-link rigid manipulator with attached torsion springs is presented using the Lagrangian approach. The Lagrangian approach is a variational method that relies on the potential and kinetic energy of the mechanism, making it well-suited for the analysis of the two-link planar manipulator considered in this study. Initially, the two-link mechanism equations of motion are derived without any attached torsion springs. Subsequently, two torsion springs are attached to the joints of the mechanism, and the existing equations of motion are modified accordingly. The study also presents the kinetic, potential and total energies of the two link-manipulator, angular positions of the links and their velocities. By considering the dynamic modelling of the torsion spring attached two-link rigid manipulator, this study contributes to understanding and analysis of the two-link manipulators and the dynamic effects of the attached springs.
... Then, for the identification, several methods are used to estimate the dynamic parameters of the robot. One of the numerical methods is least squares (LS) proposed at first by Gautier and Khalil [3] and by Mayeda et al. [4] for estimating a set of minimum dynamic parameters called as inertial parameters of serial robots. For estimating the dynamic parameters including inertia, viscous and Coulomb friction of a 6-DOF Staubli TX-90 industrial robot, Jin and Gans [5] employed the inverse dynamic model of the robot and the LS method by using a periodic trajectory which persistently excites the system. ...
The accurate dynamic model for industrial robots is required to enhance their efficiency in expanding their range of applications and carrying out complex tasks. In this research, considering the nonlinear friction model of each joint, an identification approach based on swarm intelligence algorithms for nonlinear joint dynamics of a 6-DOF UR5 robot manipulator has been proposed by using a two different excitation trajectory approach for analyzing the accuracy of parameters to be identified. The Coulomb-Viscous friction model, the Stribeck friction model and the centrosymmetric static friction model (CSFM) are chosen to describe the friction effects of the joints. By using five different arbitrary paths and a Fourier reference excitation trajectory, the nonlinear friction model and robot dynamic parameters are identified by using swarm intelligence-based optimization algorithms such as Cuckoo Search (CS), Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), and also the hybrid algorithms called GWO-CS and GWO-PSO. For the purpose of showing the prediction accuracy of the algorithms and comparing the prediction torques of the dynamic model based on the different joint friction models, the verification of parameter estimation is performed. Finally, simulation results are used to illustrate which swarm intelligence algorithms provide better estimation performance and which joint friction models achieve higher torque prediction accuracy.
... As a result, the set of standard dynamic parameters Φ s to be identified can be reduced to a minimal set of parameters known as base parameters, Φ b ∈ R b×1 , where b is the number of base parameters. These parameters can be obtained from the standard inertial parameters by eliminating those which have no effect on the dynamic model and by regrouping some others in linear relations [22][23][24]. Following numerical approach [24], a set of base parameters are computed for the Indy7 robot manipulator with coordinate systems placed as illustrated in Figure 1 and with the modified Denavit-Hartenberg (mDH) parameters in Table 1. ...
Accurate dynamic model is critical for collaborative robots to achieve satisfactory performance in model-based control or other applications such as dynamic simulation and external torque estimation. Such dynamic models are frequently restricted to identifying important system parameters and compensating for nonlinear terms. Friction, as a primary nonlinear element in robotics, has a significant impact on model accuracy. In this paper, a reliable dynamic friction model, which incorporates the influence of temperature fluctuation on the robot joint friction, is utilized to increase the accuracy of identified dynamic parameters. First, robot joint friction is investigated. Extensive test series are performed in the full velocity operating range at temperatures ranging from 19 ∘C to 51 ∘C to investigate friction dependency on joint module temperature. Then, dynamic parameter identification is performed using an inverse dynamics identification model and weighted least squares regression constrained to the feasible space, guaranteeing the optimal solution. Using the identified friction model parameters, the friction torque is computed for measured robot joint velocity and temperature. Friction torque is subtracted from the measured torque, and a non-friction torque is used to identify dynamic parameters. Finally, the proposed notion is validated experimentally on the Indy7 collaborative robot manipulator, and the results show that the dynamic model with parameters identified using the proposed method outperforms the dynamic model with parameters identified using the conventional method in tracking measured torque, with a relative improvement of up to 70.37%.
... 2.11) qui n'interviennent pas dans le modèle dynamique et en regroupant certains d'entre eux sous forme de relations linéaires. Ces opérations d'élimination et de regroupement sont basées depuis les années 80 [17] sur un calcul théorique de l'énergie mécanique des corps de robots ou sur un calcul numérique basé sur la factorisation QR ou SVD [60] [104]. En effet, ces paramètres de base sont les seuls paramètres identifiables avec le modèle linéaire et représentent un ensemble minimum de paramètres nécessaires pour calculer la dynamique inverse du robot. ...
Cette thèse a pour objectif principal de développer une loi de commande pour contrôler un robot à deux bras afin de remplir les tâches de manipulation et de garantir les aspects de sécurité pour l'homme et le robot. Pour y parvenir, nous avons présenté un aperçu des études qui ont été menées dans ce cadre. Ensuite, nous avons procédé à la modélisation cinématique géométrique et dynamique du robot. Nous avons utilisé le logiciel SYMORO+ pour calculer son modèle dynamique. Au terme d'une présentation détaillée de la méthode d'identification des paramètres des robots manipulateurs, nous avons appliqué celle-ci de manière concrète sur notre propre robot. Ceci nous a permis d'obtenir un vecteur de paramètres capable de garantir une matrice d'inertie définie positive pour toute configuration d'articulation du robot, tout en assurant une bonne qualité de reconstruction du couple pour des vitesses articulaires à la fois constantes et variables. Grâce à cette identification dynamique, nous avons pu réaliser un simulateur précis du robot sur Matlab/Simulink. Les forces externes du robot ont été estimées à partir du module dynamique identifié et une validation expérimentale a été décrite. Pour faire appliquer des lois de commande sur un robot industriel, il a été nécessaire de réfléchir à une communication externe sur le robot. L'approche adoptée a été présentée ainsi que sa réalisation sur le robot. Cette dernière, nous a permis de programmer en python toutes nos problématiques à mettre en œuvre sur le robot. Après avoir validé toutes les étapes préalablement citées nous sommes partis vers l'implémentation de la commande sur le robot. La tâche principale que nous avons adoptée est le dénudage des câbles. A cet effet, nous avons choisi de réaliser une commande hybride force/position dans laquelle les forces externes sont contrôlées afin de garantir l'absence de dommages sur les câbles à dénuder. Le robot qui a servi à réaliser toutes les expériences est le robot IRB14000 YuMi de Abb. Toutes les expériences réalisées dans le cadre de ce projet ont été décrites et présentées. Ce travail de thèse a été réalisé dans le cadre du projet Robotix Academy financé par le fonds européen de développement régional INTERREG V-A Grande Région.
... Base parameters are the minimum set to generate a dynamic equation. [29] ...
This paper first uses a decoupling modeling method to model legged robots. The method groups all the degrees of freedom according to the number of limbs, regarding each limb as a manipulator with serial structure, which greatly reduces the number of dynamic parameters that need to be identified simultaneously. On this basis, a step-by-step identification method from the end-effector link to the base link, referred to as “E-B” identification method, is proposed. Simulation verification is carried out on a quadruped robot with 16 degrees of freedom in Gazebo, and the validity of the method proposed is discussed.
... It has good convergence and provides for small estimation errors in the stationary case and the underlying normally distributed noise [15]. To further improve the performance of this algorithm, a forgetting factor (FF) term can be included [15,16]. Apart from the possibility of application of a classical algorithm such as the RLS, the use of the inverse model requires also a good prior estimation of the state and its derivatives. ...
This paper proposes an online direct closed-loop identification method based on a new dynamic sliding mode technique for robotic applications. The estimated parameters are obtained by minimizing the prediction error with respect to the vector of unknown parameters. The estimation step requires knowledge of the actual input and output of the system, as well as the successive estimate of the output derivatives. Therefore, a special robust differentiator based on higher-order sliding modes with a dynamic gain is defined. A proof of convergence is given for the robust differ-entiator. The dynamic parameters are estimated using the recursive least squares algorithm by the solution of a system model that is obtained from sampled positions along the closed-loop trajectory. An experimental validation is given for a 2 Degrees Of Freedom (2-DOF) robot manipulator, where direct and cross-validations are carried out. A comparative analysis is detailed to evaluate the algo-rithm's effectiveness and reliability. Its performance is demonstrated by a better-quality torque prediction compared to other differentiators recently proposed in the literature. The experimental results highlight that the differentiator design strongly influences the online parametric identification and, thus, the prediction of system input variables.
... After parameter identification, values need to be validated by adding them to the mathematical model and analyzing how well this model represents the dynamic behavior of a specific robot. The purpose of this validation is to verify that the robot's mathematical model is suitable for its future application [73,74]. ...
This article presents the design and validation of a regression model for the identification of dynamic parameters in manipulator robots. The model exhibits implementation advantages as it is based on the acquisition of position, speed and voltage data from the actuator in each joint rather than on the calculation of acceleration and torque. Actuators can be direct current and/or servomotor type. The regression model developed is simulated using MATLAB/Simulink software to identify the parameters of 2-DoF (Degrees of Freedom) and 5-DoF manipulator robots. Additionally, the model is experimentally validated on a real 5-DoF redundant manipulator robot. The identification model has great advantages in terms of implementation.
... Grâce à [Gautier et Khalil, 1990;Mayeda et al., 1990], on sait que le modèle dynamique d'un bras manipulateur série peut s'exprimer sous la forme Φ q,q,q θ = τ, où θ est le vecteur colonne des paramètres dynamiques du modèle, et Φ est le régresseur associé à θ. Pour adapter cette expression à notre cas où la dynamique des actionneurs est prise en compte, nous remplaçons τ par son expression donnée dans (3.20) : ...
Dans le cadre de la collecte sous-marine d’échantillons biologiques et minéraux pour larecherche scientifique par un robot sous-marin équipé de bras manipulateurs, ce projet dethèse a pour but principal le développement de nouvelles techniques demanipulation deséchantillons, plus fiables, permettant d’en assurer l’intégrité physique et leur exploitabilitépar les chercheurs. Les nouvelles techniques de manipulation proposées prennent encompte l’actionnement particulier des nouveaux bras électriques sous-marins équipantles engins récents, afin d’augmenter la précision du positionnement des outils embarquéspar le manipulateur. Un outil amovible, compliant, et mesurant les efforts d’interactionentre les bras du sous-marin et leur environnement est aussi proposé, et des méthodes permettantde tirer partie des caractéristiques de cet outil sont développées et testées expérimentalement.L’engin sous-marin hybride HROV Ariane, équipé de deux bras électriqueshétérogènes, offre la plateforme opérationnelle pour la validation expérimentale des solutionsproposées.
... Then, assuming that the values of kinematic parameters are known, if we give values to all the link inertial parameters, we can determine all the elements of 11 as function of and hence the dynamic model (1). To investigate the problem, following definitions and properties have been given in [2]. ...
A base parameter set which is defined to be a minimum set of inertial parameters that can determine dynamic model uniquely is shown for Torque-unit Manipulator (TUM) which has been proposed as a new design concept of manipulator. The elements of the base parameter set are also the parameters that can be identified independently from motion data and input data, i.e., measured values. The base parameters play very important role for dynamic modelling of manipulators such as model based control and simulation of the manipulator motion. The base parameters are given completely in closed from of linear combinations of the link inertial parameters. Also, a control strategy for all state variables of TUM is given by using the base parameters.
... En Khalil y Kleinfinger se advierte un aumento significativo de relaciones, que corresponderían a diferentes conjuntos de parámetros base, cuando se cuenta con sistemas con tres o más grados de libertad. Mayeda et al. [132] realiza la identificación de un manipulador serie, caracterizado por disponer de pares de revolución y prismáticos cuyos ejes son paralelos y perpendiculares entre sí. La metodología se basa en agrupar ciertos parámetros inerciales de un mismo elemento (agrupación predeterminada) según la dirección del par cinemático del elemento en la topología del manipulador. ...
El libro MANIPULADORES PARALELOS: SÍNTESIS, ANÁLISIS Y APLICACIONES, es fruto del proyecto de investigación titulado DESARROLLO DE MANIPULADOR PARALELO DE TIPO PLANAR Y ESPACIALES CON VISIÓN ARTIFICIAL PARA ALTERNATIVA DE AUTOMATIZACIÓN Y ACTUALIZACIÓN PARA LA INDUSTRIA, financiado por la Vicerrectoría de Investigaciones y Extensión de la Universidad Tecnológica de Pereira, con código 8-16-3.
El proyecto en mención es el resultado del trabajo mancomunado de los grupos de Investigación PROCESOS DE MANUFACTURA Y DISEÑO DE MÁQUINAS, y el grupo INVESTIGACIÓN Y DESARROLLO EN COMUNICACIONES Y HARDWARE RECONFIGURABLE de la Universidad Tecnológica de Pereira, Colombia, y del LABORATORIO DE MECATRÓNICA Y ROBÓTICA de la Universidad de los Andes, Venezuela.
Este trabajo es fruto del interés continuo de los grupos en mención en el tema de manipuladores paralelos, centrándose en el diseño, construcción, y control de manipuladores con diferentes configuraciones. Los resultados obtenidos se deben al trabajo de estudiantes de pregrado y maestría en Ingeniería Mecánica en los últimos años.
La industria en su afán por incrementar la producción en cada uno de sus procesos, ha requerido de tareas que generalmente son peligrosas para el hombre, por lo que se han desarrollado mecanismos controlados que pueden realizar operaciones de producción de una forma más segura, económica y rápida. Estos mecanismos se conocen como robots, que consiste en una serie de elementos, actuadores y sensores, que, con una adecuada estrategia de control, puede realizar tareas complejas.
En la familia de los robots existe una gran variedad de arquitecturas, siendo las más utilizadas en la industria, los manipuladores paralelos y los manipuladores serie, con estos últimos como los más estudiados y analizados en cuanto a su fabricación y control. Hasta hace unos años, los manipuladores en serie eran los encargados de realizar las tareas nombradas anteriormente. En estos robots, los actuadores se encuentran ubicados a lo largo de su estructura mecánica lo que genera un aumento en la inercia que el robot debe vencer para moverse, es decir, entre más actuadores tenga el robot, mayor es la carga en él, afectando la estabilidad de todo el mecanismo.
cerradas poseen diversas ventajas en cuanto a su contraparte, tales como: pueden alcanzar altas velocidades y aceleraciones, alta rigidez, una alta relación esfuerzo/peso y una mayor precisión. Gracias a estas ventajas, este tipo de manipuladores, en los últimos años, ha llamado la atención del campo industrial y la comunidad científica en la búsqueda de nuevos diseños y configuraciones e implementación de nuevos software para desarrollar estrategias de control más eficientes para estos mecanismos. También se ha ido incorporando la visión por computador; este tema de estudio está conformado por diferentes ramas como la Física, Óptica, Matemáticas, Lenguaje de Programación, Aprendizaje de Máquina, entre otras. Esta disciplina se desarrolló con el fin de asimilar la funcionalidad del ojo humano en el reconocimiento e interpretación de objetos. La visión por computador, en los últimos años, ha sido implementada en la industria, con el objetivo de controlar sistemas de procesos de calidad en las que se implementarían medidas y estándares rigurosos de procesos de producción, como en el caso de ensambladores o manejo de alimentos.
En el campo de la robótica industrial, a nivel latinoamericano, existen pocos trabajos o monografías que aborden el tema de los manipuladores paralelos. El esfuerzo realizado para escribir este libro tiene por objeto llenar esa falta de monografías en el área. Por lo que este trabajo se enfoca en la síntesis, análisis y aplicaciones de los manipuladores paralelos.
En el capítulo uno se enmarca el proyecto de investigación DESARROLLO DE MANIPULADOR PARALELO DE TIPO PLANAR Y ESPACIALES CON VISIÓN ARTIFICIAL PARA ALTERNATIVA DE AUTOMATIZACIÓN Y ACTUALIZACIÓN PARA LA INDUSTRIA. Se presenta en este capítulo la introducción del tema de manipuladores paralelos, describiendo sus características, y los principales temas de investigación relacionados con los manipuladores paralelos.
En el capítulo dos se muestran diversas aplicaciones industriales de los manipuladores paralelos encontrados en la literatura. Con este capítulo se pretende mostrar la evolución que ha tenido en los últimos años los manipuladores paralelos en la solución de problemas industriales. Se hace especial énfasis en el trabajo desarrollado en el Laboratorio de Robótica de la Universidad de los Andes de Venezuela.
En el capítulo tres se realiza la síntesis de tipo de manipuladores paralelos planos de dos y tres grados de libertad. En la síntesis de tipo se tiene en cuenta criterios como: espacio de trabajo, análisis de sensibilidad a los errores dimensionales de los eslabones del manipulador, y fabricación. Se presenta una tabla de diseño, y se eligen tres de las configuraciones con mejor calificación para el análisis. Con respecto a los manipuladores espaciales, se presentan las configuraciones de mayor interés en la comunidad académica, para tres, cuatro, cinco y seis grados de libertad, y se eligen dos configuraciones para el estudio. Esta selección se basó en configuraciones del Manipulador Delta, configuración de interés en la comunidad científica.
En el capítulo cuatro se realiza el análisis cinemático de los manipuladores planos de dos y tres grados de libertad elegidos, y los Manipuladores Delta de tres grados de libertad, uno con actuadores rotativos, y otro con actuadores lineales. Se realiza el análisis de la cinemática directa e inversa para cada manipulador.
En el capítulo cinco se formulan las ecuaciones para la identificación de parámetros en manipuladores planos y espaciales. Se realiza el estudio de identificación de parámetros inerciales en el caso de manipuladores paralelos planos 2-RRR y 2-RPR. En estos manipuladores se determinarán las ecuaciones de movimiento que permitan identificar los parámetros dinámicos, utilizando el método simbólico de transferencia de masas.
En el capítulo seis se presenta un estudio del control de un Manipulador Delta con actuadores lineales. En este capítulo se realiza el estudio del movimiento del manipulador sin considerar las fuerzas o pares motores que generan el movimiento, concentrándose única y exclusivamente en las restricciones al movimiento impuestas por las cadenas cinemáticas.
En el capítulo siete se presenta el sistema de control servoasistido por visión del manipulador 3-RRR utilizando una cámara. Se muestra el proceso de calibración, la identificación del objetivo, la implementación de un sistema de estimación de la posición del objetivo basado en filtro de Kalman, y el desplazamiento de los servos cuando el objetivo sigue una trayectoria circular. Finalmente se presentan las conclusiones obtenidas.
... Robot dynamics modelling and calibration techniques were widely addressed along the last three decades. Since early works [3,4] many researchers have investigated methodologies all involving a linear reduction of the rigid-body model into a base set of lumped dynamics model parameters (BP) to be estimated [5,6]. ...
The attempt to use industrial robots for technological and interaction tasks, i.e., robotic machining and robotic assembling, implies on the one hand the knowledge of the interaction force, on the other hand the reduction of physical sensors. The aim of this work is the development of a virtual force sensor to estimate the interaction force between a conventional industrial robot and the environment. The goal is achieved by exploiting a task oriented dynamics model calibration combined with of a thermal friction model of the robot. The dynamics model is calibrated by means of exciting trajectories made by suitable paths selected by a genetic-based two-stage optimization. The virtual sensor is proven by means of a polishing application. The proposed approach is successfully compared with state-of-the-art approaches. Finally, the use of the virtual force sensor in a closed-loop architecture highlights the effectiveness of the method in real applications.
It is essential for human-robot interaction to accurate joint torque value estimation of industrial robots without force/torque (F/T) sensors. The most common method to estimate the value of robot joint torque is based on dynamic model parameter identification. However, no matter how elaborate the modeling methods are used, there are always uncertainty errors when robot’s joint rotation direction changes. In this paper, an identification framework is proposed to estimate optimal model parameters, and a deep learning network is proposed to compensate for the uncertainty errors caused by the unmodeled dynamics part. At first, the dynamic parameters are estimated during the Least Squares (LS) identification process considering the noise influence and data outliers, and the nonlinear friction model is unified into the identification framework. Secondly, based on Long-Short Term Memory (LSTM) network, an error compensation model (ECM) is proposed to establish the mapping relationship between the joint motion and the identification errors. Finally, a 6-DOF robot is used for parameter identification and ECM validation. Experimental results show that the proposed identification method is better than the LS method. Compared with the torque value estimated by the identification method, the proposed ECM can compensate for the uncertainty errors and improve the torque estimation accuracy.
This paper presents an algorithm to geometrically characterize inertial parameter identifiability for an articulated robot. The geometric approach tests identifiability across the infinite space of configurations using only a finite set of conditions and without approximation. It can be applied to general open-chain kinematic trees ranging from industrial manipulators to legged robots, and it is the first solution for this broad set of systems that is provably correct. The high-level operation of the algorithm is based on a key observation: Undetectable changes in inertial parameters can be represented as sequences of inertial transfers across the joints. Drawing on the exponential parameterization of rigid-body kinematics, undetectable inertial transfers are analyzed in terms of observability from linear systems theory. This analysis can be applied recursively, and lends an overall complexity of O( N) to characterize parameter identifiability for a system of N bodies. Matlab source code for the new algorithm is provided.
By exploiting the concept of closed-loop input error (CLIE), this article proposes an identification approach for the dynamic parameters of industrial robot manipulator based on evolutionary algorithms (EAs). The proposed algorithm estimates the dynamic parameters by using joint torque residuals between the actual robot and a parallel estimated model. Both the actual robot and the estimated model use the same reference trajectories and the same control law structure tuned with the same gain. The state of the estimated model is generated by filtering the measured signal through a model state generator, so by adjusting the cutoff frequency of the filter, different estimated models can be generated. By using EA, one can search for an estimated model in the solution space corresponding to the model state generator so that the joint torque difference between the actual robot and the estimated model is minimized. In addition, EA will automatically adjust the filtering strength of the measured signals to provide a noise-free signal for the estimated model so that the identification result can be more accurate. The dynamic parameters of the estimated model obtained through the optimization process are the optimal identification results of the actual robot. Moreover, to reduce the computation cost of the estimated model, this article also provides an approximation algorithm for the observation matrix so as to enhance the search efficiency of EA. Several experiments have been conducted on a 6-DOF industrial robot manipulator to verify the effectiveness of the proposed approach.
A rapid recurrent neural network (RNN)-based physical feasibility test algorithm for base parameters during the identification process of a robot dynamic model is proposed in this paper. Firstly, related physical constraints such as inertia tensor, drive chain inertia, and friction are combined into the formulation of linear matrix inequality (LMI) to examine the physical consistency of the base parameters. The optimization problem of LMI is then solved by a matrix-oriented gradient-type RNN. Since the network structure of this type of RNN is simple and the process for solving the optimization problem of LMI is parallel distributed, the physical feasibility test can be completed more quickly than when utilizing commonly used semi-definite programming techniques. By taking advantage of highly efficient computation capabilities, the proposed physical feasibility test algorithm is particularly suitable for identification approaches that require rapid feasibility assessment such as on-line identification methods or optimization-based identification methods. An evolutionary algorithm-based identification method is used as an illustrative example to assess the performance of the proposed approach. In addition, a stability proof for the proposed gradient-type RNN is also provided. Results of the experiments conducted on a 6-DOF industrial robot manipulator verify the effectiveness of the proposed approach.
Traditional identification approaches for robotic systems based on the inverse dynamic model and the least-squares method are the most used to identify dynamic parameters of robots. However these methods often require a well-tuned filtering or estimation of the position, velocity, acceleration and torque to avoid bias in identification results. The cutoff frequency of the low-pass filter that is usually used must be well chosen, which is not always a trivial task. In this paper, we propose to use an extended Kalman filter to reduce the noise on the measured position and to estimate the velocity and acceleration. These estimates can then be fed to the controller to further reduce the noise in the control torque. The effect of the tuning of this filter is examined and the presented approach is validated through simulations and experiments on a one degree of freedom system.
This paper presents the design and development of a control scheme, for a robot master–slave teleoperation system man–machine interface. The developed system consists of JUPITER XL SCARA robot as a slave manipulator with only the first two links activated, a wireless User Datagram Protocol (UDP) network, and PC as a master controller. The system model parameters identified using the Least-Squares method. A workspace-control system was developed to deals with the problem of position-tracking of bilateral teleoperated two degrees of freedom manipulator, and aid the human operator in driving and controlling the slave robot that performs critical and difficult tasks such as underwater works. A Proportional-Integral-Derivative (PID) and Fuzzy Logic Control (FLC) controllers with different input signals were applied to the system. It was proved experimentally and by simulation on Matlab that the FLC gave a better performance than the PID controller. The two parallel loop subroutine technique proved a great enhancement to the system performance as it decreased the total delay time in the system to almost 25 ms.
Closed-chain robots have great advantages in machining complex components, especially under high-speed and heavy-load conditions. Accurate dynamic model is fundamental importance to obtain good performance. However, most existing works focus on the excitation trajectories and identification methods, but few works of literature deal with the accuracy and simplification of non-singular dynamic modelling. In this paper, we propose a general scheme to identify the non-singular dynamic model considering motor couplings, which also simplifies the elimination of redundant parameters. At first, a symbolic model is proposed for motor couplings by analysing the mapping relationships of joint rotations, and the coefficients of the model can be identified by the presented numerical method of least squares curve fitting (LSCF). Then, a unified approach is proposed to determine non-singular dynamic model by performing adjacent link mapping (ALM) with Newton–Euler formulas, which is more convenient and applicable to both serial and tree structures. Finally, a refined model of closed-chain robot is given for identification, by considering motor couplings and applying the simplified elimination of redundant parameters. Compared to the existing schemes, the proposed motor-couplings based dynamic model is more accurate, and the ALM has better applicability and efficiency. Experimental studies are conducted to validate the proposed methodology on a closed-chain robot.
Due to the important role of the manipulator dynamic model in manipulation control, the identification of the dynamic parameters of manipulators has become a research hotspot once again. In this paper, we present an overview of the modeling of manipulator dynamics, the optimization methods of excitation trajectory, the identification methods for dynamic parameters, and the identification of friction model parameters. First, the process and basic methods of identification of manipulation dynamic parameters are summarized, and the optimization methods for excitation trajectory are analyzed in detail. Further, friction model parameter identification and the physical feasibility of dynamic parameters are discussed. These are research hotspots associated with the identification of dynamic parameters of manipulators. The backgrounds and solutions of the problems of physical feasibility and identification of friction parameters are reviewed in this paper. Finally, neural networks and deep learning methods are discussed. The neural networks and deep learning methods have been used to improve the accuracy of identification. However, deep learning methods and neural networks need more in-depth analysis and experiments. At present, the instrumental variable method with complete physical feasibility constraints is an optimal choice for dynamic parameter identification. Moreover, this review aims to present the important theoretical foundations and research hotspots for the identification of manipulation dynamic parameters and help researchers determine future research areas.
Advanced robotic applications have revived interest in identification of a high-precision dynamic model. In this article, we propose an extended dynamic parameter set (EDS). The EDS breaks through the limitation that the base dynamic parameter set needs
a priori
knowledge of the gravity direction for modeling. Moreover, we present a novel parameters identification technique (RSIH), which is a complete solution and can significantly mitigate negative effects of the measurement noise and outliers. Besides, an incremental learning technique combined with a compensation limit criterion is employed to compensate for unmodeled dynamics. Simulations and experiments demonstrate the EDS-based model can adapt to any installation angle of a base plate, and confirm the RSIH technique outperforms the widely used identification techniques in industry and is equal to or even better than the state-of-the-art physical feasibility technique in terms of identification precision and robustness. In addition, the modeling errors, especially the uncertainty of the friction model, can be greatly compensated.
We present Pseudo-Symbolic Dynamic Modeling (PSDM), a novel method of deriving the closed-form equations of motion of a serial kinematic chain, using base inertial parameters. PSDM is a numerical algorithm, yet allows for model simplification and pre-computation generally only possible using symbolic software. In PSDM, we characterize the form of the dynamic equations to build a set of functions guaranteed to form a linear basis for the inverse dynamics function of the manipulator. Then, a two-step numerical analysis is performed to reduce this set into a minimal dynamic model, in regressor form. PSDM offers a fast and procedural method of generating simplified dynamic models. Extensions to the algorithm allow for fast real-time code generation, forward dynamic modeling, and increased model efficiency through the elimination of minimally important model elements. The algorithm is benchmarked on common robot configurations and shown to be attractive for the dynamic modeling of up to 7-DOF manipulators, in terms of derivation time and real-time evaluation speed. Additionally, a MATLAB implementation of the algorithm has been developed and is made available for general use.
Hydraulically actuated manipulators are commonly used for material handling or at construction sites due to the high power density of hydraulic systems. Dig assistance systems or payload monitoring systems for excavators become more common to increase the efficiency and productivity. In this paper, a novel approach for estimating the dynamic parameters of a payload (including the mass) attached to the last link of a hydraulically actuated rigid body manipulator is proposed. Motion equations for the open chain rigid body system including the payload are derived. The motion equations are formulated as a linear regression model exploiting the linearity in the base dynamic parameters. Furthermore, a dynamic model for the neglected closed kinematic chains and the friction is proposed. A least squares optimization problem for minimizing the error between the model based torque and measured torque with respect to the payload parameters is defined. The optimization problem is simplified with assumptions on the center of gravity and the inertia of the payload, which leads to a more robust estimation of the payload mass with a recursive least squares algorithm. Post processing of the estimated payload is suggested and heuristics for the calculation of characteristic values like the accumulated handled mass are shown for the special case of a material handling and an earthmoving excavator. Finally, the novel approach for the payload estimation is validated on both experimental excavators for typical working cycles. The overall performance meets the requirements of ± 3%.
Using industrial robots as machine tools is targeted by many industries for their lower cost and larger workspace. Nevertheless, performance of industrial robots is limited due to their mechanical structure involving rotational joints with a lower stiffness. As a consequence, vibration instabilities, known as chatter, are more likely to appear in industrial robots than in conventional machine tools. Commonly, chatter is avoided by using stability lobe diagrams to determine the stable combinations of axial depth of cut and spindle speed. Although the computation of stability lobes in conventional machine tools is a well-studied subject, developing them in ro-botic milling is challenging because of the lack of accurate multi-body dynamics models involving joint compliance able of predicting the posture-dependent dynamics of the robot. In this paper, two multi-body dynamics models of articulated industrial robots suitable for machining applications are presented. The link and rotor inertias along with the joint stiffness and damping parameters of the developed models are identified using a combination of multiple-input multiple-output identification approach, computer-aided design model of the robot, and experimental modal analysis. The performance of the developed models in predicting posture-dependent dynamics of a KUKA KR90 R3100 robotic arm is studied experimentally.
An auto-tuning method for a Delta robot’s P/PI cascade motion controller using multi-objective optimization algorithm is proposed. The implemented control structure consists of two controllers: A feedforward controller based on a model of the inverse dynamics of the robot, and a cascade P/PI controller to compensate for unmodeled effects. The auto-tuning is achieved in the sense of optimizing the control parameters in three stages. In the first stage, the feedback control parameters are optimized after neglecting the feedforward control term. The goal is to minimize the position error in tracking an excitation trajectory, which is used as well to identify the dynamic model parameters in the second stage. After that, the feedforward compensation term is computed offline based on the desired trajectory. In the final stage, the P/PI parameters are optimized again after adding the feedforward controller. Experimental results on an industrial 3-dof Delta robot validates the efficiency of the proposed method.
Accurate information of inertial parameters is critical to motion planning and control of space robots. Before the launch, only a rudimentary estimate of the inertial parameters is available from experiments and CAD models. After the launch, on-orbit operations substantially alter the value of inertial parameters. In this work, a new momentum model-based method is proposed for identifying the minimal parameters of a space robot while on orbit. Minimal parameters are combinations of the inertial parameters of the links and uniquely define the momentum and dynamic models. Consequently, they are sufficient for motion planning and control of both the satellite and robotic arms mounted on it. The key to the proposed framework is the unique formulation of the momentum model in the linear form of minimal parameters. Further, to estimate the minimal parameters, a novel joint trajectory planning and optimization technique based on direction combinations of joints’ velocity are proposed. The efficacy of the identification framework is demonstrated on a 12-degree-of-freedom, spatial, dual-arm space robot. The methodology is developed for tree-type space robots, requires just the pose and twist data, and is scalable with increasing number of joints.
Most existing manipulator control schemes require that the dynamic model of a manipulator be precisely known. There are some control schemes like the adaptive control scheme which do not require a detailed description of the dynamic model. However, it is necessary to verify the effectiveness of these control schemes with an exact dynamic model before applying them to real system.A dynamic model for a manipulator is defined using such mechanical parameters as the mass, center of mass, inertia tensor matrix and friction for each link. Usually, it is difficult to obtain exact values for these parameters.This paper presents a parameter identification scheme for a mechanical manipulator modeled on an open-rigid-link-chained mechanism. Dynamic equations for the manipulators are nonlinear, however linear input-ouput equations for the kinetic parameters of dynamic equations have been developed. Kinetic parameters are estimated by an instrument variable method based on these input-output equations. It is shown by theorem and simulation results that the instrument variable method asmptotically yields consistent estimates of the parameters. Moreover, the effectiveness of the proposed method is verified by experimental results using a 6-degree-of-freedom manipulator.
Developement of the methods to identify manipulator dynamics precisely is essential for the advanced control and design of the manipulator systems. Although dynamic models of manipulators are highly non linear, the form of nonlinear terms in the models are determined by the structures of the manipulators and all the coefficients are derived from the kinematic parameters of the manipulator components. A new method to identify these coefficients and to construct nonlinear dynamic mode is for serial manipulators with arbitrary number of links is proposed. The method consists of three types of simple enough tests performed without decomposing the manipulator into parts. The application to a real industrial robot arm shows that this method is very powerful and practical.
For advanced control and design of manipulator systems, developement of the methods to identify manipulator dynamics precisely is essentially important.
The dynamical model of a manipulator can be obtained by decomposing the manipulator into many components, measuring their dynamical parameters, and calculating the coefficients of the nonlinear model. But it costs quite much labor to perform these, and still the obtained model is said to be inaccurate.
A practical method to identify the coefficients of the nonlinear terms of the model from simple test motions was proposed by the authors. In this paper this method is applied to a real manipulator with three rotational joints, and the results are shown to be satisfactory.
Some important technical details for the application are also mentioned.
マニピュレータの高性能化, あるいはCADシステムの開発などのためには, その正確な動特性モデルの同定法, および逆動力学問題の効率の良い解法, の開発が必要になる.筆者等は先に, マニピュレータのための実用的な同定法を提案した.また, J.Y.S.Luhらによって, 逆動力学問題の効率の良いアルゴリズムが開発されている.ところが, 筆者らが開発した同定法に適したパラメータの形とLuhらのアルゴリズムに適したパラメータの形には相違点があった.そのために我々は, 上の二つの問題を, 別々に取り扱わなければならなかった.本論文では, 仮想パラメータなる概念を導入することによって, 同定問題と逆動力学問題との整合をとることを考える.そのためにまず, それぞれの問題に適したパラメータめ形を明らかにする.次に, 仮想パラメータを定義し, 同定問題の結果を逆動力学問題の高速解法に利用できるようにする.
The inertial parameters of manipulator rigid-body loads and links have been automatically estimated as a result of gen eral movement. The Newton-Euler equations have been recast to relate linearly the measured joint forces or torques via acceleration-dependent coefficients to the inertial parame ters, which have then been estimated by least squares. Load estimation was implemented on a PUMA 600 robot equipped with an R TI FS-B wrist force-torque sensor and on the MIT Serial Link Direct Drive Arm equipped with a Barry Wright Company Astek wrist force-torque sensor. Good estimates were obtained for load mass and center of mass, and the forces and torques due to movement of the load could be pre dicted accurately. The load moments of inertia were more difficult to estimate. Link estimation was implemented on the MIT Serial Link Direct Drive Arm. A good match was ob tained between joint torques predicted from the estimated parameters and the joint torques estimated from motor cur rents. The match actually proved superior to predicted torques based on link inertial parameters derived by CAD modeling. Restrictions on the identifiability of link inertial parameters due to restricted sensing and movement near the base have been addressed. Implications of estimation accu racy for manipulator dynamics and control have been consid ered.
Industrial robots are mechanical manipulators whose dynamic characteristics are highly nonlinear. To control a manipulator which carries a variable or unknown load and moves along a planned path, it is required to compute the forces and torques needed to drive all its joints accurately and frequently at an adequate sampling frequency (no less than 60 Hz for the arm considered). A new approach of computation is presented which is based on the method of Newton-Euler formulation which is independent of the type of manipulator configuration. This method involves the successive transformation of velocities and accelerations from the base of the manipulator out to the gripper, link by link, using the relationships of moving coordinate systems. Forces are then transformed back from the gripper to the base to obtain the joint torques. Theoretically the mathematical model is ″exact.″ A program has been written in floating point assembly language which has an average execution time of 4. 5 msec on a PDP 11/45 computer for a Stanford manipulator. This allows an on-line computation within control systems with a sampling frequency no lower than 60 Hz. A further advantage of this method is that the amount of computation increases linearly with the number of links whereas the conventional method based on Lagrangian formulation increases as the quartic of the number of links.
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 7 n -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
Orthogonal second-order Cartesian tensors are used to formulated
the Newton-Euler dynamic equations for a robot manipulator. Based on
this formulation, an efficient recursive procedure is developed to
evaluate the joint torques. The procedure is applicable to all
rigid-link manipulators with open-chain kinematic structures with
revolute and/or prismatic joints. For simplicity of presentation, only
manipulators with (kinematically more complex) revolute joints are
considered. An efficient implementation of the proposed method shows
that the joint torques for a six-degree-of-freedom manipulator with
revolute joint, can be computed in approximately 500 multiplications and
420 additions. For manipulators with 0° or 90° twist angles, the
required computations are reduced to 380 multiplications and 315
additions
An efficient method for the calculation of the inverse dynamic models of tree structure robots is presented. The given method reduces significantly the computational burden such that the inverse dynamics can be computed in real time at servo rate. The method leads almost directly to models with a minimum number of arithmetic operations. The method is based on a Newton-Euler formulation that is linear in the inertial parameters, on an iterative symbolic procedure, and on condensating the inertial parameters by regrouping and eliminating some of them. The description of the robot is carried out by a new notation inspired from Denavit and Hartenberg notation. A Fortran program has been developed to generate automatically the dynamic models of tree structure robots.
Thesis (Ph. D.)--Carnegie Mellon University, 1986. Includes bibliographical references (leaves 153-172). Microfiche.
Real-time dynamic control of robot manipulators requires on-line computation of the dynamic model that expresses the generalized forces to be applied to their joints, as a function of their generalized coordinates, velocities and accelerations. To do this, this paper presents a method of computation of this model that uses a quasiminimal number of elementary arithmetical operations and that can be applied systematically to robot manipulators with a simple kinematic chain structure and revolute and/or prismatic joints. To reach this quasi-minimal number, use if primarily made of the following : * a computation that is intrinsic rather than extrinsic, analytical rather than numerical and iterative rather than developed ; * the Newton-Euler formalism rather than the Lagrangian one and * the notion of augmented body, generalized to this type of structure. An example demonstrates that the computation of the dynamic model of an industrial robot manipulator with six revolute joints (the most complicated case in practice) can be effected with less than 300 arithmetical operations (adds and multiplies).
The author addresses the problem of generating persistently
exciting trajectories for parameter estimation. To achieve this, he
proposes an algorithm that categorizes the dynamics parameters of a
manipulator into three classes: uniquely identifiable, identifiable in
linear combinations only, and unidentifiable. Since the proposed
algorithm categorizes the parameters only on the basis of the kinematic
configuration of the manipulator, it makes it possible to determine if a
chosen trajectory (for estimation) is persistently exciting. The
categorization procedure also helps in making the estimation procedure
more robust. Based on the proposed algorithm, the parameters of the CMU
DD (Carnegie-Mellon University Direct-Drive) Arm II were categorized
An efficient method for solving inverse dynamics problem: An application of virtual pa-MAYEDA et al.: MANIPULATOR DYNAMIC MODEL PARAMETERS rameters Minimum operations and minimum parameters of the dynamic models of tree structure robots Base parameters of manip-ulator dynamic models
- K Osuka
- H Mayeda
- K Osuka
- H Mayeda
- K Yoshida
- T Ono
- W Khalil
- J F Kleinfinger
K. Osuka and H. Mayeda, " Parameter expression for modeling and inverse dynamics problem of manipulators, " Adv. Robotics, to be published. K. Osuka, H. Mayeda, K. Yoshida, and T. Ono, " An efficient method for solving inverse dynamics problem: An application of virtual pa-MAYEDA et al.: MANIPULATOR DYNAMIC MODEL PARAMETERS rameters " (in Japanese), in Proc. 3lst Ann. Conf. Syst. Contr., May W. Khalil and J. F. Kleinfinger. " Minimum operations and minimum parameters of the dynamic models of tree structure robots,'' IEEE J. Robotics Automat., vol. RA-3. no. 6. pp. 517-526, Dec. 1987. H. Mayeda, K. Yoshida. and K. Osuka, " Base parameters of manip-ulator dynamic models, " in Proc. 1988 IEEE Int. Conf. Robotics Automat., Apr. 1988. pp. 1367-1372.
An efficient method for solving inverse dynamics problem: An application of virtual parameters
- K Osuka
- H Mayeda
- K Yoshida
- T Ono
Base parameters of manipulator dynamic models
- H Mayeda
- K Yoshida
- K Osuka