Parameter estimation survey for multi-joint robot dynamic calibration case study

Shaolin ZHANG; Shuo WANG; Fengshui JING; Min TAN

doi:10.1007/s11432-018-9726-3

SCIENCE CHINA Information Sciences

Download PDF

SCIENCE CHINA Information Sciences, Volume 62 , Issue 10 : 202203(2019) https://doi.org/10.1007/s11432-018-9726-3

Parameter estimation survey for multi-joint robot dynamic calibration case study

Shaolin ZHANG ^1,2, Shuo WANG ^1,2,3,*, Fengshui JING ^1,2, Min TAN ^1,2

More info

ReceivedSep 29, 2018
AcceptedDec 12, 2018
PublishedAug 21, 2019

Previous Table of Contents Next

Rating

iFLYTEK Translation

Abstract

industrial manipulator

robot dynamics

friction calibration

dynamic models

dynamic parameter calibration

Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. U1713222, 61773378, 61421004, U1806204), Beijing Science and Technology Project (Grant No. Z181100003118006), and Youth Innovation Promotion Association CAS.

References

[1] Jamisola R. Dynamics identification and control of an industrial robot. In: Proceedings of the 9th International Conference on Advanced Robotics, Kyongju, 1999. 749--754. Google Scholar

[2] Hollerbach J, Khalil W, Gautier M. Model identification. In: Springer Handbook of Robotics. Berlin: Springer, 2016. 113--138. Google Scholar

[3] van Damme M, Beyl P, Vanderborght B, et al. Estimating robot end-effector force from noisy actuator torque measurements. In: Proceedings of 2011 IEEE International Conference Robotics and Automation, Shanghai, 2011. 1108--1113. Google Scholar

[4] Richalet J, Fiani P. The global approach in identification protocol optimization. In: Proceedings of International Conference on Control Applications, Albany, 1995. 423--431. Google Scholar

[5] Gautier M, Janot A, Vandanjon P O. A New Closed-Loop Output Error Method for Parameter Identification of Robot Dynamics. IEEE Trans Contr Syst Technol, 2013, 21: 428-444 CrossRef Google Scholar

[6] Janot A, Vandanjon P O, Gautier M. A Generic Instrumental Variable Approach for Industrial Robot Identification. IEEE Trans Contr Syst Technol, 2014, 22: 132-145 CrossRef Google Scholar

[7] Montazeri A, West C, Monk S D. Dynamic modelling and parameter estimation of a hydraulic robot manipulator using a multi-objective genetic algorithm. Int J Control, 2017, 90: 661-683 CrossRef Google Scholar

[8] Wensing P M, Kim S, Slotine J J E. Linear Matrix Inequalities for Physically Consistent Inertial Parameter Identification: A Statistical Perspective on the Mass Distribution. IEEE Robot Autom Lett, 2018, 3: 60-67 CrossRef Google Scholar

[9] Sousa C D, Cortes?o R. Physical feasibility of robot base inertial parameter identification: A linear matrix inequality approach. Int J Robotics Res, 2014, 33: 931-944 CrossRef Google Scholar

[10] Welch G, Bishop G. An Introduction to the Kalman Filter. Chapel Hill, Technical Report. 1995. Google Scholar

[11] Gautier M, Poignet P. Extended Kalman filtering and weighted least squares dynamic identification of robot. Control Eng Practice, 2001, 9: 1361-1372 CrossRef Google Scholar

[12] Bona B, Indri M. Friction compensation in robotics: an overview. In: Proceedings of the 44th IEEE Conference Decision Control, Seville, 2005. 4360--4367. Google Scholar

[13] Swevers J, Verdonck W, Schutter J D. Dynamic Model Identification for Industrial Robots. IEEE Control Syst, 2007, 27: 58-71 CrossRef Google Scholar

[14] Ding L, Wu H, Yao Y. Dynamic Model Identification for 6-DOF Industrial Robots. J Robotics, 2015, 2015: 1-9 CrossRef Google Scholar

[15] Freidovich L, Robertsson A, Shiriaev A. LuGre-Model-Based Friction Compensation. IEEE Trans Contr Syst Technol, 2010, 18: 194-200 CrossRef Google Scholar

[16] Astrom K J, Carlos C C. Revisiting the LuGre friction model. IEEE Control Syst, 2008, 28: 101-114 CrossRef Google Scholar

[17] Bompos N A, Artemiadis P K, Oikonomopoulos A S, et al. Modeling, full identification and control of the mitsubishi pa-10 robot arm. In: Proceedings of 2007 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Zurich, 2007. 1--6. Google Scholar

[18] Wernholt E, Gunnarsson S. NONLINEAR IDENTIFICATION OF A PHYSICALLY PARAMETERIZED ROBOT MODEL 1. IFAC Proc Volumes, 2006, 39: 143-148 CrossRef Google Scholar

[19] Grotjahn M, Daemi M, Heimann B. Friction and rigid body identification of robot dynamics. Int J Solids Struct, 2001, 38: 1889-1902 CrossRef Google Scholar

[20] Lee S D, Ahn K H, Song J B. Torque control based sensorless hand guiding for direct robot teaching. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, 2016. 745--750. Google Scholar

[21] Blumenkranz S J, Prisco G M, DiMaio S P, et al. US Patent, 9 895 813, 2018. Google Scholar

[22] Erden M S, Jonkman J A. PHYSICAL HUMAN-ROBOT INTERACTION BY OBSERVING ACTUATOR CURRENTS. Int J Robotics Automation, 2012, 27: 233-243 CrossRef Google Scholar

[23] Nagamatsu Y, Shirai T, Suzuki H, et al. Distributed torque estimation toward low-latency variable stiffness control for gear-driven torque sensorless humanoid. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, 2017. 5239--5244. Google Scholar

[24] Vuong N D, Marcelo Jr. A H, Li Y P. Improved dynamic identification of robotic manipulators in the linear region of dynamic friction. IFAC Proc Volumes, 2009, 42: 167-172 CrossRef Google Scholar

[25] Vuong N, Jr M. Dynamic model identification for industrial robots. Acta Polytech Hung, 2009, 6: 58--71. Google Scholar

[26] Stürz Y R, Affolter L M, Smith R S. Parameter Identification of the KUKA LBR iiwa Robot Including Constraints on Physical Feasibility. IFAC-PapersOnLine, 2017, 50: 6863-6868 CrossRef Google Scholar

[27] Duan X J, Zhi J H, Chen H M. Two novel robust adaptive parameter estimation methods with prescribed performance and relaxed PE condition. Sci China Inf Sci, 2018, 61: 129203 CrossRef Google Scholar

[28] Jahandideh H, Namvar M. Use of pso in parameter estimation of robot dynamics. Google Scholar

[29] Craig J. Introduction To Robotics: Mechanics And Control. 3rd ed. Upper Saddle River: Pearson Education, 2005. 165--200. Google Scholar

[30] Kammerer N, Garrec P. Dry friction modeling in dynamic identification for robot manipulators: theory and experiments. In: Proceedings of 2013 IEEE International Conference Mechatronics, Kagawa, 2013. 422--429. Google Scholar

[31] Wu D W, Liu Q, Xu W J, et al. External force detection for physical human-robot interaction using dynamic model identification. In: Proceedings of International Conference on Intelligent Robotics and Applications, 2017. 581--592. Google Scholar

[32] Wang X M, He X K, Bao Y. Parameter estimates of Heston stochastic volatility model with MLE and consistent EKF algorithm. Sci China Inf Sci, 2018, 61: 042202 CrossRef Google Scholar

[33] Janot A, Vandanjon P O, Gautier M. Identification of 6 DOF Rigid Industrial Robots with the Instrumental Variable Method. IFAC Proc Volumes, 2012, 45: 1659-1664 CrossRef Google Scholar

[34] Sousa C D, Cortes ao R. Physically feasible dynamic parameter identification of the 7-DOF WAM robot. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Tokyo, 2013. 2868--2873. Google Scholar

[35] Marino I P, Miquez J. Gradient-descent methods for parameter estimation in chaotic systems. In: Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, Zagreb, 2005. 440--445. Google Scholar

[36] Reeves C R. Genetic Algorithms. Boston: Springer, 2010. 109--139. Google Scholar

[37] Candy J V. Bayesian Signal Processing: Classical, Modern, and Particle Filtering Methods. Hoboken: John Wiley Sons, 2009. 237--293. Google Scholar

[38] Wu J, Wang J, You Z. An overview of dynamic parameter identification of robots. Robotics Comput-Integrated Manufacturing, 2010, 26: 414-419 CrossRef Google Scholar

[39] Sun Y, Hollerbach J M. Observability index selection for robot calibration. In: Proceedings of 2008 IEEE International Conference on Robotics and Automation, London, 2008. 831--836. Google Scholar

[40] Bargsten V, Zometa P, Findeisen R. Modeling, parameter identification and model-based control of a lightweight robotic manipulator. In: Proceedings of 2013 IEEE International Conference on Control Applications (CCA), Hyderabad, 2013. 134--139. Google Scholar

[41] Calafiore G, Indri M, Bona B. Robot dynamic calibration: Optimal excitation trajectories and experimental parameter estimation. J Robotic Syst200118. Google Scholar

[42] Swevers J, Ganseman C, Tukel D B. Optimal robot excitation and identification. IEEE Trans Robot Automat, 1997, 13: 730-740 CrossRef Google Scholar

[43] Presse C, Gautier M. New criteria of exciting trajectories for robot identification. In: Proceedings of 1993 IEEE International Conference on Robotics and Automation, Atlanta, 1993. 907--912. Google Scholar

[44] Liu J C, Wu Z X, Yu J Z. Sliding mode fuzzy control-based path-following control for a dolphin robot. Sci China Inf Sci, 2018, 61: 024201 CrossRef Google Scholar

Click to view Download high-quality image

Figure 1
(Color online) The Efort ER20-C10 robot and D-H frames.
Click to view Download high-quality image

Figure 3
The simulation platform for point sampling.
Click to view Download high-quality image

Figure 4
(Color online) A comparison of the Kalman filter and exponential forgetting method. (a) Kalman filter (slope change); (b) exponential forgetting (slope change); (c) Kalman filter (second-order change); (d) exponential forgetting (second-order change).
Table 1 The levels of torque error

Level A Level B Level C
${e_{T}}$ textless0.01 textless0.1 textgreater0.1

Table 2 The levels of parameter errors

	Level A	Level B	Level C
${e_{d}}$	textless0.2	textless1	textgreater1
${e_{f}}$	textless0.2	textless1	textgreater1
$J_e$	textless1	textless10	textgreater10
Follow changing parameter	Slope change	Step change	None

Table 3 The levels of solution time of offline methods

Level A Level B Level C
Solution time textless1 min textless1 h textgreater1 h
Table 4 The levels of anti-interference ability

Level A Level B Level C
$\Delta~{J_e}$ textless0.1 textless1 textgreater1

Table 5 Linear calibration result of joint 3

Parameter

Set

Pseudo-

inverse

Kalman

Index

forgetting

Optimization

Gradient

descent

Genetic

algorithm

Particle

filter

Mass (kg)

$m$

25.6083

17.7803

17.7782

17.7793

24.5913

24.5699

24.5250

Center (m)

$X$

0.0938

$-$0.1811

$-$0.1807

$-$0.1809

0.0672

0.0994

0.1208

$Y$

0.1383

$-$0.1121

$-$0.1140

$-$0.1132

0.1107

0.1657

0.1384

$Z$

0.1164

0.0085

0.0082

0.0083

0.0970

0.1159

0.1148

Inertia

(${\rm~kg}~\cdot~{{\rm~m}^2}$)

$I_{11}$

0.1706

3.3342

3.3206

3.3262

0.1287

0.1783

0.2189

$I_{12}$

$-$0.1498

0.5166

0.5146

0.5151

$-$0.2175

$-$0.1258

$-$0.1829

$I_{13}$

0.2140

0.6943

0.6915

0.6928

0.1790

0.1615

0.2486

$I_{22}$

0.3493

$-$3.5211

$-$3.5359

$-$3.5298

0.4161

0.2925

0.4160

$I_{23}$

$-$0.1320

$-$0.2403

$-$0.2808

$-$0.2641

$-$0.1994

$-$0.0933

$-$0.1646

$I_{33}$

0.2363

$-$0.3693

$-$0.3691

$-$0.3693

0.3062

0.3046

0.3063

Friction

$F_c$

50.0000

49.7802

49.8704

50.2227

50.2716

50.4040

$\beta$

40.0000

40.0250

40.0161

39.7539

39.6028

39.8216

Torque

error (Nm)

Mean

$-$0.0001

$-$0.0066

0.0323

0.2568

0.2725

0.0029

Std

0.0001

0.2903

0.2210

0.6332

0.8545

0.8825

Table 6 Nonlinear calibration result of joint 3

Parameter

Set

Extended

Kalman

Index

forgetting

Optimization

Gradient

descent

Genetic

algorithm

Particle

filter

Mass (kg)

$m$

25.6083

18.0803

18.0862

25.5425

29.5065

29.1977

Center (m)

$X$

0.0938

$-$0.1405

$-$0.1401

0.075

0.0964

0.1141

$Y$

0.1383

$-$0.0374

$-$0.0377

0.1107

0.1156

0.1526

$Z$

0.1164

0.0179

0.0175

0.0931

0.1143

0.1158

Inertia

(${\rm~kg}~\cdot~{{\rm~m}^2}$)

$I_{11}$

0.1706

3.9916

4.0685

0.2302

0.1447

0.2406

$I_{12}$

$-$0.1498

0.2146

0.2089

$-$0.0886

$-$0.2168

$-$0.097

$I_{13}$

0.214

0.5786

0.595

0.265

0.2368

0.1683

$I_{22}$

0.3493

$-$3.1141

$-$3.0855

0.4044

0.2933

0.2909

$I_{23}$

$-$0.132

$-$0.2575

$-$0.2548

$-$0.1994

$-$0.1421

$-$0.0809

$I_{33}$

0.2363

0.5709

0.5297

0.2828

0.302

0.2335

Friction

$F_c$

51.7727

52.183

50.625

49.9266

50.2767

$F_s$

52.1061

52.2013

59.8052

60.0016

$q_s$

0.1

5.5823

6.3761

0.08

0.1142

0.0996

$\beta$

38.2327

38.1439

39.8125

39.7704

Torque

error (Nm)

Mean

0.0355

0.0314

2.8462

$-$0.0209

0.0062

Std

1.9688

1.9705

1.2125

0.6137

0.2182

Table 7 The standard deviation of noise added to ${\boldsymbol~\tau}~_j$

Joint 1 Joint 2 Joint 3 Joint 4 Joint 5 Joint 6
Std (Nm) 10 10 10 1.78 1.78 1.78

Table 8 The comparison of $J_e$ with and without noise (linear methods)

Pseudo-

inverse

Kalman

Exponential

forgetting

Optimization

Gradient

descent

Genetic

algorithm

Particle

filter

Without

noise

$e_d$

279.8642

256.6049

255.1294

0.3839

0.8657

0.6336

$e_f$

0.0000

0.0135

0.0080

0.0032

0.0061

0.0185

$e_T$

0.0000

0.0001

0.0006

0.0001

$e_T\_{\rm~Std}$

0.0000

0.0007

0.0005

0.0006

0.0012

0.0010

$J_e$

279.8642

256.6191

255.1380

0.3879

0.8736

0.6532

With

noise

$e_d$

289.2396

261.2449

260.0939

0.9258

1.0587

0.9754

$e_f$

0.0585

0.0289

0.0314

0.1136

0.1147

0.1258

$e_T$

0.0016

0.0005

0.0013

0.0008

0.0010

$e_T\_{\rm~Std}$

0.0219

0.0203

0.0209

0.0204

$J_e$

289.3216

261.2945

260.1460

1.0610

1.1951

1.1225

Anti-interference

$\Delta~J_e$

0.0338

0.0182

0.0196

1.7352

0.3680

0.7184

Table 9 The comparison of $J_e$ with and without noise (nonlinear methods)

Extended

Kalman

Exponential

forgetting

Optimization

Gradient

descent

Genetic

algorithm

Particle

filter

Without

noise

$e_d$

71.7454

72.6643

0.2243

0.8152

0.7340

$e_f$

3.0663

3.4116

0.0681

0.0376

0.0182

$e_T$

0.0001

0.0014

0.0001

$e_T\_{\rm~Std}$

0.0061

0.0060

0.0019

0.0013

0.0007

$J_e$

74.8180

76.0820

0.2956

0.8541

0.7530

With

noise

$e_d$

74.0046

74.4194

0.8248

0.8351

0.8438

$e_f$

48.4565

54.6694

0.1287

0.1776

0.1493

$e_T$

0.0004

0.0005

0.0008

0.0006

$e_T\_{\rm~Std}$

0.0212

0.0211

0.0197

0.0207

0.0197

$J_e$

122.4827

129.1102

0.9737

1.0343

1.0135

Anti-interference

$\Delta~J_e$

0.6371

0.6970

2.2936

0.2110

0.3459

Table 10 The comparison between the IDIM-IV method and Pseudo-inverse method for model (7)

Pseudo-inverse IDIM-IV
$J_e$ (with filter) 411.5920 412.3433
$J_e$ (without filter) 1911.7927 446.4756
$\Delta~J_e$ 3.6449 0.0828

Table 11 The feature levels of different methods

Pseudo-

inverse

Kalman

Extended

Kalman

Exponential

forgetting

Optimization

Gradient

descent

Genetic

algorithm

Particle

filter

Error

$e_d$

$e_f$

$e_T$

$J_e$

(without noise)

Follow changing

parameter

Solution time

OfflineA

Online

OfflineB

OfflineC

OfflineB

Linear/

nonlinear

Linear

Nonlinear

Linear/

nonlinear

Linear/

nonlinear

Linear/

nonlinear

Linear/

nonlinear

Anti-interference

$\Delta~J_e$

Table 12 The experiment result of torque errors

Linear models Nonlinear models
Eq. (7) Eq. (8) Eq. (9) Eq. (4) Eq. (5) Eq. (6)
Mean (Nm) 0.4478 0.0469 0.4509 0.4085 2.7903 1.2232
Std (Nm) 44.7068 30.8389 44.417 19.1073 51.8087 25.5865

0

Citations
0

Altmetric
Article metrics

Email
Export

Parameter estimation survey for multi-joint robot dynamic calibration case study

Abstract

Acknowledgment

References

0

0

Interesting search

Top 5Related Articles

	Joint 1	Joint 2	Joint 3	Joint 4	Joint 5	Joint 6
Std (Nm)	10	10	10	1.78	1.78	1.78

	Pseudo-inverse	IDIM-IV
$J_e$ (with filter)	411.5920	412.3433
$J_e$ (without filter)	1911.7927	446.4756
$\Delta~J_e$	3.6449	0.0828

	Linear models			Nonlinear models
	Eq. (7)	Eq. (8)	Eq. (9)	Eq. (4)	Eq. (5)	Eq. (6)
Mean (Nm)	0.4478	0.0469	0.4509	0.4085	2.7903	1.2232
Std (Nm)	44.7068	30.8389	44.417	19.1073	51.8087	25.5865

	Level A	Level B	Level C
${e_{T}}$	textless0.01	textless0.1	textgreater0.1