1932

Abstract

This article reviews approaches to controlling robots undergoing physical contact and dynamic interaction with objects in the world. Conventional motion control is compared with a hybrid combination of position and force control. Several challenges are reviewed, most importantly the problems of instability: dynamic instability due to coupling, and static instability due to exerting force. Energetically passive interactive dynamics addresses the former; a minimum stiffness proportional to the force exerted addresses the latter. Actuators, which dominate the robot's interactive dynamics, are briefly surveyed, including series elastic, variable-stiffness, and emerging designs. A comparison with human performance is made. A bioinspired approach to controlling interactive dynamics (mechanical impedance or admittance) is reviewed. Robot configuration profoundly modulates apparent inertia, whereas force feedback control has minimal influence. Superimposing first-order mechanical impedances simplifies controlling many degrees of freedom. It manages redundancy while preserving passivity (unlike null-space projection methods) and enables seamless operation into and out of singular configurations.

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2022-05-03
2024-05-10
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Literature Cited

  1. 1. 
    Hogan N 2017. Physical interaction via dynamic primitives. Geometric and Numerical Foundations of Movements JP Laumond, JB Lassere, N Mansard 269–99 Cham, Switz: Springer
    [Google Scholar]
  2. 2. 
    Whitney DE. 1969. Resolved motion rate control of manipulators and human prostheses. IEEE Trans. Man-Mach. Syst. 10:47–53
    [Google Scholar]
  3. 3. 
    Whitney DE. 1972. The mathematics of coordinated control of prosthetic arms and manipulators. J. Dyn. Syst. Meas. Control 94:303–9
    [Google Scholar]
  4. 4. 
    Klein CA, Huang CH. 1983. Review of pseudoinverse control for use with kinematically redundant manipulators. IEEE Trans. Syst. Man Cybern. SMC-13 245–50
    [Google Scholar]
  5. 5. 
    Mussa-Ivaldi FA, Hogan N. 1991. Integrable solutions of kinematic redundancy via impedance control. Int. J. Robot. Res. 10:481–91
    [Google Scholar]
  6. 6. 
    Shamir T, Yomdin Y. 1988. Repeatability of redundant manipulators: mathematical solution of the problem. IEEE Trans. Autom. Control 33:1004–9
    [Google Scholar]
  7. 7. 
    De Luca A, Lanari L, Oriolo G 1992. Control of redundant robots on cyclic trajectories. Proceedings of the 1992 IEEE International Conference on Robotics and Automation 1500–6 Piscataway, NJ: IEEE
    [Google Scholar]
  8. 8. 
    Siciliano B. 1990. Kinematic control of redundant robot manipulators: a tutorial. J. Intell. Robot. Syst. 3:201–12
    [Google Scholar]
  9. 9. 
    Baillieul J. 1985. Kinematic programming alternatives for redundant manipulators. 1985 IEEE International Conference on Robotics and Automation722–28 Piscataway, NJ: IEEE
    [Google Scholar]
  10. 10. 
    Faverjon B, Tournassoud P. 1987. A local based approach for path planning of manipulators with a high number of degrees of freedom. Proceedings of the 1987 IEEE International Conference on Robotics and Automation1152–59 Piscataway, NJ: IEEE
    [Google Scholar]
  11. 11. 
    Nakamura Y, Hanafusa H, Yoshikawa T. 1987. Task-priority based redundancy control of robot manipulators. Int. J. Robot. Res. 6:3–15
    [Google Scholar]
  12. 12. 
    Yoshikawa T. 1985. Manipulability of robotic mechanisms. Int. J. Robot. Res. 4:439–46
    [Google Scholar]
  13. 13. 
    Lachner J, Schettino V, Allmendinger F, Fiore MD, Ficuciello F et al. 2020. The influence of coordinates in robotic manipulability analysis. Mech. Mach. Theory 146:103722
    [Google Scholar]
  14. 14. 
    Khatib O. 1987. A unified approach for motion and force control of robot manipulators: the operational space formulation. IEEE J. Robot. Autom. 3:43–53
    [Google Scholar]
  15. 15. 
    Verdi D. 2017. A compositional approach to robotic impedance control MS Thesis, Mass. Inst. Technol Cambridge, MA:
  16. 16. 
    Raibert MH, Craig JJ. 1981. Hybrid position/force control of manipulators. J. Dyn. Syst. Meas. Control 102:126–33
    [Google Scholar]
  17. 17. 
    Mason MT. 1981. Compliance and force control for computer controlled manipulators. IEEE Trans. Syst. Man Cybern. 11:418–32
    [Google Scholar]
  18. 18. 
    Ortenzi V, Stolkin R, Kuo J, Mistry M. 2017. Hybrid motion/force control: a review. Adv. Robot. 31:1102–13
    [Google Scholar]
  19. 19. 
    Stewart DE. 2011. Dynamics with Inequalities Philadelphia: Soc. Ind. Appl. Math.
  20. 20. 
    Escande A, Mansard N, Wieber PB. 2014. Hierarchical quadratic programming: fast online humanoid-robot motion generation. Int. J. Robot. Res. 33:1006–28
    [Google Scholar]
  21. 21. 
    Posa M, Cantu C, Tedrake R. 2014. A direct method for trajectory optimization of rigid bodies through contact. Int. J. Robot. Res. 33:69–81
    [Google Scholar]
  22. 22. 
    Kanoun O, Lamiraux F, Wieber PB. 2011. Kinematic control of redundant manipulators: generalizing the task-priority framework to inequality task. IEEE Trans. Robot. 27:785–92
    [Google Scholar]
  23. 23. 
    Lynch KM, Park FC. 2019. Modern Robotics: Mechanics, Planning, and Control Cambridge, UK: Cambridge Univ. Press
  24. 24. 
    Duffy J. 1990. The fallacy of modern hybrid control theory that is based on “orthogonal complements” of twist and wrench spaces. J. Robot. Syst. 7:139–44
    [Google Scholar]
  25. 25. 
    Whitney DE. 1977. Force feedback control of manipulator fine motions. J. Dyn. Syst. Meas. Control 99:91–97
    [Google Scholar]
  26. 26. 
    Paul R. 1987. Problems and research issues associated with the hybrid control of force and displacement. Proceedings of the 1987 IEEE International Conference on Robotics and Automation1966–71 Piscataway, NJ: IEEE
    [Google Scholar]
  27. 27. 
    Colgate JE, Hogan N. 1988. Robust control of dynamically interacting systems. Int. J. Control 48:65–88
    [Google Scholar]
  28. 28. 
    Rancourt D, Hogan N. 2001. Stability in force-production tasks. J. Mot. Behav. 33:193–204
    [Google Scholar]
  29. 29. 
    Hosford LA. 2016. Development and testing of an impedance controller on an anthropomorphic robot for extreme environment operations MS Thesis, Mass. Inst. Technol Cambridge, MA:
  30. 30. 
    Colgate E. 1989. On the intrinsic limitations of force feedback compliance controllers. Robotics Research—1989 K Youcef-Toumi, H Kazerooni 23–30 New York: Am. Soc. Mech. Eng.
    [Google Scholar]
  31. 31. 
    Lawrence DA. 1989. Actuator limitations on achievable manipulator impedance. Proceedings of the 1989 International Conference on Robotics and Automation 1560–65 Piscataway, NJ: IEEE
    [Google Scholar]
  32. 32. 
    Pratt GA, Williamson MM. 1995. Series elastic actuators. Proceedings of the 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems: Human Robot Interaction and Cooperative Robots 1399–406 Piscataway, NJ: IEEE
    [Google Scholar]
  33. 33. 
    Williamson MM. 1995. Series elastic actuators MS Thesis, Mass. Inst. Technol Cambridge, MA:
  34. 34. 
    Paine N, Oh S, Sentis L 2014. Design and control considerations for high-performance series elastic actuators. IEEE/ASME Trans. Mechatron. 19:1080–91
    [Google Scholar]
  35. 35. 
    Vallery H, Veneman J, van Asseldonk E, Ekkelenkamp R, Buss M, van Der Kooij H. 2008. Compliant actuation of rehabilitation robots. IEEE Robot. Autom. Mag. 15:360–69
    [Google Scholar]
  36. 36. 
    Buerger SP, Hogan N. 2007. Complementary stability and loop shaping for improved human-robot interaction. IEEE Trans. Robot. 23:232–44
    [Google Scholar]
  37. 37. 
    Sergi F, O'Malley MK. 2015. On the stability and accuracy of high stiffness rendering in non-backdrivable actuators through series elasticity. Mechatronics 26:64–75
    [Google Scholar]
  38. 38. 
    Seok S, Wang A, Chuah MY, Hyun DJ, Lee J et al. 2015. Design principles for energy-efficient legged locomotion and implementation on the MIT Cheetah robot. IEEE/ASME Trans. Mechatron. 20:1117–29
    [Google Scholar]
  39. 39. 
    Lawrence DA. 1988. Impedance control stability properties in common implementations. Proceedings of the 1988 IEEE International Conference on Robotics and Automation 21185–90 Piscataway, NJ: IEEE
    [Google Scholar]
  40. 40. 
    Asada H, Youcef-Toumi K. 1984. Analysis and design of a direct-drive arm with a five-bar-link parallel drive mechanism. J. Dyn. Syst. Meas. Control 106:225–30
    [Google Scholar]
  41. 41. 
    Hogan N, Krebs HI, Charnnarong J, Srikrishna P, Sharon A. 1992. MIT-MANUS: a workstation for manual therapy and training. I. Proceedings of the 1992 IEEE International Workshop on Robot and Human Communication161–65 Piscataway, NJ: IEEE
    [Google Scholar]
  42. 42. 
    Wensing PM, Wang A, Seok S, Otten D, Lang J, Kim S 2017. Proprioceptive actuator design in the MIT Cheetah: impact mitigation and high-bandwidth physical interaction for dynamic legged robots. IEEE Trans. Robot. 33:509–22
    [Google Scholar]
  43. 43. 
    Vanderborght B, Albu-Schäffer A, Bicchi A, Burdet E, Caldwell DG et al. 2013. Variable impedance actuators: a review. Robot. Auton. Syst. 61:1601–14
    [Google Scholar]
  44. 44. 
    Grioli G, Wolf S, Garabini M, Catalano M, Burdet E et al. 2015. Variable stiffness actuators: the user's point of view. Int. J. Robot. Res. 34:727–43
    [Google Scholar]
  45. 45. 
    Wolf S, Grioli G, Eiberger O, Friedl W, Grebenstein M et al. 2016. Variable stiffness actuators: review on design and components. IEEE/ASME Trans. Mechatron. 21:2418–30
    [Google Scholar]
  46. 46. 
    Braun D, Howard M, Vijayakumar S 2012. Optimal variable stiffness control: formulation and application to explosive movement tasks. Auton. Robots 33:237–53
    [Google Scholar]
  47. 47. 
    Braun DJ, Petit F, Huber F, Haddadin S, Van Der Smagt P et al. 2013. Robots driven by compliant actuators: optimal control under actuation constraints. IEEE Trans. Robot. 29:1085–1101
    [Google Scholar]
  48. 48. 
    Sutrisno A, Braun DJ. 2020. How to run 50% faster without external energy. Sci. Adv. 6:eaay1950
    [Google Scholar]
  49. 49. 
    Cobb M. 2002. Exorcizing the animal spirits: Jan Swammerdam on nerve function. Nat. Rev. Neurosci 3:395–400
    [Google Scholar]
  50. 50. 
    English C, Russell D. 1999. Implementation of variable joint stiffness through antagonistic actuation using rolamite springs. Mech. Mach. Theory 34:27–40
    [Google Scholar]
  51. 51. 
    English CE, Russell D. 1999. Mechanics and stiffness limitations of a variable stiffness actuator for use in prosthetic limbs. Mech. Mach. Theory 34:7–25
    [Google Scholar]
  52. 52. 
    Daerden F, Lefeber D. 2002. Pneumatic artificial muscles: actuators for robotics and automation. Eur. J. Mech. Environ. Eng. 47:11–21
    [Google Scholar]
  53. 53. 
    Mengacci R, Garabini M, Grioli G, Catalano M, Bicchi A. 2021. Overcoming the torque/stiffness range tradeoff in antagonistic variable stiffness actuators. IEEE/ASME Trans. Mechatron. 26:3186–97
    [Google Scholar]
  54. 54. 
    Groothuis SS, Rusticelli G, Zucchelli A, Stramigioli S, Carloni R. 2014. The variable stiffness actuator vsaUT-II: mechanical design, modeling, and identification. IEEE/ASME Trans. Mechatron. 19:589–97
    [Google Scholar]
  55. 55. 
    Barrett E, Fumagalli M, Carloni R. 2016. Elastic energy storage in leaf springs for a lever-arm based variable stiffness actuator. 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems537–42 Piscataway, NJ: IEEE
    [Google Scholar]
  56. 56. 
    Jafari A, Tsagarakis NG, Caldwell DG. 2013. A novel intrinsically energy efficient actuator with adjustable stiffness (AwAS). IEEE/ASME Trans. Mechatron. 18:355–65
    [Google Scholar]
  57. 57. 
    Visser LC, Carloni R, Stramigioli S 2011. Energy-efficient variable stiffness actuators. IEEE Trans. Robot. 27:865–75
    [Google Scholar]
  58. 58. 
    Morita T, Sugano S. 1995. Development of one-DOF robot arm equipped with mechanical impedance adjuster. Proceedings of the 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems: Human Robot Interaction and Cooperative Robots 1407–12 Piscataway, NJ: IEEE
    [Google Scholar]
  59. 59. 
    Morita T, Sugano S. 1996. Development of 4-DOF manipulator using mechanical impedance adjuster. Proceedings of the IEEE International Conference on Robotics and Automation 42902–7 Piscataway, NJ: IEEE
    [Google Scholar]
  60. 60. 
    Braun DJ, Chalvet V, Chong TH, Apte SS, Hogan N 2019. Variable stiffness spring actuators for low-energy-cost human augmentation. IEEE Trans. Robot. 35:1435–49
    [Google Scholar]
  61. 61. 
    Rus D, Tolley MT. 2015. Design, fabrication and control of soft robots. Nature 521:467–75
    [Google Scholar]
  62. 62. 
    Cianchetti M, Laschi C, Menciassi A, Dario P 2018. Biomedical applications of soft robotics. Nat. Rev. Mater. 3:143–53
    [Google Scholar]
  63. 63. 
    Carpi F, De Rossi D, Kornbluh R, Pelrine R, Sommer-Larsen P. 2008. Dielectric Elastomers as Electromechanical Transducers Oxford, UK: Elsevier
  64. 64. 
    Baughman RH, Cui C, Zakhidov AA, Iqbal Z, Barisci JN et al. 1999. Carbon nanotube actuators. Science 284:1340–44
    [Google Scholar]
  65. 65. 
    Bar-Cohen Y 2004. Electroactive Polymer (EAP) Actuators as Artificial Muscles: Reality, Potential, and Challenges Bellingham, WA: SPIE, 2nd ed..
  66. 66. 
    Mather PT, Luo X, Rousseau IA. 2009. Shape memory polymer research. Annu. Rev. Mater. Res. 39:445–71
    [Google Scholar]
  67. 67. 
    Tolley MT, Shepherd RF, Karpelson M, Bartlett NW, Galloway KC et al. 2014. An untethered jumping soft robot. 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems561–66 Piscataway, NJ: IEEE
    [Google Scholar]
  68. 68. 
    Camp T, Figliola R. 2011. Fluid mechanics. Mechanobiology Handbook J Nagatomi 23–44 Boca Raton, FL: CRC
    [Google Scholar]
  69. 69. 
    White FM. 2011. Fluid Mechanics New York: McGraw-Hill, 7th ed..
  70. 70. 
    Shepard RN, Metzler J. 2013. Mental rotation of three-dimensional objects. Readings in Cognitive Science: A Perspective from Psychology and Artificial Intelligence A Collins, EE Smith 598–99 San Mateo, CA: Morgan Kaufmann
    [Google Scholar]
  71. 71. 
    Lee H, Krebs HI, Hogan N. 2014. Multivariable dynamic ankle mechanical impedance with active muscles. IEEE Trans. Neural Syst. Rehabil. Eng. 22:971–81
    [Google Scholar]
  72. 72. 
    Lee H, Krebs HI, Hogan N. 2014. Multivariable dynamic ankle mechanical impedance with relaxed muscles. IEEE Trans. Neural Syst. Rehabil. Eng. 22:1104–14
    [Google Scholar]
  73. 73. 
    Lee H, Hogan N 2015. Time-varying ankle mechanical impedance during human locomotion. IEEE Trans. Neural Syst. Rehabil. Eng. 23:755–64
    [Google Scholar]
  74. 74. 
    Rouse EJ, Hargrove LJ, Perreault EJ, Kuiken TA. 2014. Estimation of human ankle impedance during the stance phase of walking. IEEE Trans. Neural Syst. Rehabil. Eng. 22:870–78
    [Google Scholar]
  75. 75. 
    Lipps DB, Baillargeon EM, Ludvig D, Perreault EJ 2020. Quantifying the multidimensional impedance of the shoulder during volitional contractions. Ann. Biomed. Eng. 48:2354–69
    [Google Scholar]
  76. 76. 
    Tsuji T, Morasso PG, Goto K, Ito K 1995. Human hand impedance characteristics during maintained posture. Biol. Cybern. 72:475–85
    [Google Scholar]
  77. 77. 
    Dolan JM, Friedman MB, Nagurka ML. 1993. Dynamic and loaded impedance components in the maintenance of human arm posture. IEEE Trans. Syst. Man Cybern. 23:698–709
    [Google Scholar]
  78. 78. 
    Burdet E, Osu R, Franklin DW, Yoshioka T, Milner TE, Kawato M. 2000. A method for measuring endpoint stiffness during multi-joint arm movements. J. Biomech. 33:1705–9
    [Google Scholar]
  79. 79. 
    Lacquaniti F, Carrozzo M, Borghese NA 1993. Time-varying mechanical behavior of multijointed arm in man. J. Neurophysiol. 69:1443–64
    [Google Scholar]
  80. 80. 
    Bennett DJ, Hollerbach JM, Xu Y, Hunter IW. 1992. Time-varying stiffness of human elbow joint during cyclic voluntary movement. Exp. Brain Res. 88:433–42
    [Google Scholar]
  81. 81. 
    Lee H, Hogan N 2016. Energetic passivity of the human ankle joint. IEEE Trans. Neural Syst. Rehabil. Eng. 24:1416–25
    [Google Scholar]
  82. 82. 
    Shahbazi M, Atashzar SF, Tavakoli M, Patel RV. 2018. Position-force domain passivity of the human arm in telerobotic systems. IEEE/ASME Trans. Mechatron. 23:552–62
    [Google Scholar]
  83. 83. 
    Rancourt D, Hogan N 2009. The biomechanics of force production. Progress in Motor Control: A Multidisciplinary Perspective D Sternad 645–61 Boston: Springer
    [Google Scholar]
  84. 84. 
    Powers JD, Malingen SA, Regnier M, Daniel TL. 2021. The sliding filament theory since Andrew Huxley: multiscale and multidisciplinary muscle research. Annu. Rev. Biophys. 50:373–400
    [Google Scholar]
  85. 85. 
    Nishikawa KC, Monroy JA, Uyeno TE, Yeo SH, Pai DK, Lindstedt SL. 2012. Is titin a “winding filament”? A new twist on muscle contraction. Proc. R. Soc. B 279:981–90
    [Google Scholar]
  86. 86. 
    Kandel ER, Schwartz JH, Jessell TM, Siegelbaum SA, Hudspeth AJ. 2013. Principles of Neural Science New York: McGraw-Hill Med, 5th ed..
  87. 87. 
    Burdet E, Franklin DW, Milner TE 2019. Human Robotics: Neuromechanics and Motor Control. Cambridge, MA: MIT Press
  88. 88. 
    Berardelli A, Hallett M, Rothwell JC, Agostino R, Manfredi M et al. 1996. Single-joint rapid arm movements in normal subjects and in patients with motor disorders. Brain 119:661–74
    [Google Scholar]
  89. 89. 
    Lewis GN, Perreault EJ, MacKinnon CD. 2005. The influence of perturbation duration and velocity on the long-latency response to stretch in the biceps muscle. Exp. Brain Res. 163:361–69
    [Google Scholar]
  90. 90. 
    Lewis GN, MacKinnon CD, Trumbower R, Perreault EJ. 2010. Co-contraction modifies the stretch reflex elicited in muscles shortened by a joint perturbation. Exp. Brain Res. 207:39–48
    [Google Scholar]
  91. 91. 
    Hu X, Ludvig D, Murray WM, Perreault EJ 2017. Using feedback control to reduce limb impedance during forceful contractions. Sci. Rep. 7:9317
    [Google Scholar]
  92. 92. 
    Kurtzer I, Crevecoeur F, Scott SH 2014. Fast feedback control involves two independent processes utilizing knowledge of limb dynamics. J. Neurophysiol. 111:1631–45
    [Google Scholar]
  93. 93. 
    Burdet E, Osu R, Franklin DW, Milner TE, Kawato M. 2001. The central nervous system stabilizes unstable dynamics by learning optimal impedance. Nature 414:446–49
    [Google Scholar]
  94. 94. 
    Franklin DW, Liaw G, Milner TE, Osu R, Burdet E, Kawato M 2007. Endpoint stiffness of the arm is directionally tuned to instability in the environment. J. Neurosci. 27:7705–16
    [Google Scholar]
  95. 95. 
    Lacquaniti F, Borghese NA, Carrozzo M. 1991. Transient reversal of the stretch reflex in human arm muscles. J. Neurophysiol. 66:939–54
    [Google Scholar]
  96. 96. 
    Perreault EJ, Kirsch RF, Crago PE. 2001. Effects of voluntary force generation on the elastic components of endpoint stiffness. Exp. Brain Res. 141:312–23
    [Google Scholar]
  97. 97. 
    Hu X, Murray WM, Perreault EJ. 2011. Muscle short-range stiffness can be used to estimate the endpoint stiffness of the human arm. J. Neurophysiol. 105:1633–41
    [Google Scholar]
  98. 98. 
    Hogan N. 1987. Modularity and causality in physical system modeling. J. Dyn. Syst. Meas. Control 109:384–91
    [Google Scholar]
  99. 99. 
    Anderson RJ, Spong MW 1989. Bilateral control of teleoperators with time delay. IEEE Trans. Autom. Control 34:494–501
    [Google Scholar]
  100. 100. 
    Niemeyer G, Slotine JJE. 1991. Stable adaptive teleoperation. IEEE J. Ocean. Eng. 16:152–62
    [Google Scholar]
  101. 101. 
    Niemeyer G, Slotine JJE. 2004. Telemanipulation with time delays. Int. J. Robot. Res. 23:873–90
    [Google Scholar]
  102. 102. 
    Colgate JE. 1993. Robust impedance shaping telemanipulation. IEEE Trans. Robot. Autom. 9:374–84
    [Google Scholar]
  103. 103. 
    Spong MW. 2022. An historical perspective on the control of robotic manipulators. Annu. Rev. Control Robot. Auton. Syst. 5:1–31
    [Google Scholar]
  104. 104. 
    Newman WS, Zhang Y. 1994. Stable interaction control and coulomb friction compensation using natural admittance control. J. Robot. Syst. 11:3–11
    [Google Scholar]
  105. 105. 
    Albu-Schäffer A, Ott C, Frese U, Hirzinger G 2003. Cartesian impedance control of redundant robots: recent results with the DLR-light-weight-arms. 2003 IEEE International Conference on Robotics and Automation 33704–9 Piscataway, NJ: IEEE
    [Google Scholar]
  106. 106. 
    Ott C, Mukherjee R, Nakamura Y. 2010. Unified impedance and admittance control. 2010 IEEE International Conference on Robotics and Automation554–61 Piscataway, NJ: IEEE
    [Google Scholar]
  107. 107. 
    Hogan N. 1985. Impedance control: an approach to manipulation: part I—theory. J. Dyn. Syst. Meas. Control 107:1–7
    [Google Scholar]
  108. 108. 
    Hogan N. 1985. Impedance control: an approach to manipulation: part III—applications. J. Dyn. Syst. Meas. Control 107:17–24
    [Google Scholar]
  109. 109. 
    Hermus J, Lachner J, Verdi D, Hogan N. 2022. Exploiting redundancy to facilitate physical interaction. IEEE Trans. Robot. 38:599–615
    [Google Scholar]
  110. 110. 
    Slotine J-JE, Li W 1991. Applied Nonlinear Control Englewood Cliffs, NJ: Prentice Hall
  111. 111. 
    Khalil HK. 2002. Nonlinear Systems Englewood Cliffs, NJ: Prentice Hall, 3rd ed..
  112. 112. 
    Wyatt JL Jr., Chua LO, Gannett JW, Goknar IC, Green DN 1981. Energy concepts in the state-space theory of nonlinear n-ports: part I—passivity. IEEE Trans. Circuits Syst CAS-28:48–61
    [Google Scholar]
  113. 113. 
    van der Schaft A. 2020. Port-Hamiltonian modeling for control. Annu. Rev. Control Robot. Auton. Syst. 3:393–416
    [Google Scholar]
  114. 114. 
    Virga EG. 2015. Rayleigh-Lagrange formalism for classical dissipative systems. Phys. Rev. E 91:013203
    [Google Scholar]
  115. 115. 
    Hogan N. 1988. On the stability of manipulators performing contact tasks. IEEE J. Robot. Autom. 4:677–86
    [Google Scholar]
  116. 116. 
    Bellman RE. 1957. Dynamic Programming Princeton, NJ: Princeton Univ. Press
  117. 117. 
    Dietrich A, Ott C, Albu-Schäffer A. 2015. An overview of null space projections for redundant, torque-controlled robots. Int. J. Robot. Res. 34:1385–400
    [Google Scholar]
  118. 118. 
    Dietrich A, Ott C, Stramigioli S. 2016. Passivation of projection-based null space compliance control via energy tanks. IEEE Robot. Autom. Lett. 1:184–91
    [Google Scholar]
  119. 119. 
    Hogan N. 2014. A general actuator model based on nonlinear equivalent networks. IEEE/ASME Trans. Mechatron. 19:1929–39
    [Google Scholar]
  120. 120. 
    Koditschek DE. 2021. What is robotics? Why do we need it and how can we get it?. Annu. Rev. Control Robot. Auton. Syst. 4:1–33
    [Google Scholar]
  121. 121. 
    Lachner J, Allmendinger F, Hobert E, Hogan N, Stramigioli S 2021. Energy budgets for coordinate invariant robot control in physical human–robot interaction. Int. J. Robot. Res. 40:968–85
    [Google Scholar]
  122. 122. 
    Crandall SH, Karnopp DC, Kurtz EF, Pridmore-Brown DC. 1982. Dynamics of Mechanical and Electronical Systems New York: McGraw-Hill
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