Stiffness control of a legged robot equipped with a serial manipulator in stance phase

Document Type : Research Paper

Authors

1 Center for Mechatronics and Intelligent Machines, School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

2 School of Mechanical Engineering, College of Engineering, University of Tehran Tehran, Iran

Abstract

The ability to perform different tasks by a serial manipulator mounted on legged robots, increases the capabilities of the robot. The position/force control problem of such a robot in the stance phase with point contacts on the ground is investigated here. A target plane with known stiffness is specified in the workspace. Active joints of the legs and serial manipulator are used to exert the desired normal force on the plane while tracking a desired trajectory on the plane. First, the equations of motion of the robot and contact forces of the feet on the ground are derived. A controller is then proposed which tracks the desired trajectory while keeping the feet contacts on the ground and prevent slipping. An optimization problem is solved in each control loop to minimize the actuation effort. This minimization is subject to position tracking for the end-effector (using inverse dynamics controller), force requirements of the feet contacts with the ground, and actuators capabilities. Simulations are conducted for the simplified model of a quadruped robot with a 2-DOF serial manipulator. To test the controller, a 20 N normal force is applied onto the target plane while moving the tip of the end-effector. It is shown that the robot can perform the task effectively without losing the ground contact and slipping.

Keywords

Main Subjects

[1]         J. Salisbury, “Active stiffness control of a manipulator in cartesian coordinates,” in Proc. IEEE Conf. on Decision and Control (CDC), 1980, vol. 19, pp. 95–100.
[2]         F. L. Lewis, D. M. Dawson, and C. T. Abdallah, Robot Manipulator Control: Theory and Practice. Taylor & Francis, 2003.
[3]         M. H. Raibert and J. J. Craig, “Hybrid Position/Force Control of Manipulators,” J. Dyn. Syst. Meas. Control, vol. 103, no. 2, p. 126, 1981.
[4]         T. Yoshikawa, “Dynamic hybrid position/force control of robot manipulators--Description of hand constraints and calculation of joint driving force,” IEEE Journal on Robotics and Automation, vol. 3, no. 5. pp. 386–392, 1987.
[5]         Q. Huang and R. Enomoto, “Hybrid position, posture, force and moment control of robot manipulators,” 2008 IEEE Int. Conf. Robot. Biomimetics, ROBIO 2008, no. 1, pp. 1444–1450, 2008.
[6]         A. C. Leite, F. Lizarralde, and Liu Hsu, “A cascaded-based hybrid position-force control for robot manipulators with nonnegligible dynamics,” Proc. 2010 Am. Control Conf., pp. 5260–5265, 2010.
[7]         M. H. Raibert, Legged Robots that Balance. MIT Press, 1986.
[8]         M. Mistry, J. Buchli, and S. Schaal, “Inverse dynamics control of floating base systems using orthogonal decomposition,” 2010 IEEE Int. Conf. Robot. Autom., no. 3, pp. 3406–3412, 2010.
[9]         L. Righetti, J. Buchli, M. Mistry, M. Kalakrishnan, and S. Schaal, “Optimal distribution of contact forces with inverse-dynamics control,” Int. J. Rob. Res., vol. 32, no. 3, pp. 280–298, 2013.
[10]       L. Righetti, M. Mistry,  j. Buchli, and S. Schaal, “Inverse Dynamics Control of Floating-Base Robots With External Contraints: an Unified View,” 2011 Ieee Int. Conf. Robot. Autom., pp. 1085–1090, 2011.
[11]       Z. Li, S. S. Ge, and S. Liu, “Contact-force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks,” IEEE Trans. Neural Networks Learn. Syst., vol. 25, no. 8, pp. 1460–1473, 2014.
[12]       F. T. Cheng and D. E. Orin, “Optimal Force Distribution in Multiple-Chain Robotic Systems,” IEEE Trans. Syst. Man Cybern., vol. 21, no. 1, pp. 13–24, 1991.
[13]       H. Takemura, M. Deguchi, J. Ueda, Y. Matsumoto, and T. Ogasawara, “Slip-adaptive walk of quadruped robot,” Rob. Auton. Syst., vol. 53, no. 2, pp. 124–141, 2005.
[14]       B. U. Rehman, M. Focchi, J. Lee, H. Dallali, D. G. Caldwell, and C. Semini, “Towards a multi-legged mobile manipulator,” Proc. - IEEE Int. Conf. Robot. Autom., vol. 2016–June, pp. 3618–3624, 2016.
[15]       L. Righetti, M. Kalakrishnan, P. Pastor, J. Binney, J. Kelly, R. C. Voorhies, G. S. Sukhatme, and S. Schaal, “An autonomous manipulation system based on force control and optimization,” Auton. Robots, vol. 36, no. 1–2, pp. 11–30, 2014.
[16]       H. Hemami and F. C. Weimer, “Modeling of Nonholonomic Dynamic Systems With Applications,” J. Appl. Mech., vol. 48, no. 1, pp. 177–182, Mar. 1981.
[17]       R. P. Singh, “Singular Value Decomposition for Constrained Dynamical Systems,” J. Appl. Mech., vol. 52, no. 4, p. 943, 1985.
[18]       S. S. Kim and M. J. Vanderploeg, “QR Decomposition for State Space Representation of Constrained Mechanical Dynamic Systems,” J. Mech. Transm. Autom. Des., vol. 108, no. 2, pp. 183–188, Jun. 1986.
[19]       P. V Nagy, S. Desa, and W. L. Whittaker, “Energy-based stability measures for reliable locomotion of statically stable walkers: Theory and application,” Int. J. Rob. Res., vol. 13, no. 3, pp. 272–287, 1994.
[20]       S. Hirose, H. Tsukagoshi, and K. Yoneda, “Normalized energy stability margin and its contour of walking vehicles on rough terrain,” in Robotics and Automation, 2001. Proceedings 2001 ICRA. IEEE International Conference on, 2001, vol. 1, pp. 181–186.
[21]       S. Zhang, J. Gao, X. Duan, H. Li, Z. Yu, X. Chen, J. Li, H. Liu, X. Li, Y. Liu, and Z. Xu, “Trot pattern generation for quadruped robot based on the ZMP stability margin,” 2013 ICME Int. Conf. Complex Med. Eng. C. 2013, pp. 608–613, 2013.
[22]       B.-S. Lin and S.-M. Song, “Dynamic modeling, stability and energy efficiency of a quadruped walking machine,” IEEE Int. Conf. Robot. Autom., pp. 367–373, 1993.
[23]       K. Yoneda and S. Hirose, “Tumble stability criterion of integrated locomotion and manipulation,” in Intelligent Robots and Systems ’96, IROS 96, Proceedings of the 1996 IEEE/RSJ International Conference on, 1996, vol. 2, pp. 870–876 vol.2.
[24]       E. Garcia and P. G. de Santos, “An improved energy stability margin for walking machines subject to dynamic effects,” Robotica, vol. 23, no. 1, pp. 13–20, 2005.
[25]       D. Zhou, K. H. Low, and T. Zielinska, “A stability analysis of walking robots based on leg-end supporting moments,” in Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065), 2000, vol. 3, pp. 2834–2839 vol.3.
[26]       J. Barraquand, B. Langlois, and J.-C. Latombe, “Numerical potential field techniques for robot path planning,” IEEE Trans. Syst. Man. Cybern., vol. 22, no. 2, pp. 224–241, 1992.
[27]       O. Montiel, U. Orozco-Rosas, and R. Sepúlveda, “Path planning for mobile robots using Bacterial Potential Field for avoiding static and dynamic obstacles,” Expert Syst. Appl., vol. 42, no. 12, pp. 5177–5191, 2015.
[28]       J. Schulman, J. Ho, A. X. Lee, I. Awwal, H. Bradlow, and P. Abbeel, “Finding Locally Optimal, Collision-Free Trajectories with Sequential Convex Optimization.,” in Robotics: science and systems, 2013, vol. 9, no. 1, pp. 1–10.
Volume 48, Issue 1
June 2017
Pages 27-38
  • Receive Date: 06 May 2017
  • Revise Date: 27 June 2017
  • Accept Date: 28 June 2017