Abstract
This paper develops a strategy for collision avoidance among a system of robotic manipulators by using joint feedback controllers in the joint space, which have a closed form. The joint positions are directly used in computing the joint torques, without any additional intermediate steps for computing shortest distances or gradients of shortest distances between the links. Furthermore the collision avoidance controller can be augmented to any stable controller with different objectives, such as position tracking, velocity consensus etc. We consider set point stabilization as a control objective in this paper, and a Lyapunov based analysis is used to show convergence of the joints to their desired positions while guaranteeing collision avoidance among the links of the manipulators and avoiding deadlocks (unwanted local minima). The proposed control methodology is illustrated using some simulation and experimental results.
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References
Barmish, B.R., WE, S., Leitmann, G.: A note on avoidance control. J. Dyn. Syst. Measur. Control 103(1), 69–70 (1981)
Brock, O., Khatib, O.: Mobile manipulation: Collision-free path modification and motion coordination. In: Proceedings of the Second International Conference on Computational Engineering in Systems Applications, vol. 4, pp. 839–845. Hammamet, Tunisia (1998)
Brock, O., Khatib, O.: Real-time obstacle avoidance and motion coordination in a multi-robot workcell. In: ISATP, pp. 274–279, Porto (1999)
Corless, M., Leitmann, G., Skowronski, J.M.: Adaptive control for avoidance or evasion in an uncertain environment. Comput. Math. Appl. 13, 1–11 (1987)
Dimarogonas, D.V., Kyriakopoulos, K.J.: Decentralized navigation functions for multiple robotic agents with limited sensing capabilities. J. Intell. Robot. Syst. 48(3), 411–433 (2007)
Glass, K., Colbaugh, R., Lim, D., Seraji, H.: Real-time collision avoidance for redundant manipulators. IEEE Trans. Robot. Autom. 11(3), 448–457 (1995)
Hokayem, P.F., Stipanovic, D.M., Spong, M.W.: Coordination and collision avoidance for lagrangian systems with disturbances. Appl. Math. Comput. 217(3), 1085–1094 (2010)
Hwang, Y., Ahuja, N.: A potential field approach to path planning. IEEE Trans. Robot. Autom. 8(1), 23–32 (1992)
Hwang, Y.K., Ahuja, N.: Gross motion planning-a survey. ACM Comput. Surv. 24(3), 219–291 (1992)
Khalil, H.: Nonlinear systems. Pearson Education. Prentice Hall. ISBN 9780130673893, London (2002)
Khansari-Zadeh, S.M., Khatib, O.: Learning potential functions from human demonstrations with encapsulated dynamic and compliant behaviors. Autonomous Robots 41, 45–69 (2017). https://doi.org/10.1007/s10514-015-9528-y
Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. Int. J. Robot. Res. 5(1), 90–98 (1986)
Khosla, P., Volpe, R.: Superquadric artificial potentials for obstacle avoidance and approach. In: Proceedings 1988 IEEE International Conference on Robotics and Automation, vol. 3, pp. 1778–1784 (1988). https://doi.org/10.1109/ROBOT.1988.12323
Jo, K., Khosla, P.K.: Real-time obstacle avoidance using harmonic potential functions. IEEE Trans. Robot. Autom. 8(3), 338–349 (1992)
King, H., Kosari, S.N., Hannaford, B.: Kinematic analysis of the raven-ii research surgical robot, s.l.: University of washington electrical engineering. Technical report (2016)
Leitmann, G.: Guaranteed avoidance feedback control. J. Optim. Theory Appl. 25(4), 850–851 (1980)
Leitmann, G.: Guaranteed avoidance strategies. J. Optim. Theory Appl. 32(4), 569–576 (1980)
Leitmann, G., Skowronski, J.: Avoidance control. J. Optim. Theory 23, 581–591 (1977)
Leitmann, G., Skowronski, J.: Avoidance control. J. Optim. Theory Appl. 23(4), 581–591 (1980)
Leitmann, G., Skowronski, J.: A note on avoidance control. Opt. Control Appl. Methods 4(4), 335–342 (1983)
Li, X., Deka, S.A., Kesavadas, T.: Interactive path planning for a telerobotic surgery training simulator platform. Submitted (2016)
Lin, C.C., Chuang, J.H.: Potential-based path planning for robot manipulators in 3-d workspace. In: 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422), vol. 3, pp. 3353–3358 (2003)
Lum, M.J.H., Friedman, D.C.W., Sankaranarayanan, G., King, H., Fodero, K., Leuschke, R., Hannaford, B., Rosen, J., Sinanan, M.N.: The raven: Design and validation of a telesurgery system. Int. J. Robot. Res. 28(9), 1183–1197 (2009). https://doi.org/10.1177/0278364909101795
Maciejewski, A.A., Klein, C.A.: Obstacle avoidance for kinematically redundant manipulators in dynamically varying environments. Int. J. Robot. Res. 4(3), 109–117 (1985)
Mastellone, S., Stipanovic, D.M., Graunke, C., Intlekofer, K.A., Spong, M.W.: Formation control and collision avoidance for multi-agent non-holonomic systems: theory and experiments. Int. J. Robot. Res. 27(1), 107–126 (2008)
Munasinghe, S.R., Oh, C., Lee, J.J., Khatib, O.: Obstacle avoidance using velocity dipole field method. In: Proceedings of the International Conference on Control, Automation and Systems, pp. 1657–1661, Gyeonggi-DO (2005)
Pawluszewicz, E., Torres, D.: Avoidance control on time scales. J. Optim. Theory Appl. 145(3), 527–542 (2010)
Rahmanian-Shahri, N., Troch, I.: Collision-avoidance for redundant robots through control of the self-motion of the manipulator. J. Intell. Robot. Syst. 16(2), 123–149 (1996)
Rimon, E., Koditschek, D.: Exact robot navigation using artificial potential functions. IEEE Trans. Robot. Autom. 8(5), 510–518 (1992)
Rodríguez-Seda, E.J, Stipanovic, D.M., Spong, M.W.: Collision avoidance control with sensing uncertainties. s.l. In: Proceedings of the 2011 American Control Conference, pp. 3363–3368. IEEE, San Francisco (2011)
Rodríguez-Seda, E.J., Stipanovic, D.M., Spong, M.W.: Guaranteed collision avoidance for autonomous systems with acceleration constraints and sensing uncertainties. J. Optim. Theory Appl. 168(3), 1014–1038 (2016)
Rodríguez-Seda, E.J., Tang, C., Spong, M.W., Stipanovic, D.M.: Trajectory tracking with collision avoidance for nonholonomic vehicles with acceleration constraints and limited sensing. Int. J. Robot. Res. 33(12), 1569–1592 (2014)
Schlegl, T., Kröger, T., Gaschler, A., Khatib, O., Zangl, H.: Virtual whiskers - highly responsive robot collision avoidance. In: 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 5373–5379 (2013). https://doi.org/10.1109/IROS.2013.6697134
Shevitz, D., Paden, B.: Lyapunov stability theory of nonsmooth systems. IEEE Trans. Autom. Control 39(9), 1910–1914 (1994)
Stipanovic, D.M., Hokayem, P.F., Spong, M.W., Siljak, G.D.: Cooperative avoidance control for multiagent systems. J. Dyn. Syst. Measur. Control 129(5), 699–707 (2007)
Zlajpah, L., Nemec, B.: Kinematic control algorithms for on-line obstacle avoidance for redundant manipulators. In: Conference I (ed.) Proceedings of the International Conference on Intellegent Robots and Systems, pp. 1898–1903. IEEE, Switzerland (2002)
Acknowledgements
This work was partially supported by the National Science Foundation under Award Numbers CNS 13-14891 and CNS 15-45069, and a grant through the JUMP-ARCHES (Applied Research for Community Health through Engineering and Simulation) program for addressing safety and reliability of surgical robots. This project was carried out at the Health Care Engineering Systems Center at Illinois.
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Deka, S.A., Li, X., Stipanović, D.M. et al. Robust and Safe Coordination of Multiple Robotic Manipulators. J Intell Robot Syst 90, 419–435 (2018). https://doi.org/10.1007/s10846-017-0699-y
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DOI: https://doi.org/10.1007/s10846-017-0699-y