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Hybrid Potential Field Based Control of Differential Drive Mobile Robots

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Abstract

This paper suggests a new way for nonholonomic mobile robots to navigate in obstacle environments using potential fields based on navigation functions. The proposed strategy is a time-invariant feedback control design with the distinguishing feature that it requires almost no switching compared to alternative methodologies of the same nature. Asymptotic convergence with collision avoidance for the proposed approach is established analytically, and the method is demonstrated on a differential-drive skid steering mobile robot.

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References

  1. Astolfi, A.: Discontinuous control of nonholonomic systems. Syst. Control. Lett. 27, 37–45 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barraquand, J., Langlois, B., Latombe, J.C.: Numerical potential fields techniques for robot path planning. IEEE Trans. Syst. Man Cybern. 22, 224–241 (1992)

    Article  MathSciNet  Google Scholar 

  3. Bloch, A.M., Drakunov, S.V., Kinyon, M.K.: Stabilization of nonholonomic systems using isospectral flows. SIAM J. Control Optim. 38(3), 855–874 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Brockett, R.: Asymptotic stability and feedback stabilization, pp. 181–191. Differential Geometric Control Theory. Birkhauser, Boston (1983)

    Google Scholar 

  5. Brockett, R.W.: Asymptotic stability and feedback stabilization. In: Brockett R., Millman R., Sussmann H. (eds.) Differential Geometric Control Theory, pp. 181–191. Birkhauser, Boston (1983)

    Google Scholar 

  6. Chen, J., Dixon, W.E., Dawson, D.M., Galluzzo, T.: Navigation and control of a wheeled mobile robot. In: Proceedings of the IEEE/ASME Conference on Advanced Intelligent Mechatronics, pp. 1145–1150. Monteray CA (2005)

  7. Choset, H., Lynch, K.M., Hutchinson, S., Kantor, G., Burgard, W., Kavraki, L.E., Thrun, S.: Principles of Robot Motion: Theory, Algorithms, and Implementations. MIT Press, Boston (2005)

    MATH  Google Scholar 

  8. Clarke, F.H., Ledyaev, Y.S., Sontag, E.D., Subbotin, A.I.: Asymptotic controllability implies feedback stabilization. IEEE Trans. Automat. Contr. 42(10), 1397–1407 (1997)

    Article  MathSciNet  Google Scholar 

  9. Conner, D.C., Choset, H., Rizzi, A.A.: Flow-through policies for hybrid controller synthesis applied to fully actuated systems. IEEE Trans. Robot. 25(1), 136–146 (2009)

    Article  Google Scholar 

  10. Connolly, C., Burns, J., Weis, R.: Path planning using laplace’s equation. In: Proceedings of IEEE Conference on Robotics and Automation, pp. 2102–2106. Cincinnati, OH (1990)

    Chapter  Google Scholar 

  11. Coron, J.M., Rosier, L.: A relation between continuous time-varying and discontinuous feedback stabilization. Journal of Mathematical Systems, Estimation, and Control 4(1), 67–84 (1994)

    MathSciNet  MATH  Google Scholar 

  12. D. Tilbury, R.M., Sastry, S.: Trajectory generation for the n-trailer problem using Goursat normal forms. IEEE Trans. Robot. Autom. 40, 802–819 (1995)

    MATH  Google Scholar 

  13. Dimarogonas, D.V., Kyriakopoulos, K.J.: On the state agreement problem for multiple unicycles with varying communication links. In: Proceedings of the 45th Conference on Decision and Control, pp. 4283–4288 (2006)

  14. Ferrara, A., Rubagotti, M.: Second-order sliding-mode control of a mobile robot based on a harmonic potential field. IET Control Theory Appl. 2(9), 807–818 (2008)

    Article  MathSciNet  Google Scholar 

  15. Filippov, A.: Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers (1988)

  16. Guldner, J., Utkin, V.: Sliding mode control for an obstacle avoidance strategy based on an harmonic potential field. In: Proceedings of the 32nd IEEE Conference on Decision and Control, pp. 424–429 (1993)

  17. Guldner, J., Utkin, V.: Sliding mode control for gradient tracking and robot navigation using artificial potential fields. IEEE Trans. Robot. Autom. 11(2), 247–254 (1995)

    Article  Google Scholar 

  18. Kallem, V., Komoroski, A.T., Kumar, V.: Sequential composition for navigating a nonholonomic system in the presense of obstacles. IEEE Trans. Robot. 27(6), 1152–1159 (2011)

    Article  Google Scholar 

  19. Khalil, H.K.: Nonlinear Systems, 2nd edn. Prentice-Hall Inc. (1996)

  20. Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. Int. J. Rob. Res. 5(1), 90–98 (Spring, 1986)

    Article  MathSciNet  Google Scholar 

  21. Kim, J., Khosla, P.: Real-time obstacle avoidance using harmonic potential functions. IEEE Trans. Robot. Autom. 8(3), 338–349 (1992)

    Article  Google Scholar 

  22. Koditschek, D.E., Rimon, E.: Robot navigation functions on manifolds with boundary. Adv. Appl. Math. 11, 412–442 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  23. Koksal, M., Gazi, V., Fidan, B., Ordonez, R.: Tracking a maneuvering target with a non-holonomic agent using artificial potentials and sliding mode control. In: 16th Mediterranean Conference on Control and Automation, pp. 1174–1179 (2008)

  24. Krogh, B.: A generalized potential field approach to obstacle avoidance control. In: Proc. of SME Conference on Robotics Research. Bethlehem, PA (1984)

    Google Scholar 

  25. Kyriakopoulos, K.J., Kakambouras, P., Krikelis, N.J.: Navigation of nonholonomic vehicles in complex environments with potential fields and tracking. In: Proceedings of the 1996 IEEE International Conference on Robotics and Automation, pp. 3389–3394 (1996)

  26. Lafferriere, G., Sontag, E.: Remarks on control lyapunov functions for discontinuous stabilizing feedback. In: Proceedings of the 32nd IEEE Int. Conf. on Decision and Control, pp. 2398–2403. San Antonio, TX (1993)

  27. Lafferriere, G., Sussmann, H.: A differential geometric approach to motion planning. In: Li Z., Canny J. (eds.) Nonholonomic Motion Planning, pp. 235–270. Kluwer Academic Publishers (1993)

  28. Lamiraux, F., Bonnafous, D., Lefebvre, O.: Reactive path deformation for nonholonomic mobile robots. IEEE Trans. Robot. 20(6), 967–977 (2004)

    Article  Google Scholar 

  29. Laumond, J.P., Jacobs, P.E., Taïx, M., Murray, R.M.: A motion planner for nonholonomic mobile robots. IEEE Trans. Robot. Autom. 10(5), 577–592 (1994)

    Article  Google Scholar 

  30. Liu, Z., Jing, R., Ding, X., Li, J.: Trajectory tracking control of wheeled mobile robots based on the artificial potential field. In: Proceedings of the Fourth International Conference on Natural Computation, vol. 7, pp. 382–387 (2008)

  31. Loizou, S.G., Kyriakopoulos, K.J.: Centralized feedback stabilization of multiple nonholonomic agents under input constraints. In: 5th IFAC Symposium on Intelligent Autonomous Vehicles (2004)

  32. Loizou, S.G., Tanner, H.G., Kumar, V., Kyriakopoulos, K.: Closed loop motion planning and control for mobile robots in uncertain environment. In: 42th IEEE Conference on Decision and Control, pp. 2010–2015. Maui, Hawaii (2003)

  33. Lopes, G.A., Koditschek, D.E.: Navigation functions for dynamical, nonholonomically constrained mechanical systems. In: Kawamura S., Svinin M. (eds.) Advances in Robot Control; From Everyday Physics to Human-Like Movements, pp. 135–156. Springer, New York (2006)

    Google Scholar 

  34. Lopes, G.A.D., Koditschek, D.E.: Visual servoing for nonholonomically constrained three degree of freedom kinematic systems. Int. J. Rob. Res. 26(7), 715–736 (2007)

    Article  Google Scholar 

  35. Luca, A.D., Oriolo, G., Samson, C.: Feedback control of a nonholonomic car-like robot. In: Laumond J.P. (ed.) Robot Motion Planning and Control (Lecture Notes in Control and Information Sciences), vol. 229, pp. 171–253. Springer-Verlag (1998)

  36. Masoud, A.: A harmonic potential field approach for navigating a rigid, nonholonomic robot in a cluttered environment. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 3993–3999 (2009)

  37. Murray, R., Sastry, S.: Nonholonomic motion planning: steering using sinusoids. IEEE Transactions on Automatic Control, pp. 700–716 (1993)

  38. Oriolo, G., Luca, A.D., Vantittelli, M.: WMR control via dynamic feedback linearization: design, implementation, and experimental validation. IEEE Trans. Control Syst. Technol. 10(6), 835–852 (2002)

    Article  Google Scholar 

  39. Panagou, D., Tanner, H.G., Kyriakopoulos, K.J.: Dipole-like fields for stabilization of systems with Pfaffian constraints. In: Proc. of the 2010 IEEE International Conference on Robotics and Automation, pp. 4499–4504. Anchorage, Alaska (2010)

  40. Pathak, K., Agrawal, S.: Planning and control of a nonholonomic unicycle using ring shaped local potential fields. In: Proceedings of the American Control Conference, vol. 3, pp. 2368–2373 (2004)

  41. Pomet, J.P.: Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift. Syst. Control. Lett. 18, 147–158 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  42. Rimon, E., Koditschek, D.: Exact robot navigation using artificial potential functions. IEEE Trans. Robot. Autom. 8(5), 501–518 (1992)

    Article  Google Scholar 

  43. Roussos, G., Dimarogonas, D.V., Kyriakopoulos, K.J.: 3D navigation and collision avoidance for nonholonomic aircraft-like vehicles. Int. J. Adapt. Control Signal Process. 24(10), 900–920 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  44. Samson, C.: Time-varying feedback stabilization of a car-like wheeled mobile robot. Int. J. Rob. Res. 12(1), 55–66 (1993)

    Article  MathSciNet  Google Scholar 

  45. Sekhavat, S., Laumond, J.P.: Topological property for collision-free nonholonomic motion planning: The case of sinusoidal inputs for chained form systems. IEEE Trans. Robot. Autom. 14(5), 671–680 (1998)

    Article  Google Scholar 

  46. Sekhavat, S., Švestka, P., Laumond, J.P., Overmars, M.H.: Multi-level path planning for nonholonomic robots using semi-holonomic subsystems. Int. J. Rob. Res. 17(8), 840–857 (1998)

    Article  Google Scholar 

  47. Singh, L., Stephanou, H., Wen, J.: Real-time robot motion control with circulatory fields. In: Proc. of IEEE Conference on Robotics and Automation, pp. 2737–2742. Minneapolis, MN (1996)

  48. Tanner, H., Kyriakopoulos, K.: Nonholonomic motion planning for mobile manipulators. In: Proc. of the 2000 IEEE International Conference on Robotics and Automation, pp. 1233–1238. San Francisco (2000)

  49. Tanner, H.G., Loizou, S.G., Kyriakopoulos, K.J.: Nonholonomic stabilization with collision avoidance for mobile robots. In: Proc. of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1220–1225. Maui, Hawaii, USA (2001)

  50. Tanner, H.G., Loizou, S.G., Kyriakopoulos, K.J.: Nonholonomic navigation and control of cooperating mobile manipulators. IEEE Trans. Robot. Autom. 19(1), 53–64 (2003)

    Article  Google Scholar 

  51. Urakubo, T., Okuma, K., Tada, Y.: Feedback control of a two wheeled mobile robot with obstacle avoidance using potential functions. In: Proceedings of the 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 3, pp. 2428–2433 (2004)

  52. Utkin, V., Drakunov, S., Hashimoto, H., Harashima, F.: Robot path obstacle avoidance control via sliding mode approach. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1287–1290 (1991)

  53. Canudas de Wit, C., Sordalen, O.: Exponential stabilization of mobile robots with nonholonomic constraints. IEEE Trans. Automat. Contr. 13(11), 1791–1797 (1992)

    Article  MathSciNet  Google Scholar 

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  1. Department of Mechanical Engineering, University of Delaware, Newark, DE, USA

    Luis Valbuena & Herbert G. Tanner

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  1. Luis Valbuena
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  2. Herbert G. Tanner
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Correspondence to Herbert G. Tanner.

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Valbuena, L., Tanner, H.G. Hybrid Potential Field Based Control of Differential Drive Mobile Robots. J Intell Robot Syst 68, 307–322 (2012). https://doi.org/10.1007/s10846-012-9685-6

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