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A Stable Switched-System Approach to Collision-Free Wheeled Mobile Robot Navigation

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Abstract

This paper presents a novel switched-system approach for obstacle avoidance by mobile robots. This approach does not suffer from common drawbacks of existing methods, such as needing prior knowledge of obstacles, or local minima or chattering in control laws. We define an attractive and an avoidance vector in obstacle-free and obstacle-avoidance regions, respectively. Next, we define an unified velocity vector, which represents either the attractive vector or the avoidance vector, and drives the robot away from the obstacle and ultimately towards the goal. The avoidance vector differs from the repulsive vector commonly used in potential field approaches, rather it is defined always perpendicular to such a repulsive vector and projects positively onto the attractive vector. The unified velocity vector enables the use of a common Lyapunov function in analyzing the stability of the system under arbitrary switching. Novel switching rules are proposed for obstacles that can be well bounded by a circle in the local subset of SE(2). To better handle large, non-circular obstacles, a separate switching signal is proposed. Through the choice of switching rule, we investigate the chattering problem that can hinder some switching controllers. We present two control laws, one with bounded inputs and one with no bounds on inputs. We prove both control schemes are asymptotically stable and guide the robot to the goal while avoiding obstacles. To verify the effectiveness of the proposed approach, as well as compare the control laws and switching rules, several simulations and experiments have been conducted.

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References

  1. Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. The International Journal of Robotics Research 5(1), 90–98 (1986)

    Article  Google Scholar 

  2. Arkin, R.C.: Motor schema-based mobile robot navigation. The International Journal of Robotics Research 8(4), 92–112 (1989)

    Article  MathSciNet  Google Scholar 

  3. Koren, Y., Borenstein, J.: Potential field methods and their inherent limitations for mobile robot navigation. In: IEEE International Conference on Robotics and Automation, pp 1398–1404 (1991)

  4. Ge, S.S., Cui, Y.J.: New potential functions for mobile robot path planning. IEEE Trans. Robot. Autom. 16(5), 615–620 (2000)

    Article  Google Scholar 

  5. Shimoda, S., Kuroda, Y., Iagnemma, K.: Potential field navigation of high speed unmanned ground vehicles on uneven terrain. In: IEEE Internation Conference on Robotics and Automation, pp 2828–2833 (2005)

  6. Fahimi, F., Nataraj, C., Ashrafiuon, H.: Real-time obstacle avoidance for multiple mobile robots. Robotica 27(2), 189–198 (2009)

    Article  Google Scholar 

  7. Lindemann, S.R., LaValle, S.M.: Simple and efficient algorithms for computing smooth, collision-free feedback laws over given cell decompositions. The International Journal of Robotics Research 28(5), 600–621 (2009)

    Article  Google Scholar 

  8. Dietrich, A., Albu-Schaffer, A., Hirzinger, G.: On continuous null space projections for torque-based, hierarchical, multi-objective manipulation. In: IEEE International Conference on Robotics and Automation, pp 2978–2985 (2012)

  9. Shiller, Z., Sharma, S., Stern, I., Stern, A.: Online obstacle avoidance at high speeds. The International Journal of Robotics Research 32(9-10), 1030–1047 (2013)

    Article  Google Scholar 

  10. Ge, S., Cui, Y.: Dynamic motion planning for mobile robots using potential field method. Auton. Robot. 13, 207–222 (2002)

    Article  MATH  Google Scholar 

  11. Karagoz, C., Bozma, H., Koditschek, D.: Coordinated navigation of multiple independent disk-shaped robots. IEEE Trans. Robot. 30(6), 1289–1304 (2014)

    Article  Google Scholar 

  12. Ma, Y., Zheng, G., Perruquetti, W., Qiu, Z.: Motion planning for non-holonomic mobile robots using the i-pid controller and potential field. In: IEEE/RSJ Conference on Intelligent Robots and Systems (2014)

  13. Connolly, C.I., Burns, J., Weiss, R.: Path planning using laplace’s equation. In: IEEE International Conference on Robotics and Automation, pp 2102–2106. IEEE (1990)

  14. Panagou, D., Tanner, H.G., Kyriakopoulos, K.J.: Control of nonholonomic systems using reference vector fields. In: the 50th IEEE Conference on Decision and Control and European Control, pp 2831–2836 (2011)

  15. Ren, J., McIsaac, K., Patel, R.: Modified newtons method applied to potential field based navigation for nonholonomic robots in dynamic environments. Robotica 26, 285–294 (2008)

    Google Scholar 

  16. Welzl, E.: Constructing the visibility graph for n-line segments in o (n2) time. Inf. Process. Lett. 20(4), 167–171 (1985)

    Article  MATH  Google Scholar 

  17. Aurenhammer, F.: Voronoi diagramsa survey of a fundamental geometric data structure. ACM Computing Surveys (CSUR) 23(3), 345–405 (1991)

    Article  Google Scholar 

  18. Amato, N.M., Wu, Y.: A randomized roadmap method for path and manipulation planning. In: IEEE International Conference on Robotics and Automation, vol. 1, pp 113–120 (1996)

  19. Amato, N.M., Bayazit, O.B., Dale, L. K., Jones, C., Vallejo, D.: Choosing good distance metrics and local planners for probabilistic roadmap methods. In: IEEE International Conference on Robotics and Automation, vol. 1, pp 630–637 (1998)

  20. Garrido, S., Moreno, L., Blanco, D., Jurewicz, P.: Path planning for mobile robot navigation using voronoi diagram and fast marching. Int. J. Robot. Autom. 2(1), 42–64 (2011)

    Google Scholar 

  21. LaValle, S.M., Kuffner, J.J.: Randomized kinodynamic planning. The International Journal of Robotics Research 20(5), 378–400 (2001)

    Article  Google Scholar 

  22. Arkin, R.C.: Behavior-based robot navigation for extended domains. Adaptove Behavior 1(2), 201–225 (1992)

    Article  Google Scholar 

  23. Egerstedt, M., Johansson, K., Lygeros, J., Sastry, S.: Behavior based robotics using regularized hybrid automata. In: Proceedings of the 38th IEEE Conference on Decision and Control, vol. 4, pp 3400–3405 (1999)

  24. Bennett, A.A., Leonard, J.J.: A behavior-based approach to adaptive feature detection and following with autonomous underwater vehicles. IEEE J. Ocean. Eng. 25(2), 213–226 (2000)

    Article  Google Scholar 

  25. Li, S., Li, Y., Lu, H.: Mobile robot collision avoidance algorithm based on hybrid zeno behavior automaton. In: IEEE International Conference on Robotics and Biomimetics, pp 474–479 (2006)

  26. Droge, G., Egerstedt, M.: Adaptive look-ahead for robotic navigation in unknown environments. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp 1134–1139 (2011)

  27. Sgorbissa, A., Zaccaria, R.: Planning and obstacle avoidance in mobile robotics. Robot. Auton. Syst. 60(4), 628–638 (2012)

    Article  Google Scholar 

  28. Arrichiello, F., Chiaverini, S., Indiveri, G., Pedone, P.: The null-space-based behavioral control for mobile robots with velocity actuator saturations. The International Journal of Robotics Research 29(10), 1317–1337 (2010)

    Article  Google Scholar 

  29. Flacco, F., Luca, A.D., Khatib, O.: Motion control of redundant robots under joint constraints: Saturation in the null space. In: IEEE International Conference on Robotics and Automation, pp 285–292 (2012)

  30. Egerstedt, M.: Behavior based robotics using hybrid automata, pp 103–116. Springer (2000)

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

    Article  Google Scholar 

  32. Minguez, J., Montano, L., Santos-Victor, J.: Abstracting vehicle shape and kinematic constraints from obstacle avoidance methods. Auton. Robot. 20(1), 43–59 (2006)

    Article  Google Scholar 

  33. Khansari-Zadeh, S., Billard, A.: A dynamical system approach to realtime obstacle avoidance. Auton. Robot. 32(4), 433–454 (2012)

    Article  Google Scholar 

  34. Klancar, G., Skrjanc, I.: Tracking-error model-based predictive control for mobile robots in real time. Robot. Auton. Syst. 55, 460–469 (2007)

    Article  Google Scholar 

  35. Klancar, G., Matko, D., Blaic, S.: Wheeled mobile robots control in a linear platoon. J. Intell. Robot. Syst. 54, 709–731 (2009)

    Article  Google Scholar 

  36. Do, K.D.: Bounded controllers for global path tracking control of unicycle-type mobile robots. Robot. Auton. Syst. 61(8), 775–784 (2013)

    Article  Google Scholar 

  37. Liberzon, D.: Switching in Systems and Control. Birkhauser (2003)

  38. Bacciotti, A., Mazzi, L.: An invariance principle for nonlinear switched systems. Syst. Control Lett. 54(11), 1109–1119 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  39. Kanayama, Y., Kimura, Y., Miyazaki, F., Noguchi, T.: A stable tracking control method for an autonomous mobile robot. In: IEEE International Conference on Robotics and Automation, pp 384–389 (1990)

  40. Jin, J., Green, A., Gans, N.: A stable switched-system approach to obstacle avoidance for mobile robots in se(2). In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp 1533–1539 (2014)

  41. Steinbrucker, F., Sturm, J., Cremers, D.: Real-time visual odometry from dense rgb-d images. In: IEEE International Conference on Computer Vision Workshops, pp 719–722 (2011)

  42. Jin, J., Kim, Y., Wee, S., Gans, N.: A stable switched-system approach to shared robust control and obstacle avoidance for mobile robots. In: Proceedings of the ASME 2014 Dynamic Systems and Control Conferences (2014)

  43. Mastellone, S., Stipanovic, D., Spong, M.: Remote formation control and collision avoidance for multi-agent nonholonomic systems. In: IEEE International Conference on Robotics and Automation (2007)

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Texas at Dallas, Richardson, TX, 75080, USA

    Jingfu Jin & Nicholas Gans

  2. Robotics System Research Division, DGIST, Daegu, 711-873, South Korea

    YoonGu Kim, SungGil Wee & DongHa Lee

  3. Convergence Research Center for Collaborative Robots, Daegu Gyeongbuk Institute of Science and Technology, Daegu, 711-873, South Korea

    SungGil Wee

  4. Convergence Research Center for Wellness, Daegu Gyeongbuk Institute of Science and Technology, Daegu, 711-873, South Korea

    DongHa Lee

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  1. Jingfu Jin
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  2. YoonGu Kim
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  3. SungGil Wee
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  4. DongHa Lee
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  5. Nicholas Gans
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Corresponding author

Correspondence to Nicholas Gans.

Additional information

This work was supported by the DGIST R&D Program of the Ministry of Science, ICT and Technology of Korea(15-BD-01)

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Jin, J., Kim, Y., Wee, S. et al. A Stable Switched-System Approach to Collision-Free Wheeled Mobile Robot Navigation. J Intell Robot Syst 86, 599–616 (2017). https://doi.org/10.1007/s10846-017-0467-z

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  • DOI: https://doi.org/10.1007/s10846-017-0467-z

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