Page 1


ORBITAL OBSTACLE AVOIDANCE ALGORITHM FOR RELIABLE AND ON-LINE MOBILE ROBOT NAVIGATION ABSTRACT This paper proposes an orbital obstacle avoidance algorithm which permits to obtain safe and smooth robot navigation in very cluttered environments. This algorithm uses specific reference frame which gives accurate indication on robot situation. The robot knows thus if it must avoid the obstacle in clockwise or counter-clockwise direction. Moreover, it knows the moment to go into the orbit of the obstacle and the moment to go out. These orbital behaviors are performed using adaptive limit-cycle trajectories. The later with a specific conflicting situations module permit to prevent robot oscillations, local minima and dead ends. The proposed algorithm is embedded in a specific bottom-up control architecture with stability proof given according to Lyapunov synthesis. The overall proposed structure of control allows to decrease significantly the time to reach the target. In fact, according to the proposed algorithm, robot anticipates the collisions with obstacles according to smooth local trajectory modifications. A large number of simulations in different environments are performed to demonstrate the efficiency and the reliability of the proposed control architecture.

I. INTRODUCTION Obstacle avoidance controllers have a predominating function to achieve autonomously and safely the navigation of mobile robots in cluttered and unstructured environments. Khatib in [1] proposes a real-time obstacle avoidance approach based on the principle of artificial potential fields. He assumes that the robot actions are guided by the sum of attractive and repulsive fields. Arkin in [2] extends Khatib’s approach while proposing specific schema motors for mobile robots navigation. Nevertheless, these methods suffer from the local minima problem when for instance, the sum of local gradient is null. In [3], Elnagar et al., propose to model the repulsive potential field characterizing obstacles by Maxwell’s equations which have the merit to completely eliminate the local minima problem. Fuzzy control is widely used to perform robust obstacle avoidance [4], [5]. This formalism allows to integrate several linguistic rules to avoid dead ends or local minima [6]. Unfortunately, its lacks of stability demonstration of the applied control laws. Another interesting approach, based on a reflex behavior reaction, uses the Deformable Virtual Zone (DVZ) concept, in which a robot kinematic dependent risk zone surrounds the robot [7]. If an obstacle is detected, it will deform the DVZ and the approach consists to minimize this deformation by modifying the control vector. An interesting overview of other obstacle avoidance methods is accurately given in [8]. Nevertheless, the obstacle avoidance controller is only a part of the different functions which must constitute an overall control architecture for navigation tasks. One part of the literature in this domain considers that the robot is fully actuated with no control bound and focuses the attention on path planning. Voronoï diagrams and visibility graphs [9] or navigation functions [10] are among these roadmap-based methods. However, the other part of the literature considers that to control a robot with safety, flexibility and reliability, it is essential to accurately take into account: robot’s structural constraints (e.g., nonholonomy); avoid command discontinuities and set-point jerk, etc. Nevertheless, even in this method, there are two schools of thought, one uses the notion of planning and re-planning to reach the target, e.g., [11] and [12] and the other more reactive (without planning) like in [13], [14] or [15]. Our proposed control architecture is linked to this last approach. Therefore, where the stability of robot control is rigourously demonstrated and the overall



robot behavior is constructed with modular and bottom-up approach [16]. The proposed on-line obstacle avoidance algorithm uses specific orbital trajectories given by limit-cycle differential equations [17], [18]. The proofs of controllers stability are given using Lyapunov functions. The proposed algorithm provides also several mechanisms to prevent oscillations, local minima and dead end robot situations. The rest of the paper is organized as follows. Section II gives the specification of the task to achieve. The details of the proposed control architecture are given in section III. It presents the model of the considered robot and the implemented elementary controllers laws. Section IV gives in details the proposed obstacle avoidance algorithm whereas section V introduces the conflicting situations management module. Section VI is devoted to the description and analysis of simulation results. This paper ends with some conclusions and further work.

II. NAVIGATION IN PRESENCE OF OBSTACLES The objective of the navigation task in an unstructured environment is to lead the robot towards one target while avoiding statical and dynamical obstacles. One supposes in the setup that obstacles and the robot are surrounded by bounding cylindrical boxes with respectively 52 and 55 radii [19]. The target to reach is also characterized by a circle of 57 radius. Several perceptions are also necessary for the robot navigation (cf. Figure 1):

Figure 1 . The used perceptions for mobile robot navigation


ments proves the efficiency and the flexibility of the control. The proposed algorithm allows also to reduce the time needed to reach the target. In fact, according to this algorithm, robot anticipates the collisions with obstacles according to smooth local trajectory modifications. Future work will first test the proposed control architecture on the CyCab vehicle [20]. The second step is to adapt the proposed structure of control to more complex tasks like the navigation in highly dynamical environment.

REFERENCES Figure 10 . Evolution of Lyapunov functions for the two used controllers

Figure 11 . Smooth trajectory obtained with the proposed orbital algorithm

VII. CONCLUSION AND FURTHER WORK In this paper, an obstacle avoidance algorithm based on orbital limit-cycle trajectories is proposed. This algorithm was embedded in an on-line behavioral control architecture and permits for a mobile robot to navigate in cluttered environments with safe and reliable way. In addition to the use of limitcycles, the algorithm uses specific reactive rules which allows to the robot to avoid deadlocks, local minima and oscillations. These simple rules are efficient and permits to the proposed algorithm to do not becomes more and more complex. In other terms, the proposed control structure is open and flexible in the sense that it can manage a lot of other conflicts situations while only adding simple reactive rules. Otherwise, the stability proof of the overall control architecture is given. Statistical survey in different environ-

[1] O. Khatib, “Real-time obstacle avoidance for manipulators and mobile robots,” The International Journal of Robotics Research, vol. 5, pp. pp.90–99, Spring 1986. [2] R. C. Arkin, “Motor schema-based mobile robot navigation,” International Journal of Robotics Research, vol. 8, no. 4, pp. pp.92–112, 1989. [3] A. Elnagar and A. Hussein, “Motion planning using maxwell’s equations,” in IEEE/RSJ International Conference on Intelligent Robots and System, Lausanne, Switzerland, 2002. [4] A. Saffiotti, E. Ruspini, and K. Konolige, “Robust execution of robot plans using fuzzy logic,” in in Fuzzy Logic in Artificial Intelligence : IJCAI’93 Workshop, Springer-Velag, Ed., Chambéry-France, 1993, pp. 24–37. [5] O. Motlagh, T. S. Hong, and N. Ismail, “Development of a new minimum avoidance system for a behavior-based mobile robot,” Fuzzy Sets and Systems, 2008. [6] C. Ordonez, E. G. C. Jr., M. F. Selekwa, and D. D. Dunlap, “The virtual wall approach to limit cycle avoidance for unmanned ground vehicles,” Robotics and Autonomous Systems, vol. 56, no. 8, pp. pp.645–657, 2008. [7] L. P. Zapata R., Cacitti A., “Dvz-based collision avoidance control of non-holonomic mobile manipulators,” JESA, European Journal of Automated Systems, vol. 38(5), pp. 559–588, 2004. [8] J. Minguez, F. Lamiraux, and J.-P. Laumond, Handbook of Robotics, 2008, ch. Motion Planning and Obstacle Avoidance, pp. pp.827–852. [9] J.-C. Latombe, Robot Motion Planning. Kluwer Academic Publishers, Boston, MA, 1991. [10] E. Rimon and D. E. Koditschek, “Exact robot navigation using artficial potential flelds,” IEEE Transactions on Robotics and Automation, vol. 8(5), pp. 501–518, Oct. 1992. [11] C. Belta, V. Isler, and G. J. Pappas, “Discrete abstractions for robot motion planning and control in polygonal environments,” IEEE Transactions on Robotics, vol. 21(5), pp. 864–874, Oct. 2005. [12] D. C. Conner, H. Choset, and A. Rizzi, “Integrated planning and control for convex-bodied nonholonomic systems using local feedback,” in Proceedings of Robotics: Science and Systems II. Philadelphia, PA: MIT Press, August 2006, pp. 57–64. [13] M. Egerstedt and X. Hu, “A hybrid control approach to action coordination for mobile robots,” Automatica, vol. 38(1), pp. 125–130, 2002. [14] J. Toibero, R. Carelli, and B. Kuchen, “Switching control of mobile robots for autonomous navigation in unknown environments,” in IEEE International Conference on Robotics and Automation, 2007, pp. 1974–1979. [15] L. Adouane, “An adaptive multi-controller architecture for mobile robot navigation,” in 10th IAS, Intelligent Autonomous Systems, Baden-Baden, Germany, July 23-25 2008, pp. 342–347. [16] L. Adouane and N. Le Fort-Piat, “Behavioral and distributed control architecture of control for minimalist mobile robots,” Journal Européen des Systèmes Automatisés, vol. 40, no. 2, pp. pp.177–196, 2006. [17] A. Stuart and A. Humphries, Dynamical systems and numerical analysis. Cambridge University Press, 1996. [18] H. K. Khalil, Frequency domain analysis of feedback systems, P. Hall, Ed. Nonlinear Systems: Chapter7, 3 edition, 2002. [19] M. Yerry and M. Shephard, “A modified quadtree approach to finite element mesh generation,” Computer, Graphics and Applications, 1983. [20] C. Pradalier, J. Hermosillo, C. Koike, C. Braillon, P. Bessière, and C. Laugier, “The cycab: a car-like robot navigating autonomously and safely among pedestrians,” Robotics and Autonomous Systems, vol. 50, no. 1, pp. 51–68, 2005. [21] W. H. Huang, B. R. Fajen, J. R. Fink, and W. H. Warren, “Visual navigation and obstacle avoidance using a steering potential function,” Robotics and Autonomous Systems, vol. 54, no. 4, pp. 288–299, April 2006. [22] H. Zhang, S. Liu, and S. X. Yang, “A hybrid robot navigation approach based on partial planning and emotion-based behavior coordination,” in International Conference Intelligent Robots and Systems, Beijing, China, October 2006, pp. 1183–1188. [23] R. A. Brooks, “A robust layered control system for a mobile robot,” IEEE Journal of Robotics and Automation, vol. RA-2, pp. pp.14–23, March 1986. [24] D.-H. Kim and J.-H. Kim, “A real-time limit-cycle navigation method for fast mobile robots and its application to robot soccer,” Robotics and Autonomous Systems, vol. 42(1), pp. 17–30, 2003. [25] L. Adouane, “Hybrid and safe control architecture for mobile robot navigation,” in 9th Conference on Autonomous Robot Systems and Competitions, Portugal, May 2009. [26] J.-P. Laumond, La robotique mobile. Hermès, 2001. [27] M. S. Jie, J. H. Baek, Y. S. Hong, and K. W. Lee, “Real time obstacle avoidance for mobile robot using limit-cycle and vector field method,” Knowledge-Based Intelligent Information and Engineering Systems, pp. 866–873, October 2006. [28] M. Wang and J. N. Liua, “Fuzzy logic-based real-time robot navigation in unknown environment with dead ends,” Robotics and Autonomous Systems, vol. 56, no. 7, pp. pp.625–643, 2008.


Orbital obstacle avoidance algorithm for reliable and on-line mobile robot navigation  
Orbital obstacle avoidance algorithm for reliable and on-line mobile robot navigation  

Autor: Lounis Adouane; Revista: robótica nº79