Abstract
This paper presents a kinematic controller for a differentially driven mobile robot. The controller is based on the navigation function (NF) concept that guarantees goal achievement from almost all initial states. Slow convergence in some cases is a significant disadvantage of this approach, especially when narrow passages exist in the environment and/or specific values of design parameters are set. The main reason of this phenomenon is that the velocity control strongly depends on the slope of the NF. The algorithm proposed in this paper is based on a method introduced in Urakubo (Nonlin. Dyn. 81(3): 1475–1487 2015), that extends NF to nonholonomic mobile platforms and allows stabilizing not only the position of robots but also their orientation. This algorithm is used as a reference in experimental performance comparison. In the new algorithm, the gradient of the NF is used to generate motion direction but the velocity is computed as a function of position and orientation errors. This approach results in much better state converge. Analysis of the convergence shows how the location of the eigenvalues of linearized system affects time of goal achievement. The paper describes saddle point detection and avoidance methodology and presents their experimental verification. It also shows what happens in practice if initial position is located exactly in the saddle point and its detection/avoidance procedures are turned off.
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References
Brockett, R.W.: Asymptotic stability and feedback stabilization, Differential Geometric Control Theory, pp 181–191. Birkhauser, Boston (1983)
Dimarogonasa, D.V., Loizoua, S.G., Kyriakopoulos, K.J., Zavlanosb, M.M.: A feedback stabilization and collision avoidance scheme for multiple independent non-point agents. Automatica 42(2), 229–243 (2005)
Filippidis, I., Kyriakopoulos, K.J.: Adjustable navigation functions for unknown sphere worlds. In: IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), pp. 4276–4281 (2011)
Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. Int. J. Robot. Res. 5(1), 90–98 (1986)
Kowalczyk, W.: Rapidly converging navigation function control for differentially driven mobile robots. In: 11th International Workshop on Robot Motion and Control (RoMoCo), p. 244 (2017)
Kowalczyk, W., Kozłowski, K.: Control of the differentially-driven mobile robot in the environment with a non-convex star-shape obstacle: Simulation and experiments. Acta Polytechnica Hungarica 13(1), 123–135 (2016)
Kowalczyk, W., Przybyła, M., Kozłowski, K.: Rapid navigation function control for omnidirectional mobile platform. In: 2017 22nd International Conference on Methods and Models in Automation and Robotics (MMAR), p. 137 (2017)
Kowalczyk, W., Przybyła, M., Kozłowski, K.: Set-point control of mobile robot with obstacle detection and avoidance using navigation function-experimental verification. J. Intell. Robot. Syst. 85(3-4), 539–552 (2017)
Kowalczyk, W., Przybyła, M., Kozłowski, K.: Control of a mobile robot and collision avoidance using navigation function-experimental verification. In: 2015 10th International Workshop on Robot Motion and Control (RoMoCo), pp. 148–152
Kowalczyk, W, Przybyła, M., Kozłowski, K.: Saddle point detection of the navigation function in nonholonomic mobile robot control. In: 2016 21st International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 936–941, Miedzyzdroje (2016). https://doi.org/10.1109/MMAR.2016.7575263
Lionis, G, Papageorgiou, X., Kyriakopoulos, K.: Locally computable navigation functions for sphere worlds. In: Proc. IEEE International Conference on Robotics & Automation (ICRA-2007), pp. 1998–2003. Roma (2007)
Rimon, E., Koditschek, D.E.: Exact robot navigation using cost functions: the case of distinct spherical boundaries. IEEE Int. Conf. Robot. Autom. 3, 1791–1796 (1988)
Rimon, E., Koditschek, D.E.: The construction of analytic diffeomorphisms for exact robot navigation on star worlds. Trans. Amer. Math. Soc. 327, 71–116 (1991)
Rimon, E., Koditschek, D.: Exact robot navigation using artificial potential functions. IEEE Trans. Robot. Autom. 8(5), 501–518 (1992)
Roussos, G., Kyriakopoulos, K.J.: Completely decentralised navigation of multiple unicycle agents with prioritisation and fault tolerance. In: IEEE Conference on Decision and Control (CDC), pp. 1372–1377 (2010)
Roussos, G., Kyriakopoulos, K.J.: Decentralized and prioritized navigation and collision avoidance for multiple mobile robots. Distrib. Autonom. Robot. Sys. - Springer Tracts Adv. Robot. 83, 189–202 (2013)
Roussos, G., Kyriakopoulos, K: Decentralized navigation and conflict avoidance for aircraft in 3-D space. IEEE Trans. Control Syst. Technol. 20(6), 1622–1629 (2012). https://doi.org/10.1109/TCST.2011.2167974
Roussos, G., Dimarogonas, D., Kyriakopoulos, K.: 3D navigation and collision avoidance for nonholonomic aircraft-like vehicles. Int. J. Adapt. Control Signal Process. Special Issue: Air Traffic Manag.: Challenges Opport. Adv. Control 24(10), 900–920 (2010)
Trevisan, M., Idiart, M., Prestes, E., Engel, P.: Exploratory navigation based on dynamical boundary value problems. J. Intell. Robot. Syst. 45(2), 101–114 (2006)
Urakubo, T.: Feedback stabilization of a nonholonomic system with potential fields: Application to a two-wheeled mobile robot among obstacles. Nonlin. Dyn. 81(3), 1475–1487 (2015)
Urakubo, T., Okuma, K., Tada, Y.: Feedback control of a two wheeled mobile robot with obstacle avoidance using potential functions. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) 3, 2428–2433 (2004)
Xu, Z., Hess, R., Schilling, K.: Constraints of potential field for obstacle avoidance on car-like mobile robots. In: IFAC Proceedings Volumes, vol. 45, no. 4, pp. 169–175. Wurzburg, Germany (2012)
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Kowalczyk, W. Rapid Navigation Function Control for Two-Wheeled Mobile Robots. J Intell Robot Syst 93, 687–697 (2019). https://doi.org/10.1007/s10846-018-0879-4
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DOI: https://doi.org/10.1007/s10846-018-0879-4