Application of transverse functions to control differentially driven wheeled robots using velocity fields

• Autorzy: Pazderski D.

Identyfikatory

DOI

10.1515/bpasts-2016-0092

• Języki publikacji: EN

Abstrakty

EN

This paper deals with control of a nonholonomic unicycle-like robot in a cluttered environment with static obstacles. The proposed solution is based on a combination of a universal motion controller taking advantage of transverse functions with a navigation velocity field determining a path in a free task space. The motion controller is used to imitate an omnidirectional planar kinematics such that nonholonomic constraints become hidden for a navigation layer. Then it is possible to generate vector fields which govern motion of the omnidirectional frame. The controller using the transverse function is discussed in depth. In particular, a possible parametrization of this function is considered and analysis of an augmented dynamics is provided for different motion patterns. Next, construction of obstacles and potential design for star-like shapes are presented. The navigation algorithm is verified experimentally and the results are discussed.

Słowa kluczowe

EN

transverse functions; nonholonomic systems; systems on Lie groups; potential function; velocity fields

PL

pola prędkości; funkcja transwersalna; system nieholonomiczny; grupa Liego; funkcja potencjalna

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2016
• Tom: Vol. 64, nr 4
• Strony: 831--851
• Opis fizyczny: Bibliogr. 47 poz., rys., wykr.

Twórcy

autor

Pazderski D.

• Chair of Control and Systems Engineering, Poznań University of Technology, 3A Piotrowo St., 60-965 Poznań, Poland

Bibliografia

• [1] R.W. Brockett, “Asymptotic stability and feedback stabilization”, in Differential geometric control theory, 181–191, Birkhäuser, Boston, 1983.
• [2] C. Canudas de Wit, H. Khennouf, C. Samson, and O.J. Sørdalen, “Nonlinear control design for mobile robots”, in Recent trends in mobile robots, 121–156, World Scientific, Singapore, 1993.
• [3] R. Fierro and F.L. Lewis, “Control of a nonholonomic mobile robot: backstepping kinematics into dynamics”, Proc. 34th IEEE Conf. on Decision and Control, 3805–3810 (1995).
• [4] G. Oriolo, A. De Luca, and M. Venditteli, “WMR control via dynamic feedback linearization: design, implementation and experimental validation”, IEEE Trans. Control Syst. Technol. 10 (6), 835–852 (2002).
• [5] M. Michałek and K. Kozłowski, “Vector-Field-Orientation feedback control method for a differentially driven vehicle”, IEEE Trans. Control Syst. Technol. 18 (1), 45–65 (2010).
• [6] C. Samson, “Velocity and torque feedback control of a nonholonomic cart”, in Advanced robot control, 125–151, Birkhauser, Boston, MA, 1991.
• [7] J.B. Pomet, “Explicit design of time varying stabilization control laws for a class of controllable systems without drifts”, Syst. Control Lett. 18 (2), 147–158 (1992).
• [8] C. Canudas de Wit and O.J. Sørdalen, “Exponential stabilization of mobile robots with nonholonomic constraints”, IEEE Trans. Autom. Control 37 (11), 1791–1797 (1992).
• [9] A. Astolfi, “Asymptotic stabilization of nonholonomic systems with discontinuous control”, PhD thesis, Swiss Federal Intitute of Technology, Zurich, 1996.
• [10] D.A. Lizárraga, “Obstructions to the existence of universal stabilizers for smooth control systems”, Math. Control Signal. 16 (4), 255–277 (2004).
• [11] P. Morin and C. Samson, “A characterization of the Lie Algebra Rank Condition by transverse periodic functions”, SIAM J. Control Optim. 40 (4), 1227–1249 (2001).
• [12] P. Morin and C. Samson, “Control of nonholonomic mobile robots based on the transverse function approach”, IEEE Trans. Robot. 25 (5), 1058–1073 (2009).
• [13] P. Morin and C. Samson, “Transverse function control of a class of non-invariant driftless systems. application to vehicles with trailers”, Proc. 47th IEEE Conf. on Decision and Control, 4312–4319 (2008).
• [14] D. Pazderski, K. Kozłowski, and D.K. Waśkowicz, “Control of a unicycle-like robot with trailers using transverse function approach”, Bull. Pol. Ac.: Tech. 60 (3), 537–546 (2012).
• [15] P. Morin and C. Samson, “Stabilization of trajectories for systems on Lie groups. Application to the rolling sphere”, Proc. 17th IFAC World Congress, 508–513 (2008).
• [16] M. Ishikawa, P. Morin, and C. Samson, “Tracking control of the trident snake robot with the transverse function approach”, Proc. 48th IEEE Conf. on Decision and Control and 28th Chinese Control Conf., 4137–4143 (2009).
• [17] W. Magiera, “Nonsymetric trident snake: the transverse function approach”, Robotics Advances 1, 451–460 (2012), (in Polish).
• [18] D. Pazderski and K. Kozłowski, “Control of planar robot in the flight phase using transverse function approach”, Bull. Pol. Ac.: Tech. 63 (3), 759–770 (2015).
• [19] B. Krysiak and K. Kozłowski, “Kinematic singularities avoidance for the planar three-link nonholonomic manipulator”, Proc. 10th Int. Workshop on Robot Motion and Control, 252–256 (2015).
• [20] J. Jakubiak, W. Magiera, and K. Tchoń, “Control and motion planning of a nonholonomic parallel orienting platform”, ASME. J. Mechanisms Robotics 7 (4), (2015), DOI:10.1115/1.4029891.
• [21] D.A. Lizárraga, P. Morin, and C. Samson, “Non-robustness of continuous homogeneous stabilizers for affine control systems”, Proc. 37th IEEE Conf. on Decision and Control, 855–860 (1999).
• [22] Z.-P. Jiang, “Robust exponential regulation of nonholonomic systems with uncertainties”, Automatica 36 (2), 189–209 (2000).
• [23] D. Pazderski, B. Krysiak, and K. Kozłowski, “A comparison study of discontinuous control algorithms for three-link nonholonomic manipulator”, Lecture Notes in Control and Inform. Sci. Robot Motion Control: Recent Developments 396, 35–44 (2012).
• [24] I. Dulęba, Algorithms of Motion Planning for Nonholonomic Robots, Publishing House of Wrocław University of Technology, Wrocław, 1998, (in Polish).
• [25] S. M. LaValle, Planning Algorithms. Cambridge University Press, Cambridge, UK, 2006.
• [26] O. Khatib, “Real-time obstacle avoidance for manipulators and mobile robots”, Int. J. Robot. Res. 5 (1), 90–98 (1986).
• [27] D. Koditschek, “Exact robot navigation by means of potential functions: Some topological considerations”, Proc. IEEE Int. Conf. Robot. and Autom., 1–6 (1987).
• [28] E. Rimon and D.E. Koditschek, “Exact robot navigation using artificial potential fields”, IEEE Trans. Robot. and Autom. 8 (5), 501–518 (1992).
• [29] T. Urakubo, K. Okuma, and Y. Tada, “Feedback control of a two wheeled mobile robot with obstacle avoidance using potential functions”, Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 2428–2433 (2004).
• [30] W. Kowalczyk, M. Michałek, and K. Kozłowski, “Trajectory tracking control with obstacle avoidance capability for unicycle-like mobile robot”, Bull. Pol. Ac.: Tech. 60 (3), 537–546 (2012).
• [31] J. Kim and P. Khosla. “Real-time obstacle avoidance using harmonic potential functions”, IEEE Trans. Robot. Autom. 8 (3), 338–349 (1992).
• [32] S. Waydo and R. M. Murray, “Vehicle motion planning using stream functions”, Proc. IEEE Int. Conf. Robot. and Autom., 2484–2491 (2003).
• [33] R. Soukieh, I. Shames, and B. Fidan. “Obstacle avoidance of non-holonomic unicycle robots based on fluid mechanical mod-18 Bull. Pol. Ac.: Tech. XX(Y) 2016 Application of transverse functions eling”, Proc. European Control Conf., 3269–3274 (2009).
• [34] P. Szulczyński, D. Pazderski, and K. Kozłowski, “Obstacle avoidance and trajectory tracking using fluid-based approach in 2D space”, Lecture Notes in Control and Inform. Sci. Robot Motion and Control 2011 422, 293–304 (2012).
• [35] S. Akishita, S. Kawamura, and K Hayashi. “Laplace potential for moving obstacle avoidance and approach of a mobile robot”, Proc. Japan-USA Symposium on Flexible Automation/A Pacific Rim Conference, 139–142 (1990).
• [36] C.I. Connolly, J.B. Burns, and R. Weiss, “Path planning using Laplace’s equation”, Proc. IEEE Int. Conf. on Robot. Autom., 2102–2106 (1990).
• [37] D. Panagou, H.G. Tanner, and K.J. Kyriakopoulos, “Dipole-like fields for stabilization of systems with Pfaffian constraints”, Proc. IEEE Int. Conf. Robot. Autom., 4499–4504 (2010).
• [38] S. Mastellone, D.M. Stipanović, C.R. Graunke, K.A. Intlekofer, and M.W. Spong, “Formation control and collision avoidance for multi-agent non-holonomic systems: Theory and experiments”, Int. J. Robot. Res. 27 (1), 107–126 (2008).
• [39] D. Panagou. “Dipole-like fields for stabilization of systems with Pfaffian constraints”, Proc. IEEE Int. Conf. Robot. and Autom., 2513 – 2518 (2014).
• [40] E.J. Rodríguez-Seda, C. Tang, M.W. Spong, and D.M. Stipanović, “Trajectory tracking with collision avoidance for nonholonomic vehicles with acceleration constraints and limited sensing”, Int. J. Robot. Res. 33 (12), 1569–1592 (2014).
• [41] G. Artus, P. Morin, and C. Samson, “Tracking of an omnidirectional target with a unicycle-like robot: control design and experimental results”, Research Report INRIA 4849, INRIA, 2003.
• [42] D. Pazderski, D.K. Waśkowicz, and K. Kozłowski, “Motion control of vehicles with trailers using transverse function approach”, J. Intell. Robotic Syst. 77 (3‒4), 457–479 (2015).
• [43] P. Morin and C. Samson, “Practical stabilization of driftless systems on Lie groups: the transverse function approach”, IEEE Trans. Autom. Control 48 (9), 1496–1508 (2003).
• [44] H. Hermes. “Nilpotent and high-order approximations of vector field systems”, SIAM Rev. 33 (2), 238–264 (1991).
• [45] R. Volpe and P. Khosla, “Artificial potentials with elliptical isopotential contours for obstacle avoidance”, Proc. 26th IEEE Conf. Decision and Control, 180–185 (1987).
• [46] K. Kozłowski, W. Kowalczyk, B. Krysiak, M. Kiełczewski, and T. Jedwabny, “Modular architecture of the multi-robot system for teleoperation and formation control purposes”, In Proc. 9th Int. Workshop Robot Motion and Control, 19–24 (2013).
• [47] A.H. Barr, “Superquadrics and angle-preserving transformations”, IEEE Comput. Graph. Appl. 1 (1), 11–23 (1981).

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.