Advertisement

A high-performance control algorithm based on a curvature-dependent decoupled planning approach and flatness concepts for non-holonomic mobile robots

  • Oussama BoutalbiEmail author
  • Khier Benmahammed
  • Khadidja Henni
  • Boualem Boukezata
Original Research Paper
  • 36 Downloads

Abstract

This paper proposes a high-performance control strategy for an efficient manipulation of non-holonomic mobile robots in environments cluttered with static obstacles. Firstly, and based on the decoupled planning approach, a new algorithm for fast and safe motions planning is introduced. This algorithm defines the robot path as a sequence of smoothly interpolated functions using (\(\eta ^3\)) splines and then assigns a suitable curvature-dependent smooth motion profile to describe the robot velocity along such path. In order to achieve fast motions which fulfill all system constraints, the velocity profile is defined as a chain of local profiles smoothly linked together. Each of the local profiles is defined as a smooth limited-jerk function, which is obtained by applying a moving average FIR filter to a classic limited-acceleration profile. The appropriate bounds on velocities and accelerations of trapezoidal acceleration profiles are fixed according to the physical limits of the robot and the maximum bounds on the curvature in the corresponding path segment. The boundary conditions of the local profiles are assigned to ensure that the robot moves from its starting position without stopping until it reaches the goal configuration. Once the motion reference trajectories are obtained, a robust flatness-based feedback controller was defined to ensure the robust and the accurate execution of the planned tasks. Practical tests, using the P3DX model, have been reported to evaluate the performances of the proposed control strategy.

Keywords

Constrained motion optimization Curvature-dependent decoupled trajectory planning approach Non-holonomic mobile robots Robust flatness feedback control 

Notes

References

  1. 1.
    Béarée R, Olabi A (2013) Dissociated jerk-limited trajectory applied to time-varying vibration reduction. Robot Comput-Integrated Manuf 29(2):444–453.  https://doi.org/10.1016/j.rcim.2012.09.014 Google Scholar
  2. 2.
    Biagiotti L, Melchiorri C (2012) FIR filters for online trajectory planning with time- and frequency-domain specifications. Control Eng Pract 20(12):1385–1399.  https://doi.org/10.1016/j.conengprac.2012.08.005 Google Scholar
  3. 3.
    Blajer W, Kołodziejczyk K (2007) Motion planning and control of gantry cranes in cluttered work environment. IET Control Theory Appl 1(5):1370–1379Google Scholar
  4. 4.
    Braghin F, Cheli F, Melzi S, Sabbioni E (2008) Race driver model. Comput Struct 86(13–14):1503–1516.  https://doi.org/10.1016/j.compstruc.2007.04.028 Google Scholar
  5. 5.
    Campion G, Chung W (2008) Wheeled robots. In: Siciliano B, Khatib O (eds) Springer handbook of robotics. Springer, Berlin, pp 391–410Google Scholar
  6. 6.
    Choset HM, Lynch KM, Hutchinson S, Kantor GA, Burgard W, Kavraki LE, Thrun S (2006) Principles of robot motion, theory, algorithms and implementations. Robotica 24(02):271.  https://doi.org/10.1017/S0263574706212803 zbMATHGoogle Scholar
  7. 7.
    Fliess M, Levine J, Martin P, Rouchon P (1993) On differentially flat nonlinear systems. In: IFAC Symposia series, number 7, pp 159–163. ISBN 0080419011Google Scholar
  8. 8.
    Fritscht FN, Carlson RE (1980) Monotone piecewise cubic interpolation*. SIAM J Numer Anal 17(2):238–246.  https://doi.org/10.1137/0717021 MathSciNetzbMATHGoogle Scholar
  9. 9.
    Gasparetto A, Boscariol P, Lanzutti A, Vidoni R (2012) Trajectory planning in robotics. Math Comput Sci 6(3):269–279.  https://doi.org/10.1007/s11786-012-0123-8 MathSciNetGoogle Scholar
  10. 10.
    Gonzalez D, Pérez J, Milanés V, Nashashibi F (2016) A review of motion planning techniques for automated vehicles. IEEE Trans Intell Transp Syst 17(4):1135–1145.  https://doi.org/10.1109/TITS.2015.2498841 Google Scholar
  11. 11.
    Hagenmeyer V, Delaleau E (2003) Robustness analysis of exact feedforward linearization based on differential flatness. Automatica 39:1941–1946.  https://doi.org/10.1016/S0005-1098(03)00215-2 MathSciNetzbMATHGoogle Scholar
  12. 12.
    Khalil W, Dombre E (2000) Modeling identification and control of robots. Butterworth-Heinemann, OxfordzbMATHGoogle Scholar
  13. 13.
    Kim Y, Kim BK (2017) Time-optimal trajectory planning based on dynamics for differential-wheeled mobile robots with a geometric corridor. IEEE Trans Ind Electron 64(7):5502–5512Google Scholar
  14. 14.
    Klančar G, Zdešar A, Blažič S, Škrjanc I (2017) Wheeled mobile robotics: from fundamentals towards autonomous systems’. Butterworth-Heinemann, OxfordGoogle Scholar
  15. 15.
    Lambrechts P, Boerlage M, Steinbuch M (2005) Trajectory planning and feedforward design for electromechanical motion systems. Control Eng Pract 13(2):145–157.  https://doi.org/10.1016/j.conengprac.2004.02.010 Google Scholar
  16. 16.
    Laumond J-P (1998) Robot motion planning and control. Springer, Berlin, Heidelberg.  https://doi.org/10.1007/BFb0036069. ISBN 3540762191
  17. 17.
    Levant A (1998) Robust exact differentiation via sliding mode technique. Automatica 34(3):379–384.  https://doi.org/10.1016/S0005-1098(97)00209-4 MathSciNetzbMATHGoogle Scholar
  18. 18.
    Liu GH, Wong YS, Zhang YF, Loh HT (2002) Adaptive fairing of digitized point data with discrete curvature. Comput Aided Des 34(4):309–320.  https://doi.org/10.1016/S0010-4485(01)00091-4 Google Scholar
  19. 19.
    Lo Bianco CG, Gerelli O (2010) Generation of paths with minimum curvature derivative with \(\eta \)3-splines. IEEE Trans Autom Sci Eng 7(2):249–256.  https://doi.org/10.1109/TASE.2009.2023206 Google Scholar
  20. 20.
    Luviano-Juárez A, Cortés-Romero J, Sira-Ramírez H (2014) Trajectory tracking control of a mobile robot through a flatness-based exact feedforward linearization scheme. J Dyn Syst Meas Control 137(5):051001.  https://doi.org/10.1115/1.4028872 Google Scholar
  21. 21.
    Oriolo G, De Luca A, Vendittelli M (2002) WMR control via dynamic feedback linearization: design, implementation, and experimental validation. IEEE Trans Control Syst Technol 10(6):835–852.  https://doi.org/10.1109/TCST.2002.804116 Google Scholar
  22. 22.
    Piazzi A, Lo Bianco CG, Romano M (2007) Splines for the smooth path generation of wheeled mobile robots. IEEE Trans Robot 23(5):1089–1095.  https://doi.org/10.1109/TRO.2007.903816 Google Scholar
  23. 23.
    Ping R, Chan M, Stol KA, Roger Halkyard C (2013) Annual reviews in control: review of modelling and control of two-wheeled robots. Annu Rev Control 37(1):89–103.  https://doi.org/10.1016/j.arcontrol.2013.03.004 Google Scholar
  24. 24.
    Shin KG, Mckay ND (1985) Minimum-time control of robotic manipulators with geometric path constraints. IEEE Trans Autom Control 30(6):531–541.  https://doi.org/10.1109/TAC.1985.1104009 zbMATHGoogle Scholar
  25. 25.
    Veslin E, Slama J, Suell Dutra M, Lengerke O (2011) Motion planning on mobile robots using differential flatness. IEEE Latin Am Trans 9(7):1006–1011.  https://doi.org/10.1109/TLA.2011.6129695 Google Scholar
  26. 26.
    Siciliano B, Sciavicco L, Villani L, Oriolo G (2008) Robotics: modelling, planning and control, 1st edn. Springer, LondonGoogle Scholar
  27. 27.
    Yang H, Guo M, Xia Y, Cheng L (2018) Trajectory tracking for wheeled mobile robots via model predictive control with softening constraints. IET Control Theory Appl 12:206–214.  https://doi.org/10.1049/iet-cta.2017.0395 MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Oussama Boutalbi
    • 1
    Email author
  • Khier Benmahammed
    • 1
  • Khadidja Henni
    • 2
  • Boualem Boukezata
    • 3
  1. 1.Intelligent Systems Laboratory, Electronics DepartmentFerhat Abbas Setif 1 UniversitySetifAlgeria
  2. 2.LICEF Research CenterTELUQ UniversityMontrealCanada
  3. 3.Laboratory of Power Quality in Electrical Networks (QUERE)Electrical Engineering, Ferhat Abbas Setif 1 University SetifAlgeria

Personalised recommendations