iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://link.springer.com/article/10.1134/S000511792206008X
Safe Interval Path Planning and Flatness-Based Control for Navigation of a Mobile Robot among Static and Dynamic Obstacles | Automation and Remote Control Skip to main content
Springer Nature Link
Log in

Safe Interval Path Planning and Flatness-Based Control for Navigation of a Mobile Robot among Static and Dynamic Obstacles

  • THEMATIC ISSUE
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

In this work we study a navigation problem for a nonholonomic differential drive robot operating in the environment with static and dynamic obstacles. We present a multi-phase approach to solve it, which is based on heuristic search to tackle the trajectory planning problem and specific methods of the control theory to solve the path following problem. Results of the experimental evaluation show that the suggested controller is one order of magnitude faster than the widely used in robotics Model-Predictive Control (MPC) and is capable of accurately following the reference trajectory. On the planning side we show that the suggested planner is scalable and is able to plan in reasonable time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

Similar content being viewed by others

REFERENCES

  1. McGuire, K.N., de Croon, G.C.H.E., and Tuyls, K.A., Comparative study of bug algorithms for robot navigation, Rob. Auton. Syst., 2019, vol. 121, p. 103261.

    Article  Google Scholar 

  2. Berg, J. et al., Reciprocal \( n \)-body collision avoidance, in Robotics Research, Berlin–Heidelberg: Springer, 2011, pp. 3–19.

  3. Koenig, S. and Likhachev, M., D* Lite, 18th Natl. Conf. Artif. Intell., 2002„ pp. 476–483.

  4. Phillips, M. and Likhachev, M., SIPP: safe interval path planning for dynamic environments, 2011 IEEE Int. Conf. Rob. Autom., IEEE, 2011, pp. 5628–5635.

  5. Mayne, D.Q. et al., Constrained model predictive control: stability and optimality, Automatica, 2000, vol. 36, no. 6, pp. 789–814.

    Article  MathSciNet  Google Scholar 

  6. Bocharov, A.V. and Verbovetskii, A.M., Simmetrii i zakony sokhraneniya matematicheskoi fiziki (Symmetries and Conservation Laws of Mathematical Physics), Moscow: Faktorial, 2005.

    Google Scholar 

  7. Likhachev, M. and Ferguson, D., Planning long dynamically feasible maneuvers for autonomous vehicles, Int. J. Rob. Res., 2009, vol. 28, no. 8, pp. 933–945.

    Article  Google Scholar 

  8. Sakcak, B. et al., Sampling-based optimal kinodynamic planning with motion primitives, Auton. Rob., 2019, vol. 43, no. 7, pp. 1715–1732.

    Article  Google Scholar 

  9. Pivtoraiko, M. and Kelly, A., Generating near minimal spanning control sets for constrained motion planning in discrete state spaces, 2005 IEEE/RSJ Int. Conf. Intell. Rob. Syst., IEEE, 2005, pp. 3231–3237.

  10. Hwan Jeon, J., Karaman, S., and Frazzoli, E., Anytime computation of time-optimal off-road vehicle maneuvers using the RRT, 2011 50th IEEE Conf. Decis. Control & Eur. Control Conf., IEEE, 2011, pp. 3276–3282.

  11. Webb, D.J. and Van Den Berg, J., Kinodynamic RRT*: asymptotically optimal motion planning for robots with linear dynamics, 2013 IEEE Int. Conf. Rob. Autom., IEEE, 2013, pp. 5054–5061.

  12. Flores, M.E. and Milam, M.B., Trajectory generation for differentially flat systems via NURBS basis functions with obstacle avoidance, 2006 Am. Control Conf., IEEE, 2006, pp. 5769–5775.

  13. Rufli, M., Ferguson, D., and Siegwart, R., Smooth path planning in constrained environments, 2009 IEEE Int. Conf. Rob. Autom., IEEE, 2009, pp. 3780–3785.

  14. Silver, D., Cooperative pathfinding, Proc. AAAI Conf. Artif. Intell. Interact. Digital Entertainment, 2005, vol. 1, no. 1, pp. 117–122.

  15. Isidori, A., Nonlinear Control Systems, Berlin: Springer, 1995.

    Book  Google Scholar 

  16. Khalil, H.K., Nonlinear Systems, Upper Saddle River, NJ: Prentice Hall, 2002, 3rd ed.

  17. Utkin, V.I., Sliding mode control design principles and applications to electric drives, IEEE Trans. Ind. Electron., 1993, vol. 40, no. 1, pp. 23–36.

    Article  Google Scholar 

  18. Yu, S. et al., MPC for path following problems of wheeled mobile robots, IFAC-PapersOnLine, 2018, vol. 51, no. 20, pp. 247–252.

    Article  Google Scholar 

  19. Fliess, M. et al., Flatness and defect of non-linear systems: introductory theory and examples, Int. J. Control, 1995, vol. 61, no. 6, pp. 1327–1361.

    Article  MathSciNet  Google Scholar 

  20. Bascetta, L., Arrieta, I.M., and Prandini, M., Flat-RRT*: a sampling-based optimal trajectory planner for differentially flat vehicles with constrained dynamics, IFAC-PapersOnLine, 2017, vol. 50, no. 1, pp. 6965–6970.

    Article  Google Scholar 

  21. Sahoo, S.R. and Chiddarwar, S.S., Mobile robot control using bond graph and flatness based approach, Procedia Comput. Sci., 2018, vol. 133, pp. 213–221.

    Article  Google Scholar 

  22. Chetverikov, V.N., Flatness of dynamically linearizable systems, Differ. Equations, 2004, vol. 40, no. 12, pp. 1747–1756.

    Article  MathSciNet  Google Scholar 

  23. Belinskaya, Yu.S. and Chetverikov, V.N., Covering method for terminal control with regard of constraints, Differ. Equations, 2014, vol. 50, no. 12, pp. 1632–1642.

    Article  MathSciNet  Google Scholar 

  24. Tang, C.P., Differential flatness-based kinematic and dynamic control of a differentially driven wheeled mobile robot, 2009 IEEE Int. Conf. Rob. Biomimetics (ROBIO), IEEE, 2009, pp. 2267–2272.

  25. Andersson, O. et al., Receding-horizon lattice-based motion planning with dynamic obstacle avoidance, 2018 IEEE Conf. Decis. Control (CDC), IEEE, 2018, pp. 4467–4474.

  26. Belinskaya, Y.S. and Chetverikov, V.N., Covering method for point-to-point control of constrained flat systems, IFAC-PapersOnLine, 2015, vol. 48, no. 11, pp. 924–929.

    Article  Google Scholar 

  27. Yap, P., Grid-based path-finding, Conf. Can. Soc. Comput. Studies Intell., Berlin–Heidelberg: Springer, 2002, pp. 44–55.

  28. Hart, P.E., Nilsson, N.J., and Raphael, B., A formal basis for the heuristic determination of minimum cost paths, IEEE Trans. Syst. Sci. Cybern., 1968, vol. 4, no. 2, pp. 100–107.

    Article  Google Scholar 

  29. Cohen, L. et al., Optimal and bounded-suboptimal multi-agent motion planning, 12th Annu. Symp. Comb. Search, 2019, pp. 44–51.

  30. Sturtevant, N.R., Benchmarks for grid-based pathfinding, IEEE Trans. Comput. Intell. AI Games, 2012, vol. 4, no. 2, pp. 144–148.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia

    K. S. Yakovlev, J. S. Belinskaya & D. A. Makarov

  2. AIRI, Moscow, 121165, Russia

    A. A. Andreychuk

  3. RUDN University, Moscow, 117198, Russia

    A. A. Andreychuk

Authors
  1. K. S. Yakovlev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Andreychuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. S. Belinskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. A. Makarov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to K. S. Yakovlev, A. A. Andreychuk, J. S. Belinskaya or D. A. Makarov.

Additional information

The code is open sourced: bit.ly/3mEBK59.

The video-demo can be found at youtu.be/cYm3Q1tHRnU.

Translated by The Author(s)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yakovlev, K.S., Andreychuk, A.A., Belinskaya, J.S. et al. Safe Interval Path Planning and Flatness-Based Control for Navigation of a Mobile Robot among Static and Dynamic Obstacles. Autom Remote Control 83, 903–918 (2022). https://doi.org/10.1134/S000511792206008X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S000511792206008X

Keywords

Search

Navigation