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Minimum-Energy Trajectory Generation for Cornering with a Fixed Heading for Three-Wheeled Omni-Directional Mobile Robots

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Abstract

The minimum-energy trajectory generation problem of cornering with a fixed heading is solved for three-wheeled omni-directional mobile robots (TOMRs). To maximize the total operation time of a mobile robot with carried batteries having finite energy, we have chosen a practical cost function to be the total energy drawn from the batteries. Then, we formulate the minimum-energy trajectory generation problem of executing a cornering motion with a fixed heading for TOMRs with given dynamics including actuator motors. The optimal control theory using a Hamiltonian function and a numerical method are used to obtain the minimum-energy trajectory, which gives the velocity profile in analytic form. Performance analyses are conducted with various simulations and the consumed energy using obtained minimum-energy trajectory is compared with a typical conventional trajectory with a trapezoidal velocity profile, which reveals that an energy savings of up to 18.7 % is achieved. To validate the actual performance of our trajectory, we implemented and tested an accurate trajectory following system which utilizes a resolved acceleration controller.

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References

  1. Francois, G.P., Stephen, M.K.: A new family of omnidirectional and holonomic wheeled platforms for mobile robots. IEEE Trans. Robot. Autom. 10(4), 480–489 (1994)

    Article  Google Scholar 

  2. Diegel, O., Badve, A., Bright, G., Potgieter, J.: Improved mecanum wheel design for omni-directional robots. In: Proceedings of 2002 Australasian Conference on Robotics and Automation, pp. 117–121 (2002)

  3. Salih, J.E.M., Rizon, M., Yaacob, S.: Designing omnidirectional mobile robot with mecanum wheel. Am. J. Appl. Sci. 3(5), 1831–1835 (2006)

    Article  Google Scholar 

  4. Watanabe, K.: Control of an omnidirectional mobile robot. In: Proceeding of the International Conference on Knowledge-Based Intelligent Electronic Systems, pp. 51–60 (1998)

  5. Watanabe, K., Shiraishi, Y., Tzafestas, S.G., Tang, J., Fukuda, T.: Feedback control of an omnidirectional autonomous platform for mobile service robots. J. Intell. Robot. Syst. 22(3–4), 315–330 (1998)

    Article  Google Scholar 

  6. Kalmar-Nagy, T., D’Andrea, R., Ganguly, P.: Near-optimal dynamic trajectory generation and control of an omnidirectional vehicle. Robot. Auton. Syst. 46(1), 47–64 (2004)

    Article  Google Scholar 

  7. Kim, K.B., Kim, B.K.: Minimum-time trajectory for three-wheeled omni-directional mobile robots following a bounded curvature path with a referenced heading profile. IEEE Trans. Robot. 27(4), 800–808 (2011)

    Article  Google Scholar 

  8. Leng, C., Cao, Q., Huang, Y.: A motion planning method for omni-directional mobile robot based on the anisotropic characteristics. Int. J. Adv. Robot. Syst. 5(4), 327–340 (2008)

    Google Scholar 

  9. Wu, J., Williams II, R.L., Lew, J.: Velocity and acceleration cones for kinematics and dynamic constraints on omni-directional mobile robots. J. Dyn. Syst. Meas. Control. 128(4), 788–799 (2006)

    Article  Google Scholar 

  10. Balakrishna, R., Ghosal, A.: Modeling of slip for wheeled mobile robots. IEEE Trans. Robot. Autom. 11(1), 126–132 (1995)

    Article  Google Scholar 

  11. Mei, Y., Lu, Y.-H., Hu, Y.C., Lee, C.S.G.: Energy-efficient motion planning for mobile robots. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 4344–4349 (2004)

  12. Rojas, R., Gloye Forster, A.: Holonomic Control of a Robot with an Omni-Directional Drive, Kunstliche Intelligenz. BottcherIT Verlag, Bremen (2006)

  13. Muir, P.F., Neuman, C.P.: Resolved motion rate and resolved acceleration servo-control of wheeled mobile robots. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1133–1140 (1990)

  14. Byun, K.-S., Song, J.-B.: CVT control of an omnidirectional mobile robot with steerable omnidirectional wheels for energy efficient drive. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 503–508 (2003)

  15. Ribeiro, F., Moutinho, I., Silva, P., Fraga, C., Pereira, N.: Three Omni-Directional Wheels Control on a Mobile Robot, Control 2004. University of Bath, UK (2004)

  16. Huang, H.-C., Tsai, C.-C.: FPGA implementation of an embedded robust adaptive controller for autonomous omnidirectional mobile platform. IEEE Trans. Ind. Electron. 56(5), 1604–1616 (2009)

    Article  Google Scholar 

  17. Tsai, C.-C., Huang, H.-C., Lin, S.-C.: FPGA-based parallel DNA algorithm for optimal configurations of an omnidirectional mobile service robot performing fire extinguishment. IEEE Trans. Ind. Electron. 58(3), 1016–1026 (2011)

    Article  Google Scholar 

  18. Huang, H.-C. Tsai, C.-C.: Adaptive robust control of an omnidirectional mobile platform for autonomous service robots in polar coordinates. J. Intell. Robot. Syst. 51(4), 439–460 (2008)

    Article  Google Scholar 

  19. Gawthrop, P.J., Ballance, D.J., Chen, W.H.: Optimal control of nonlinear systems: a predictive control approach. Automatica 39(4), 633–641 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  20. Ouhrouche, M., Chen, W.-H., Trzynadlowski, A.M.: Robust nonlinear predictive controller for permanent-magnet synchronous motors with an optimized cost function. IEEE Trans. Ind. Electron. 59(7), 2849–2858 (2012)

    Article  Google Scholar 

  21. Kim, H., Kim, B.K.: Minimum-energy trajectory planning and control on a straight line with rotation for three-wheeled omni-directional mobile robots. In: Proceedings of the IEEE International Conference on Intelligent Robots and Systems, pp. 3119–3124 (2012)

  22. Du Toit, N.E. Burdick, J.W.: Robot motion planning in dynamic, uncertain environments. IEEE Trans. Robot. 28(1), 101–115 (2012)

    Article  Google Scholar 

  23. Cowlagi, R.V., Tsiotras, P.: Hierarchical motion planning with dynamical feasibility guarantees for mobile robotic vehicles. IEEE Trans. Robot. 28(2), 379–395 (2012)

    Article  Google Scholar 

  24. Chu, K., Lee, M., Sunwoo, M.: Local path planning for off-road autonomous driving with avoidance of static obstacles. IEEE Trans. Intell. Transp. Syst. 13(4), 1599–1616 (2012)

    Article  Google Scholar 

  25. Bestaoui, Y.: An optimal velocity generation of a rear wheel drive tricycle along a specified path. In: Proceedings of the American Control Conference, pp. 2907–2911 (2000)

  26. Sergaki, E.S., Stavrakakis, G.S., Pouliezos, A.D.: Optimal robot speed trajectory by minimization of the actuator motor electromechanical losses. J. Intell. Robot. Syst. 33(2), 187–207 (2002)

    Article  MATH  Google Scholar 

  27. Kim, J., Yeom, H., Park, F.C., Park, Y.I., Kim, M.: On the energy efficiency of CVT-based mobile robots. In: Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, pp. 1539–1544 (2000)

  28. Leonhard, W.: Control of Electrical Drivers, 2nd edn. Springer (1996)

  29. Barili, A., Ceresa, M., Parisi, C.: Energy-saving motion control for an autonomous mobile robot. In: Proceedings of the IEEE International Symposium on Industrial Electronics, pp. 674–676 (1995)

  30. Corporation, E.-C.: DC Motors, Speed Control, Servo Systems, An Engineering Handbook. Electro-Craft Corporation, Hopkins, MN (1973)

  31. Scott, J., McLeish, J., Round, W.H.: Speed control with low armature loss for very small sensorless brushed DC motors. IEEE Trans. Ind. Electron. 56(4), 1223–1229 (2009)

    Article  Google Scholar 

  32. Margaris, N., Goutas, T., Doulgeri, Z., Paschali, A.: Loss minimization in DC drives. IEEE Trans. Ind. Electron. 38(5), 328–336 (1991)

    Article  Google Scholar 

  33. Tal, J.: The optimal design of incremental motion servo systems. In: Proceedings of the 2nd Annual Symposium on Incremental Motion Control Systems and Devices, pp. 72–76 (1973)

  34. Kwok, S.T., Lee, C.K.: Optimal velocity profile design in incremental servo motor systems based on a digital signal processor. In: Proceedings of the 16th Annual Conference of the IEEE Industrial Electronics Society, pp. 262–266 (1990)

  35. Trzynadlowski, A.M.: Energy optimization of a certain class of incremental motion DC drives. IEEE Trans. Ind. Electron. 35(1), 60–66 (1988)

    Article  Google Scholar 

  36. Kim, C.H., Kim, B.K.: Minimum-energy translational trajectory generation for differential-driven wheeled mobile robots. J. Intell. Robot. Syst. 49(4), 367–383 (2007)

    Article  Google Scholar 

  37. Kim, K.B., Kim, B.K.: Minimum-time straight-line trajectory for three-wheeled omni-directional mobile robots with voltage constraint. In: Proceedings of the 39th International Symposium on Robotics, pp. 755–760 (2008)

  38. Lewis, F.L., Syrmos, V.L.: Optimal Control, 2nd edn. Wiley (1995)

  39. Luh, J.Y.S., Walker, M.W., Paul, R.P.C.: Resolved-acceleration control of mechanical manipulators. IEEE Trans. Automat. Control 25(3), 468–474 (1980)

    Article  MATH  Google Scholar 

  40. Craig, J.J.: Introduction to Robotics, 2nd edn. Addison-Wesley (1989)

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  1. Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Republic of Korea

    Hongjun Kim & Byung Kook Kim

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  1. Hongjun Kim
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  2. Byung Kook Kim
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Correspondence to Hongjun Kim.

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Kim, H., Kim, B.K. Minimum-Energy Trajectory Generation for Cornering with a Fixed Heading for Three-Wheeled Omni-Directional Mobile Robots. J Intell Robot Syst 75, 205–221 (2014). https://doi.org/10.1007/s10846-013-9855-1

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  • DOI: https://doi.org/10.1007/s10846-013-9855-1

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