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An Ergodic Selection Method for Kinematic Configurations in Autonomous, Flexible Mobile Systems

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Abstract

Selecting suitable kinematic configurations for autonomous, flexible mobile systems remains a prominent challenge in various applications of trajectory tracking, including path solver planning, redundant robot control, grasping, and robotic system design. Current techniques based on the inverse kinematic problem suggest that the classic manipulability index referencing the local frame’s velocity is sufficient to infer the behavior of the kinematic constraints. Successful constraint inference then allows the control strategy to be updated when the performance becomes suboptimal with respect to the target path. However, these approaches become deficient when the joint space is flexible, making it necessary to explicitly account for the structural parameters of the mobile system (e.g., number of joints, mass, wheel size, and links) in order to infer the behavior of the kinematic constraints. Instead, the dynamic confined space of velocities (DCSV), initially proposed by the author, suggests a Markovian process relating the local frame’s velocity, kinematic constraint violations, and implicit flexibility. Hence, the present paper analyzes the DCSV’s behavior and proposes an offline method to reconfigure the structural parameters, thus demonstrating how the DCSV’s behavior can be used to reduce the violation of kinematic constraints. To this end, two lemmas and one theorem provide a new viewpoint regarding manipulability by using invariant and ergodic measurement conditions corresponding to the kinematic constraint evolution to compose DCSV-based selection criteria. The results are based on tracking problems and path-planning solvers in which the manipulability of a kinematic configuration is improved by updating the configuration according to optimal paths.

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References

  1. Mark, W.: Spong. An historical perspective on the control of robotic manipulators. Ann. Rev. Control Robot Auton. Syst. 5(1), 1–31 (2022)

  2. Tahk, M., Speyer, J.L.: Target tracking problems subject to kinematic constraints. IEEE Trans. Autom. Control 35(3), 324–326 (1990)

    Article  MATH  Google Scholar 

  3. Alouani, A.T., Blair, W.D.: Use of a kinematic constraint in tracking constant speed, maneuvering targets. IEEE Trans. Autom. Control 38(7), 1107–1111 (1993)

    Article  MathSciNet  Google Scholar 

  4. Choi, B.W., Won, J.H., Chung, J.M.: Evaluation of dexterity measures for a 3-link planar redundant manipulator using constraint locus. IEEE Trans. Robot. Autom. 11(2), 282–285 (1995)

    Article  Google Scholar 

  5. Duan, Z., Li, X.R.: Modeling of target motion constrained on straight line. IEEE Trans. Aerosp. Electron. Syst. 52(2), 548–562 (2016)

    Article  Google Scholar 

  6. Li, K., Kirubarajan, T., Zhou, G.: State estimation with implicit constraints of circular trajectory using pseudomeasurements. IEEE Trans. Aerosp. Electron.Syst. 56(6), 4406–4425 (2020)

    Article  Google Scholar 

  7. Nahon, M.A., Angeles, J.: Real-time force optimization in parallel kinematic chains under inequality constraints. IEEE Trans. Robot. Autom. 8(4), 439–450 (1992)

    Article  Google Scholar 

  8. Cui, L., Jian S. Dai.: Reciprocity-based singular value decomposition for inverse kinematic analysis of the metamorphic multifingered hand. J. Mech. Robot. 4(3) (2012)

  9. Chong, Z., Xie, F., Liu, X.-J., Wang, J., Li, P.: Worst case identification based topology optimization of a 2-DoF hybrid robotic arm. Int. J. Intell. Robot. Appl. 4(2), 136–148 (2020)

    Article  Google Scholar 

  10. Sunkara, V., Chakravarthy, A., Ghose, D.: Collision avoidance of arbitrarily shaped deforming objects using collision cones. IEEE Robot. Autom. Lett. 4(2), 2156–2163 (2019)

    Article  Google Scholar 

  11. Zheng, Y., Ming C. Lin, Manocha, D.: On computing reliable optimal grasping forces. IEEE Trans. Robot. 28(3), 619–633 (2012)

  12. Cortez, W.S., Oetomo, D., Manzie, C., Choong, P.: Control barrier functions for mechanical systems: Theory and application to robotic grasping. IEEE Trans. Control Syst. Technol. 29(2), 530–545 (2021)

    Article  Google Scholar 

  13. Hassan, M., Khajepour, A.: Analysis of bounded cable tensions in cable-actuated parallel manipulators. IEEE Trans. Robot. 27(5), 891–900 (2011)

    Article  Google Scholar 

  14. Cibicik, A., Egeland, O.: Kinematics and dynamics of flexible robotic manipulators using dual screws. IEEE Trans. Robot. 37(1), 206–224 (2021)

    Article  Google Scholar 

  15. Wang, D., Low, C.B.: Modeling and analysis of skidding and slipping in wheeled mobile robots: Control design perspective. IEEE Trans. Robot. 24(3), 676–687 (2008)

    Article  Google Scholar 

  16. Dai, S.-L., He, S., Lin, H.: Transverse function control with prescribed performance guarantees for underactuated marine surface vehicles. Int. J. Robust Nonlinear Control 29(5), 1577–1596 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  17. D’Andréa-Novel, B., Campion, G., Bastin, G.: Control of wheeled mobile robots not satisfying ideal velocity constraints: A singular perturbation approach. Int. J. Robust Nonlinear Control 5(4), 243–267 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  18. Peña Fernández, C.A., Cerqueira, J.J.F., Lima, A.M.N.: Nonlinear trajectory tracking controller for wheeled mobile robots by using a flexible auxiliary law based on slipping and skidding variations. Robot. Auton. Syst., 118, 231–250 (2019)

  19. Motte, I., Campion, G.: A slow manifold approach for the control of mobile robots not satisfying the kinematic constraints. IEEE Trans. Robot. Autom. 16(6), 875–880 (2000)

    Article  Google Scholar 

  20. Cui, L., Wang, H., Chen, W.: Trajectory planning of a spatial flexible manipulator for vibration suppression. Robot. Auton. Syst. 123 (2020)

  21. Pliego-Jiménez, J., Martínez-Clark, R., Cruz-Hernández, C., Arellano-Delgado, A.: Trajectory tracking of wheeled mobile robots using only cartesian position measurements. Autom. 133,(2021)

  22. Jiang, Z.-P.: Robust exponential regulation of nonholonomic systems with uncertainties. Autom. 36(2), 189–209 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  23. Tutsoy, O.: Cpg based rl algorithm learns to control of humanoid robot leg. Int. J. Robot. Autom. 30,(2) (2015)

  24. Tutsoy, O., Barkana, D.E., Colak, S.: Learning to balance an NAO robot using reinforcement learning with symbolic inverse kinematic. Trans. Inst. Meas. Control 39(11), 1735–1748 (2016)

    Article  Google Scholar 

  25. Zheng, C., Sane, S., Lee, K., Kalyanram, V., Lee, K.: Alpha-WaLTR: Adaptive wheel-and-leg transformable robot for versatile multiterrain locomotion. IEEE Trans. Robot., pages 1–18, 2

  26. Porta, J.M., Ros, L., Thomas, F., Torras, C.: A branchand-prune solver for distance constraints. IEEE Trans. Robot. 21(2), 176–187 (2005)

    Article  Google Scholar 

  27. Borras, J., Thomas, F., Torras, C.: On deltatransforms. IEEE Trans. Robot. 25(6), 1225–1236 (2009)

    Article  Google Scholar 

  28. Corrado Guarino Lo Bianco Gerelli, O.: Online trajectory scaling for manipulators subject to high-order kinematic and dynamic constraints. IEEE Trans. Robot., 27(6), 1144–1152 (2011)

  29. Nunzio A. Letizia, Salamat, B., M.Tonello, A.: A novel recursive smooth trajectory generation method for unmanned vehicles. IEEE Trans. Robot. 37(5), 1792–1805 (2021)

  30. Goncalves, V.M., Adorno, B.V., Crosnier, A., Fraisse, P.: Stable-by-design kinematic control based on optimization. IEEE Trans. Robot. 36(3), 644–656 (2020)

    Article  Google Scholar 

  31. Faroni, M., Beschi, M., Pedrocchi, N., Visioli, A.: Predictive inverse kinematics for redundant manipulators with task scaling and kinematic constraints. IEEE Trans. Robot. 35(1), 278–285 (2019)

    Article  Google Scholar 

  32. Antonelli, G.: Stability analysis for prioritized closed-loop inverse kinematic algorithms for redundant robotic systems. IEEE Trans. Robot. 25(5), 985–994 (2009)

    Article  Google Scholar 

  33. Zhang, Y., Li, S., Zou, J., Khan, A.H.: A passivity-based approach for kinematic control of manipulators with constraints. IEEE Trans. Ind. Inform. 16(5), 3029–3038 (2020)

    Article  Google Scholar 

  34. Murray, R.M., Li, Z. Sastry, S.S.: A Mathematical Introduction to Robotic Manipulation. CRC Press LLC, First edition (1994)

  35. Peña Fernández, C.A., Cerqueira, J.J.F., Lima, A.M.N.: Trajectory control of wheeled mobile robots not satisfying ideal velocity constraints by using slipping and skidding variations: A singular perturbation approach. In Commun. Comput Inform. Sci., pages 74–95. Springer Berlin Heidelberg (2015)

  36. Peña Fernández, C.A.: Control of flexible manipulator robots based on dynamic confined space of velocities: Dynamic programming approach. J. Robot. Control 3(06) (2022)

  37. Yang, H., Wang, S., Zuo, Z., Li, P.: Trajectory tracking for a wheeled mobile robot with an omnidirectional wheel on uneven ground. IET Control Theory & Appl. 14(7), 921–929 (2020)

    Article  MathSciNet  Google Scholar 

  38. Korayem, M.H., Ghobadi, N., Dehkordi, S.F.: Designing an optimal control strategy for a mobile manipulator and its application by considering the effect of uncertainties and wheel slipping. Optim. Control Appl. Methods 42(5), 1487–1511 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  39. Gao, X., Yan, L., Gerada, C.: Modeling and analysis in trajectory tracking control for wheeled mobile robots with wheel skidding and slipping: Disturbance rejection perspective. Actuators 10(9), 222 (2021)

    Article  Google Scholar 

  40. Peña Fernández, C.A.: Oriented manifold-based error tracking control for nonholonomic wheeled autonomous vehicles on lie group for curvilinear approach. Lat. Am. J. Dev. 3(6), 3608–3626 (2021)

    Article  Google Scholar 

  41. Liu, S., Liu, K., Zhong, Z., Yi, J., Aliev, H.: A novel wheeled mobile robots control based on robust hybrid controller: Mixed h2/h\(\infty \) and predictive algorithm approach. J. King Saud Univ. - Comput. Inform. Sci. (2021)

  42. Peña Fernández, C.A., Cerqueira, J.J.F., Lima, A.M.N.: Control of nonholonomic mobile bases supported by measuring of the slipping and skidding variations. In IEEE Proceedings of the 2014 Joint Conference on Robotics: SBR-LARS Robotics Symposium and Robocontrol, São Carlos, Brazil, 2014. IEEE Comput. Soc. (2014)

  43. Campion, G., Bastin, G., D’Andréa-Novel, B.: Structural Properties and Classification of Kinematic and Dynamic Models of Wheeled Mobile Robots. IEEE Trans. Robot. Autom. 12(1), 47–62 (1996)

    Article  Google Scholar 

  44. Kevin M. Lynch, Frank Chongwoo Park.: Modern Robotics: Mechanics, Planning, and Control (2017)

  45. Spong, M., Khorasani, K., Kokotovic, P.: An integral manifold approach to the feedback control of flexible joint robots. IEEE J. Robot. Autom. 3(4), 291–300 (1987)

  46. Peña Fernández, C.A., Cerqueira, J.J.F., Lima, A.M.N.: Control of wheeled mobile robots singularly perturbed by using slipping and skidding variations: Curvilinear coordinates approach (part i). In Proc. 11th IFAC Symp. Robot Control (2015)

  47. Peña Fernández, C.A., Cerqueira, J.J.F., Lima, A.M.N.: Control of wheeled mobile robots singularly perturbed by using slipping and skidding variations: curvilinear coordinates approach (part ii). In Proc. 11th IFAC Symp. Robot Control (2015)

  48. Peña Fernández, C.A.: Stabilizing model predictive control for wheeled mobile robots with linear parametervarying and different time-scales. In Latin American Robotic Symposium, 2018 Brazilian Symposium on Robotics (SBR) and 2018 Workshop on Robotics in Education (WRE). IEEE (2018)

  49. Kokotovic, P.V., Khalil, H.K.: Singular Perturbations in Syst. Control. IEEE Press, New York, N.Y., USA (1986)

    Google Scholar 

  50. Khalil, H.: Nonlinear Syst. Prentice Hall, New Jersey, N.Y., USA, Third edition (2002)

    Google Scholar 

  51. Barreto, J.C.L., Conceição, A.G.S., Dorea, C.E.T., Martinez, L., de Pieri, E.R.: Design and Implementation of Model-Predictive Control With Friction Compensation on an Omnidirectional Mobile Robot. IEEE/ASME Trans. Mechatron. 19(2), 467–476 (2014)

    Article  Google Scholar 

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Acknowledgements

The author would like to thank the Federal Institute of Bahia (IFBA) and the Technological Innovation Center (PIS/IFBA) for the research grant and financial support subject to Announcement n.01/2021-PIS/IFBA.

Funding

Announcement n.01/2021-PIS/IFBA and Research Procedure SEI n.23279.005450/2022-48.

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  1. Electrical Engineering Department and Technological Innovation Center of Federal Institute of Bahia, Salvador, Brazil

    C. A. Peña Fernández

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The single author contributed to the conception and design of the study. Material preparation and analysis were performed by C. A. Peña Fernández. The first draft of the manuscript was written by C. A. Peña Fernández. The single author read and approved the final manuscript.

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Correspondence to C. A. Peña Fernández.

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Peña Fernández, C.A. An Ergodic Selection Method for Kinematic Configurations in Autonomous, Flexible Mobile Systems. J Intell Robot Syst 109, 11 (2023). https://doi.org/10.1007/s10846-023-01933-z

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