Modeling and trajectory tracking control of non-holonomic mobile robot with revolute-prismatic joints

Document Type : Research Article

Authors

Shahid Bahonar university of Kerman, Kerman

Abstract

One of the main topics in the field of robotics is the modeling and control of mobile robots in the trajectory tracking problem. In this paper, the kinematic and dynamic models of a manipulator connected by revolute-prismatic joints and installed in a non-holonomic wheeled mobile platform are first derived by applying the recursive Gibbs-Appell method. Indeed, by employing this dynamic methodology, one gets rid of the difficulties of Lagrange Multipliers that originate from non-holonomic constraints. Then, a nonlinear predictive approach is applied to design the kinematic and dynamic control laws to generate trajectory tracking control commands of the non-holonomic robot. In this method, the nonlinear responses of the mobile robot are predicted using the Taylor series. The optimal control laws are analytically developed by minimizing the difference between the predicted and the desired responses of the system outputs. The obtained control inputs from a multivariable kinematic controller in the first stage are then used as the desired values to be tracked by the dynamic controller. Finally, the results of numerical simulations are then presented to emphasize the ability of the proposed method in the mathematical modeling and simultaneous trajectory tracking control of the mobile base and end-effector of such complex robotic systems.

Keywords

Main Subjects

References

[1] O. Khatib, K. Yokoi, K. Chang, D. Ruspini, R. Holberg, A. Casal, A. Baader, Force strategies for cooperative tasks in multiple mobile manipulation systems, Robotics Research 148(2) (1996) 333-342.
[2] K. Thanjavur, R. Rajagopalan, Ease of dynamic modeling of wheeled mobile robots (WMRs) using Kane's approach, International Conference on Robotics and Automation, Albuquerque, New Mexico: IEEE, (1997) 2926-2931.
[3] H. G. Tanner, K.J. Kyriakopouos, Mobile manipulator modeling with Kane's approach, Robotica, 19(6) (2001) 675-690.
[4] M. H. Korayem, R. A. Esfeden, S. R. Nekoo, Path planning algorithm in wheeled mobile manipulators based on motion of arms, Journal of Mechanical Science and Technology, 29(4)(2015) 1753-1763.
[5] M. H. Korayem, S. R. Nekoo, The SDRE control of mobile base cooperative manipulators: Collision free path planning and moving obstacle avoidance, Robotics and Autonomous Systems, 86 (2016) 86-105.
[6] A. H. Korayem, S. R. Nekoo, M. H. Korayem, Optimal sliding mode control design based on the state-dependent Riccati equation for cooperative manipulators to increase dynamic load carrying capacity, Robotica, 37(2) (2019) 321-337.
[7] Q. Yu, I. M. Chen, A general approach to the dynamics of nonholonomic mobile manipulator systems, Journal of Dynamic Systems, Measurement, and Control, Transactions of the ASME, 124 (4) (2002) 512-521.
[8] M. Vukobratovic, V. Potkonjak, Applied dynamics and CAD of manipulation robots, Springer-Verlag, Berlin, (1985).
[9] A. F. Vereshchagin, Computer simulation of the dynamics of complicated mechanisms of robot-manipulators, Engineering Cybernetics, 12(6) (1974) 65-70.
[10] I. J. Rudas, A. Toth, Efficient recursive algorithm for inverse dynamics, Mechatronics, 3(2) (1993) 205-214.
[11] V. Mata, S. Provenzano, J. I. Cuadrado, F. Valero, Inverse Dynamic Problem in Robots using Gibbs-Appell Equations, Robotica, 20(1) (2002) 59-67.
[12] S. Provenzano, V. Mata, M. Ceccarelli, J. L. Suner, An algorithm for solving the inverse dynamic problem in robots by using the Gibbs–Appell formulation, Robotica 21(1) (2002) 138-145.
[13] V. Mata, S. Provenzano, J. I. Cuadrado, F. Valero, Efficient Computation of the generalized inertial tensor of robots by using the Gibbs–Appell equations, Robotica, 21(1) (2002) 739-755.
[14] A. M. Shafei, H. R. Shafei, Planar multibranch open-loop robotic manipulators subjected to ground collision, Journal of Computational and Nonlinear Dynamics, Transactions of the ASME, 12(6) (2017)1-14.
[15] M. H. Korayem, A. M. Shafei, F. Absalan, B. Kadkhodaei, A. Azimi, Kinematic and dynamic modeling of viscoelastic robotic manipulators using Timoshenko beam theory: theory and experiment, International Journal of Advanced Manufacturing Technology, 71 (5-8) (2014) 1005-1018.
[16] A. M. Shafei, H. R. Shafei, Dynamic modeling of tree-type robotic systems by combining 3×3 rotation matrices and 4×4 transformation ones, Multibody System Dynamics, 44(4) (2018) 367-395.
[17] A. M. Shafei, H. R. Shafei, Dynamic behavior of flexible multiple links captured inside a closed space, Journal of Computational and Nonlinear Dynamics, Transactions of the ASME, 11(5) (2016) 1-13.
[18] M. H. Korayem, A. M. Shafei, S. F. Dehkordi, Systematic modeling of a chain of N-flexible link manipulators connected by revolute-prismatic joints using recursive Gibbs-Appell formulation, Archive of Applied Mechanics, 84 (2) (2014) 187-206.
[19] A. M. Shafei, H. R. Shafei, Dynamic modeling of planar closed-chain robotic manipulators in flight and impact phases, Mechanism and Machine Theory, 126 (2018) 141-154.
[20] A. M. Shafei, H. R. Shafei, A systematic method for the hybrid dynamic modeling of open kinematic chains confined in a closed environment, Multibody System Dynamics, 38(1) (2016) 21-42.
[21]  M. H. Korayem, A. M. Shafei, Application of recursive Gibbs-Appell formulation in deriving the equations of motion of N-viscoelastic robotic manipulators in 3D space using Timoshenko beam theory, Acta Astronautica, 83 (2013) 273-294.
[22] V. Rezaei, A. M. Shafei, Dynamic analysis of flexible robotic manipulators constructed of functionally graded materials, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 43(1) (2019) 327–342.
[23] M. H. Korayem,  A. M. Shafei, M. Doosthoseini, F. Absalan, B. Kadkhodaei, Theoretical and experimental investigation of viscoelastic serial robotic manipulators with motors at the joints using Timoshenko beam theory and Gibbs–Appell formulation, Proc IMechE Part K: J Multi-body Dynamics, 230 (1) (2016) 37-51.
[24] A. M. Shafei, H. R. Shafei, Considering link flexibility in the dynamic synthesis of closed-loop mechanisms: A general approach, Journal of Vibration and Acoustics, Transactions of the ASME, 142(2) (2020) 1-12.
[25] M. Ahmadizadeh, A. M. Shafei, M. Fooladi, A recursive algorithm for dynamics of multiple frictionless impact-contacts in open-loop robotic mechanisms, Mechanism and Machine Theory, 146 (2020) 1-20.
[26] A. M. Shafei, H. R. Shafei, Oblique Impact of Multi-Flexible-Link Systems, Journal of Vibration and Control, 24(5) (2018) 904-923.
[27] A. M. Shafei, M. H. Korayem, Theoretical and experimental study of DLCC for flexible robotic arms in point-to-point motion, Optimal Control Applications and Methods, 38(6) (2017) 963-972.
[28] M. H. Korayem, A. M. Shafei, Motion equation of nonholonomic wheeled mobile robotic manipulator with revolute-prismatic joints using recursive Gibbs-Appell formulation, Applied Mathematical Modeling, 39(5) (2015) 1701-1716.
[29]  M. H. Korayem, A. M. Shafei,A New Approach for Dynamic Modeling of n-Viscoelastic-link Robotic Manipulators Mounted on a Mobile Base, Nonlinear Dynamics, 79(4) (2015) 2767-2786.
[30] M. H. Korayem, A. M. Shafei, E. Seidi, Symbolic derivation of governing equations for dual-arm mobile manipulators used in fruit-picking and the pruning of tall trees, Computers and Electronics in Agriculture, 105 (2014) 95-102.
[31] M. H. Korayem, A. M. Shafei, H. R. Shafei, Dynamic modeling of nonholonomic wheeled mobile manipulators with elastic joints using recursive Gibbs-Appell formulation, Scientia Iranica Transaction b: Mechanical engineering, 19(4) (2012) 1092-1104.
[32] R. W. Brockett, Asymptotic stability and feedback stabilization, R. W. Brockett, R. S. Millman, H. J. Sussmann, Differential Geometric Control Theory, Boston, MA: Birkhuser, (1983)181-191.
[33] G. D. White, R. M. Bhatt, C. P. Tang, V. N. Krovi, Experimental evaluation of dynamic redundancy resolution in a nonholonomic wheeled mobile manipulator, IEEE/ASME Transactions on Mechatronics, 14(3) (2009) 349-357, 2009.
[34] S. Yi, J. Zhai, Adaptive second-order fast nonsingular terminal sliding mode control for robotic manipulators, ISA Transactions, 90 (2019), 41-51.
[35] M. Boukens, A. Boukabou, M. Chadli, Robust adaptive neural network-based trajectory tracking control approach for nonholonomic electrically driven mobile robots, Robotics and Autonomous Systems, 92 (2017) 30-40.
[36] S. G. Tzafestas, K. M. Deliparaschos, G. P. Moustris, Fuzzy logic path tracking control for autonomous non-holonomic mobile robots: Design of System on a Chip, Robotics and Autonomous Systems, 58(8) (2010) 1017-1027.
[37] L. Xin, Q. Wang, J. She, Y. Li, Robust adaptive tracking control of wheeled mobile robot, Robotics and Autonomous Systems, 78 (2016) 36-48.
[38] G. Yi, J. Mao, Y. Wang, S. Guo, Z. Miao, Adaptive tracking control of nonholonomic mobile manipulators using recurrent neural networks, International Journal of Control, Automation and Systems, 16(3) (2018) 1390-1403.
[39] A. Bakdi, A. Hentout, H. Boutami, A. Maoudj, O. Hachour, B. Bouzouia, Optimal path planning and execution for mobile robots using genetic algorithm and adaptive fuzzy-logic control, Robotics and Autonomous Systems, 89 (2017) 95-109.
[40]  Z. Li, Y. Kang, Dynamic coupling switching control incorporating support vector machines for wheeled mobile manipulators with hybrid joints, Automatica, 46(5) (2010) 832-842.
[41] M. Boukattaya, M. Jallouli, T. Damak, On trajectory tracking control for nonholonomic mobile manipulators with dynamic uncertainties and external torque disturbances, Robotics and autonomous systems, 60(12) (2012) 1640-1647.
[42] N. Chen, F. Song, G. Li, X. Sun, C. Ai, An adaptive sliding mode backstepping control for the mobile manipulator with nonholonomic constraints, Communications in Nonlinear Science and Numerical Simulation, 18(10) (2013) 2885-2899.
[43] J. Peng, J. Yu, J. Wang, Robust adaptive tracking control for nonholonomic mobile manipulator with uncertainties, ISA Transactions, 53(4) (2014) 1035-1043.
[44] H. Mirzaeinejad, A. M. shafei, Modeling and trajectory tracking control of a two-wheeled mobile robot: Gibbs–Appell and prediction-based approaches, Robotica, 36(10) (2018) 1551-1570.
[45] J. R. Forbes, Adaptive approaches to nonlinear state estimation for mobile robot localization: an experimental comparison ,Transactions of the Institute of Measurement and Control, 35 (2013) 971-985.
[46] B. Zhou,Y. Peng, J. Han, UKF based estimation and tracking control of nonholonomic mobile robots with slipping, IEEE International Conference on Robotics and Biomimetics, Sanya, China, (2007) 2058–2063.
[47] D. Simon,Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches, Hoboken, NY: Wiley-Interscience, (2006).
[48] J. J. E. Slotine, W. Li,Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, N J, (1991).
[49] M. Mirzaei, H. Mirzaeinejad,Fuzzy Scheduled Optimal Control of Integrated Vehicle Braking and Steering Systems, IEEE/ASME Transactions on Mechatronics, 22 (2017) 2369-2379.
[50] H. Mirzaeinejad, M. Mirzaei, R. Kazemi, Enhancement of vehicle braking performance on split-k roads using optimal integrated control of steering and braking systems, Proceedings of the Institution of Mechanical Engineers, Part K: J Multi-body Dynamics, 230 (2016) 401-415.
[51] H. Mirzaeinejad , M. Mirzaei, S. Rafatnia, A novel technique for optimal integration of active steering and differential braking with estimation to improve vehicle directional stability, ISA Transactions, 80 (2018) 513-527.
[52] M. Jafari, M. Mirzaei, and H. Mirzaeinejad, Optimal nonlinear control  of vehicle braking torques to generate practical stabilizing yaw moments, International Journal of Automotive and Mechanical Engineering, 11 (2015) 2639.
[53] W. H. Chen, D. J. Balance, P. J. Gawthrop, Optimal control of nonlinear   systems: A predictive control approach, Automatica, 39 (2013) 633–641.
[54] H. Mirzaeinejad, Optimization-based nonlinear control laws with increased robustness for trajectory tracking of non-holonomic wheeled mobile robots, Journal of Transportation Research Part C, 101 (2019) 1-17.
[55] H. Mirzaeinejad, Robust predictive control of wheel slip in antilock braking systems based on radial basis function neural network, Applied Soft Computing, 70 (2018) 318-329.
Amirkabir Journal of Mechanical Engineering
Volume 53, Issue 2 (Special Issue)
May 2021
Pages 1041-1064

Files

Share

How to cite

Statistics