A New Optimal Method for Calculating the Null Space of a Robot using NOC Algorithm; Application on Parallel 3PRS Robot
Subject Areas : optimization and simulationHami Tourajizadeh 1 , oveas gholami 2
1 - Department of Mechanical Engineering, Faculty of Engineering,
University of Kharazmi, Tehran, Iran
2 - Department of Mechanical Engineering, Faculty of Engineering,
University of Kharazmi, Tehran, Iran
Keywords:
Abstract :
[1] Stewart, D., A Platform with Six Degrees of Freedom, Proceedings of the Institution of Mechanical Engineers, Vol. 180, No. 1, 1965, pp. 371-386.
[2] Ruiz, F., Campa, C., Roldán-Paraponiaris, and Altuzarra, O., Dynamic Model of a Compliant 3PRS Parallel Mechanism for Micromilling, in Microactuators and Micromechanisms: Springer, 2017, pp. 153-164.
[3] Li, Y., Xu, Q., Kinematics and Inverse Dynamics Analysis for a General 3-PRS Spatial Parallel Mechanism, Robotica, Vol. 23, No. 02, 2005, pp. 219-229.
[4] Li, Y., Staicu, S., Inverse Dynamics of a 3-PRC Parallel Kinematic Machine, Nonlinear Dynamics, Vol. 67, No. 2, 2012, pp. 1031-1041.
[5] Altuzarra, O., Gomez, F. C., Roldan-Paraponiaris, C., and Pinto, C., Dynamic Simulation of a Tripod Based in Boltzmann-Hamel Equations, in Proceedings of ASME International Design Engineering Technical Conferences, Vol. 5, 2015, pp. 8-22.
[6] Nikravesh, P., Haug, E., Generalized Coordinate Partitioning for Analysis of Mechanical Systems with Nonholonomic Constraints, ASME Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 105, 1983, pp. 379-384.
[7] Singh, R., Likins, P., Singular Value Decomposition for Constrained Dynamical Systems, Journal of Applied Mechanics, Vol. 52, No. 4, 1985, pp. 943-948.
[8] Kim, S., Vanderploeg, M., A General and Efficient Method for Dynamic Analysis of Mechanical Systems using Velocity Transformations, Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 108, No. 2, 1986, pp. 176-182.
[9] Liang, Lance, G. M., A Differentiable Null Space Method for Constrained Dynamic Analysis, Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 109, No. 3, 1987, pp. 405-411.
[10] Angeles, J., Lee, S. K., The Formulation of Dynamical Equations of Holonomic Mechanical Systems using a Natural Orthogonal Complement, Journal of Applied Mechanics, Vol. 55, 1988, pp. 243-249.
[11] Angeles, J., Ma, O., Dynamic Simulation of N-Axis Serial Robotic Manipulators using a Natural Orthogonal Complement, The International Journal of Robotics Research, Vol. 7, No. 5, 1988, pp. 32-47.
[12] Saha, S. K., Angeles, J., Dynamics of No Holonomic Mechanical Systems using a Natural Orthogonal Complement, Journal of Applied Mechanics, Vol. 58, No. 1, 1991, pp. 238-243.
[13] Terze, Z., Lefeber, D., and Muftić, O., Null Space Integration Method for Constrained Multibody Systems with no Constraint Violation, Multibody System Dynamics, Vol. 6, No. 3, 2001, pp. 229-243.
[14] Pendar, H., Vakil, M., and Zohoor, H., Efficient Dynamic Equations of 3-RPS Parallel Mechanism through Lagrange Method, in Proceedings of the Robotics, Automation and Mechatronics, IEEE Conference, Vol. 2, 2004, pp. 1152-1157.
[15] Rao, K., Saha, S., and Rao, P., Dynamics Modelling of Hexaslides using the Decoupled Natural Orthogonal Complement Matrices, Multibody System Dynamics, Vol. 15, No. 2, 2006, pp. 159-180.
[16] Phong, V., Hoang, N. Q., Singularity-Free Simulation of Closed Loop Multibody Systems by using Null Space of Jacobian Matrix, Multibody System Dynamics, Vol. 27, No. 4, 2012, pp. 487-503.
[17] Marino, Parker, L. E., Antonelli, G., and Caccavale, F., A Decentralized Architecture for Multi-Robot Systems Based on the Null-Space-Behavioral Control with Application to Multi-Robot Border Patrolling, Journal of Intelligent & Robotic Systems, Vol. 71, No. 3-4, 2013, pp. 423-444.
[18] Raoofian, Kamali, A., and Taghvaeipour, A., Forward Dynamic Analysis of Parallel Robots using Modified Decoupled Natural Orthogonal Complement Method, Mechanism and Machine Theory, Vol. 115, 2017, pp. 197-217.
[19] Coleman, T. F., Sorensen, D. C., A Note on the Computation of an Orthonormal Basis for the Null Space of a Matrix, Mathematical Programming, Vol. 29, No. 2, 1984, pp. 234-242.
[20] Berry, M., Heath, M., Kaneko, I., Lawo, M., Plemmons, R., and Ward, R., An Algorithm to Compute a Sparse Basis of the Null Space, Numerische Mathematik, Vol. 47, No. 4, 1985, pp. 483-504.
[21] Coleman, T. F., Pothen, A., The Null Space Problem I. Complexity, SIAM Journal on Algebraic Discrete Methods, Vol. 7, No. 4, 1986, pp. 527-537.
[22] Dai, J. S., Jones, J. R., Null–Space Construction using Cofactors from a Screw–Algebra Context, in Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol. 458, No. 2024, 2002, pp. 1845-1866.
[23] Bourdoux, Khaled, N., Joint TX-RX Optimisation for MIMO-SDMA Based on a Null-Space Constraint, Proceedings of the Vehicular Technology Conference, Vol. 1, 2002, pp. 171-174.
[24] Nie, P. Y., A Null Space Method for Solving System of Equations, Applied Mathematics and Computation, Vol. 149, No. 1, 2004, pp. 215-226.
[25] Ye, J., Xiong, T., Computational and Theoretical Analysis of Null Space and Orthogonal Linear Discriminant Analysis, Journal of Machine Learning Research, Vol. 7, No. Jul, 2006, pp. 1183-1204.
[26] Betsch, P., The Discrete Null Space Method for the Energy Consistent Integration of Constrained Mechanical Systems: Part I: Holonomic Constraints, Computer Methods in Applied Mechanics and Engineering, Vol. 194, No. 50, 2005, pp. 5159-5190.
[27] Betsch, P., Leyendecker, S., The Discrete Null Space Method for the Energy Consistent Integration of Constrained Mechanical Systems, Part II: Multibody Dynamics, International Journal for Numerical Methods in Engineering, Vol. 67, No. 4, 2006, pp. 499-552.
[28] Leyendecker, S., Betsch, P., and Steinmann, P., The Discrete Null Space Method for the Energy-Consistent Integration of Constrained Mechanical Systems. Part III: Flexible Multibody Dynamics, Multibody System Dynamics, Vol. 19, No. 1, 2008, pp. 45-72.
[29] Leyendecker, S., Ober‐Blöbaum, S., Marsden, J. E., and Ortiz, M., Discrete Mechanics and Optimal Control for Constrained Systems, Optimal Control Applications and Methods, Vol. 31, No. 6, 2010, pp. 505-528.
[30] Spivak, M., Calculus on Manifolds: a Modern Approach to Classical Theorems of Advanced Calculus. CRC Press, 2018.
[31] Spong, M. W., Hutchinson, S., and Vidyasagar, M., Robot Modeling and Control, Jon Wiley & Sons, 2005, ISBN-100-471-649.