Abstract
This chapter reports the kinematics and dynamics models of the parallel mechanism known as Hexapod, which has a structure of the type known as 6-3-PUS. For computing the dynamics model, we start considering a non-minimal set of generalized coordinates and employ the Euler–Lagrange formulation; after that, we apply the so-called projection method to get a minimal model. It is worth noticing that the modeling approach presented here can be used for similar robotic structures, and the resulting models are suitable for automatic control applications. The computed analytical kinematics and dynamics models are validated by comparing their results with numerical simulations carried out using the SolidWorks Motion platform. In addition, this chapter describes the implementation of two motion tracking controllers in a real Hexapod robot. The tested controllers are one with a two-loop structure (a kinematic controller in the outer loop and a PI velocity controller in the inner loop) and other with an inverse dynamics structure. The experimental results of both controllers show a good performance.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arczewski, K., & Blajer, W. (1996). A unified approach to the modelling of holonomic and nonholonomic mechanical systems. Mathematical Modelling of Systems, 2(3), 157–174.
Betsch, P. (2005). 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, 194, 5159–5190.
Blajer, W. (1997). A geometric unification of constrained system dynamics. Multibody System Dynamics, 1, 3–21.
Camarillo, K., Campa, R., Santibáñez, V., & Moreno-Valenzuela, J. (2008). Stability analysis of the operational space control for industrial robots using their own joint velocity PI controllers. Robotica, 26(6), 729. https://doi.org/10.1017/S0263574708004335.
Campa, R., Bernal, J., & Soto, I. (2016). Kinematic modeling and control of the Hexapod parallel robot. In Proceedings of the 2016 American Control Conference (pp. 1203–1208). IEEE. http://doi.org/10.1109/ACC.2016.7525081.
Campa, R., & de la Torre, H. (2009). Pose control of robot manipulators using different orientation representations: A comparative review. In Proceedings of the American Control Conference. St. Louis, MO, USA.
Carbonari, L., Krovi, V. N., & Callegari, M. (2011). Polynomial solution to the forward kinematics problem of a 6-PUS parallel-architecture robot (in Italian). In Proceedings of the Congresso dell’Associazione Italiana di Meccanica Teorica e Applicata. Bologna, Italy.
Cheah, C. C., & Haghighi, R. (2014). Motion control of robot manipulators. In Handbook of Manufacturing Engineering and Technology (pp. 1–40). London: Springer London. http://doi.org/10.1007/978-1-4471-4976-7_93-1.
Craig, J. J. (2004). Introduction to robotics: Mechanics and control. Pearson.
Dasgupta, B., & Mruthyunjaya, T. S. (2000). The Stewart platform manipulator: A review. Mechanism and Machine Theory, 35(1), 15–40.
Dontchev, A. L., & Rockafellar, R. T. (2014). Implicit functions and solution mappings: A view from variational analysis. Springer.
Geng, Z., Haynes, L. S., Lee, J. D., & Carroll, R. L. (1992). On the dynamic model and kinematic analysis of a class of Stewart platforms. Robotics and Autonomous Systems, 9(4), 237–254.
Ghorbel, F. H., Chételat, O., Gunawardana, R., & Longchamp, R. (2000). Modeling and set point control of closed-chain mechanisms: Theory and experiment. IEEE Transactions on Control Systems Technology, 8(5), 801–815.
Hopkins, B. R., & Williams, R. L., II. (2002). Kinematics, design and control of the 6-PSU platform. Industrial Robot: An International Journal, 29(5), 443–451.
Kapur, D. (1995). Algorithmic elimination methods. In Tutorial Notes of the International Symposium on Symbolic and Algebraic Computation. Montreal, Canada.
Kelly, R., Santibáñez, V., & Loría, A. (2005). Control of robot manipulators in joint space. Springer.
Khatib, O. (1987). A unified approach for motion and force control of robot manipulators: The operational space formulation. IEEE Journal on Robotics and Automation, 3(1), 43–53. https://doi.org/10.1109/JRA.1987.1087068.
Liu, C. H., Huang, K. C., & Wang, Y. T. (2012). Forward position analysis of 6-3 Linapod parallel manipulators. Meccanica, 47(5), 1271–1282.
Liu, M. J., Li, C. X., & Li, C. N. (2000). Dynamics analysis of the Gough-Stewart platform manipulator. IEEE Transactions on Robotics and Automation, 16(1), 94–98.
Merlet, J.-P. (1999). Parallel robots: Open problems. In Proceedings of the International Symposium of Robotics Research. Snowbird, UT, USA.
Merlet, J.-P. (2006). Parallel robots. Springer.
Murray, J. J., & Lovell, G. H. (1989). Dynamic modeling of closed-chain robotic manipulators and implications for trajectory control. IEEE Transactions on Robotics and Automation, 5(4), 522–528. https://doi.org/10.1109/70.88066.
Nanua, P., Waldron, K. J., & Murthy, V. (1990). Direct kinematic solution of a Stewart platform. IEEE Transactions on Robotics and Automation, 6(4), 438–444.
Narayanan, M. S., Chakravarty, S., Shah, H., & Krovi, V. N. (2010). Kinematic, static and workspace analysis of a 6-PUS parallel manipulator. In Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B (pp. 1456–1456.8). Montreal, Canada: ASME. http://doi.org/10.1115/DETC2010-28978.
Siciliano, B., Sciavicco, L., Villani, L., & Oriolo, G. (2009). Robotics. London: Springer London. https://doi.org/10.1007/978-1-84628-642-1.
Tsai, L. W. (1999). Robot analysis: The mechanics of serial and parallel manipulators. Wiley.
Whitney, D. (1969). Resolved motion rate control of manipulators and human prostheses. IEEE Transactions on Man Machine Systems, 10(2), 47–53. https://doi.org/10.1109/TMMS.1969.299896.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Campa, R., Bernal, J., Soto, I. (2018). Modeling and Motion Control of the 6-3-PUS-Type Hexapod Parallel Mechanism. In: Vergara Villegas, O., Nandayapa , M., Soto , I. (eds) Advanced Topics on Computer Vision, Control and Robotics in Mechatronics. Springer, Cham. https://doi.org/10.1007/978-3-319-77770-2_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-77770-2_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-77769-6
Online ISBN: 978-3-319-77770-2
eBook Packages: EngineeringEngineering (R0)