Abstract
By considering the dexterous hand manipulation problem as a hybrid system, we propose a mixed logic dynamical (MLD) modeling formulation which encapsulates phases of continuous motion, switching between types of motion, and occurrence of impacts. We first formulates the multi-contact manipulation system into a general nonlinear dynamical equation subject to (in)equality and complementarity constraints, then transform the constrained system to a MLD system model. Based on the derived MLD model, dexterous hand manipulation can be realized optimally via mixed integer quadric programming (MIQP) algorithm. This modeling formulation and an optimization approach are applied to a whole body manipulation task as an example.
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References
Bemporad A, Morari M (1999) Control of systems integrating logic, dynamics, and constraints. Automatica 35(3):407–427
Bemporad A, Morari M, Dua V, Pistikopoulos EN (2002) The explicit linear quadratic regulator for constrained systems. Automatica 38(3):3–20
Heemels WPM, De Schutter B, Bemporad A (2001) Equivalence of hybrid dynamical models. Automatica 37(7):1085–1091
Hikisaka O (1998) Procedural learning of sequential hand movements. Adv Neurol Sci 42(1):106–116
Murray RN et al. (1993) A mathematical introduction to robotic manipulation. CRC, Boca Raton
Pang JS, Trinkle JC (1996) Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with coulomb friction. Math Program 73:199–226
Schlegl T, Buss M (1998) Hybrid closed-loop control of robotic hand regrasping. In: Proceedings of the IEEE International conference on robotics and automation, Leuven, Belgium
van der Schaft AJ, Schumacher JM (1998) Complementarity modeling of hybrid systems. IEEE Trans Autom Control 43(4):483–490
Yashima M, Yamaguchi H (2003) On motion planning for enveloping grasp by multi-fingered hand based on switching contact modes. Trans. Soc. Instrum. Control. Eng. 39(2):150–158 (in Japanese)
Yin YJ, Hosoe S (2004) Tracking control of mixed logic dynamical systems. IEICE Trans Fundam Electron Commun Comput Sci E87-A(11):2929–2936
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Yin, Y., Hosoe, S. & Luo, Z. A mixed logic dynamical modeling formulation and optimal control of intelligent robots. Optim Eng 8, 321–340 (2007). https://doi.org/10.1007/s11081-007-9017-z
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DOI: https://doi.org/10.1007/s11081-007-9017-z