Ball-and-finger system: modeling and optimal trajectories. (English) Zbl 1407.70015
Summary: A rigid-body model of a finger interacting with a trackball is considered. The proposed system is a suitable candidate for studying trajectory generation when interaction plays an important role, such as in assembly and manipulation tasks. The mathematical model consists of a ball with a spherical joint constraint, a finger with three degrees of freedom, and the Coulomb friction model. From first principles, we derive a hybrid, high-index differential-algebraic equation for modeling the system dynamics, which is used for both simulation and finding optimal trajectories. For this problem, task planning, path planning, and trajectory generation are strongly interrelated, which makes using an integrated approach to trajectory generation inevitable. Moreover, the trajectory generation algorithm has to handle a number of important features, e.g., unilateral and non-holonomic constraints.
MSC:
| 70E60 | Robot dynamics and control of rigid bodies |
| 70F35 | Collision of rigid or pseudo-rigid bodies |
| 70F25 | Nonholonomic systems related to the dynamics of a system of particles |
Keywords:
hybrid dynamic optimization; optimal trajectory; dynamics with contacts; non-holonomic constraintReferences:
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