| Summary: | 博士 === 國立清華大學 === 資訊工程學系 === 91 === Grasping analysis is one of the traditional topics in robotics research. In general, it deals with the problems induced by using multiple fingers to grasp an object. Good grasps can increase the performance of a robot hand and reduce the complexity of manipulations. In this dissertation, we focus on the stabilities of multi-fingered grasps. Two topics of multi-fingered grasping stabilities were investigated, namely, “the stability under external perturbations” and “the stability using minimal grasping angles”.
In analyzing the stability under external perturbations, we proposed a measurement to evaluate the performance of different grasping configurations on a given object under the influence of external perturbations. A rotation-displacement geometry model was used in computing the changes of equilibrium grasping forces under external perturbations. Using these results, we have presented the concept of perturbation closure, which plays a central role in our analysis. The local minimal perturbation resisting force required for non-slip contacts can be found by using the perturbation closure properties. Then, from the local minimal perturbation resisting force, the optimal grasps can be found. The solution so obtained is based on non-slip contact under a given perturbation of bounded magnitude. Hence, it is guaranteed to be stable if the magnitudes of the external perturbations do not exceed the threshold.
In the second topic of stability analysis, we use the maximal grasping angle as the performance measurement and defined the optimal grasps as the grasps whose measurement are minimized. Follow this definition of optimality, we proved the existence of optimal grasps and divided the set of optimal grasps into the simple solutions and the complex solutions. We also presented an algorithm in finding the set of optimal grasps. In this algorithm, we divided the complex solutions into the pure-complex solutions and the unpure-complex solutions. And, this algorithm includes different procedures to simple, pure-complex, and unpure-complex solutions, respectively. In particular, the gradient algorithm is used to solve the pure-complex solutions and an adequate initial guess is suggested to ensures the convergence of the searching process.
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