Abstract
For motion planning of a manipurator, the use of a configuration space is highly efficient. Algorithms of the collision-free planning in static environments have been proposed in many papers. The efficiency of the algorithms depends on the description of obstacles in a configuration space. In general, the complexity of a configuration space map exponentially increases with the number of joints. Therefore, building the configuration space map is a time-consuming process, and the collision-free path can not be searched in real time. In this paper, we illustrate mathematical properties of a new kind of configuration space and propose an approach to parameterizing an obstacle in the configuration space. A spherical obstacle in a work space is transformed into a characteristic subspace in the configuration space. Therefore, we can approximate parameters of a sphere as a set of geometric entities. The transformation of a complex work space into the configuration space is described in terms of integrating the transformation of each element of a set of spheres. A collision-free path in a dynamic environment is found by using a Penalty-Function-Method. The Penalty-Function is modified according to the factors of the velocity along axes in a polar coordinates system.
