Kinematically Adapted Sampling-Based Motion Planning Algorithm for Robotic Manipulators

Abstract

We introduce modifications to the sampling-based motion planning approach in robotics to adapt the method to the positioning problem of robotic manipulators. The proposed method combines the information from configuration and task spaces of the mechanisms to cluster and subsequently reduce the number of the samples. The clustering process results in construction of a graph, dubbed kinematic graph $\mathfrak {G}_k(\mathfrak {V}_k,\mathfrak {E}_k)$. We present a step by step instruction of the construction of the kinematic graph. The kinematic graph introduces interesting advantages to the planning algorithm. For instance, planning using the kinematic graph will sort the possibilities of sudden configuration changes, due to the surjection of forward kinematics function for robotic manipulators, in planning phase out. Moreover, combination of information from configuration and task spaces can be utilized to form the cost and heuristic functions for the heuristic search algorithms, like A$^{\text {*}}$. Furthermore, the clustering and reduction of the number of the samples has direct effect on the solution depth, that is, the shortest path found by the search algorithm. This in turn reduces the expense of computation and worst-time complexity of the search algorithm. Finally, the information from the vertices of the kinematic graph can be used for a Boolean collision check of the sampled configuration, without the need of extra calls on the forward kinematics function.