AN ALGORITHM FOR AN OBJECT GRASPING BY A MANIPULATOR IN AN UNKNOWN STATIC ENVIRONMENT

Abstract

An algorithm for a n-link manipulating robot (MR) control in an environment with unknown static obstacles is considered. A theorem is proved which states that following the algorithm a MR in a finite number of steps will either grasp an object or will give a proved conclusion that an object cannot be grasped in any configuration.

Full Text

In MR control the following typical problem arises: a MR should move from a start configuration q0 and grasp an object Obj by its gripper. Herewith sometimes the Obj may be grasped not in one but in several and sometimes in an infinite number of target configurations qi T. The target configurations are united into a target set BT. The set BT has an arbitrary shape. Let us consider that the BT does not grow during the whole movement of MR. Consider also that the coordinates of every point from BT are known and defined reliably. A MR is represented in the configuration space (generalized coordinate space) as a point. MR functioning should take place in the bounded region X of the configuration space. Let’s consider that X is such that for any q ∈ X the following inequalities are fulfilled: a1 ≤ q ≤ a2, (1) where a1 = (a1 1, a2 1, …, an 1) is a vector of lower bounds on the generalized coordinates values, a2 = (a1 2, a2 2, …, an 2) is a vector of upper bounds on the generalized coordinates values of a MR, q = (q1, q2,..., qn) is a vector of the generalized coordinates of a MR. So X is a hyper parallelepiped. We will consider all points not satisfying (1) as forbidden. Moreover, it is necessary to take into account that there also may be forbidden states inside X. Firstly these are the states (configurations) conditioned by constructive limitations of a MR, for example, those in which inadmissible intersection of MR links takes place. It is possible to calculate such forbidden configurations in advance. Secondly we will consider a configuration as forbidden in case when it intersects obstacles. It is impossible to calculate all such configurations in advance in the conditions of an unknown environment.