Motion Planning of an N-Joint Planar Mechanism : A Non-Heuristic Approach

Abstract

Algorithms of a non-numerical and non-heuristic nature are developed and implemented in this work for the analysis of motion planning. In particular, the most complete analysis of the motion planning problem is performed for a 2-link planar mechanism and the problem is formulated in purely geometric terms. We describe an algorithm which determines the shortest path between any two points in the joint space. Moreover, the algorithm can be used to choose a path such that the variation of the joint angles along the path guarantees the fastest transference of an arm end-effector between two generic points, i.e., from A to B, in the workspace. Finally, the problem of planning the shortest path for a 2-link arm is considered in an environment containing obstacles in the form of points which the manipulator cannot cross.