Inverse kinematics of a serial manipulator: kinematic redundancy and two approaches for closed-form solutions

The inverse kinematics problem of a reclaimer which excavates and transports raw materials in a raw yard is investigated Because of the geometric feature of the equipment of which scooping buckets are attached around a rotating disk, kinematic redundancy occurs in determining joint variables. Link coordinates are introduced following the Denavit-Hatenberg representation. For a given excavation point the forward kinematics yields 3 equations however the number of involved joint variables in the equations is four. It is shown that the rotating disk at the end of the boom provides an extra passive degree of freedom. Two approaches are investigated in obtaining inverse kinematics solution. The first method pre-assigns the height of excavation point which can be determined through path planning. A closed form solution is obtained for the first approach. The second method exploits the orthogonality between the normal vector at an excavation point and the z axis of the end-effector coordinate system. The geometry near the reclaiming point has been approximated as a plane, and the plane equation has been obtained by the least square method considering 8 adjacent points near the point. A closed form solution is not found for the second approach, however a linear approximate solution is provided.