Collision avoidance of a redundant manipulator operating through a window

The problem of collision-free operation of a redundant robot manipulator through a window is addressed. The window is modeled by a polygon with the sides representing the edges of the window. A performance criterion is defined to maximize the shortest distances between the arm link axes and the edges of the window. An efficient gradient projection optimization scheme for the kinematic control of manipulators with multiple degrees of redundancy is developed and used. The effectiveness of this scheme and the validity of the performance criterion are verified through simulations of the seven-degree-of-freedom NASA Laboratory Telerobotic Manipulator (LTM), where controlling only the position of the end-effector provides three degrees of redundancy.