Planning and Execution of Straight Line Manipulator Trajectories

Recently developed manipulator control languages typically specify motions as sequences of points through which a tool affixed to the end of the manipulator is to pass. The effectiveness of such motion specification formalisms is greatly increased if the tool moves in a straight line between the user-specified points. This paper describes two methods for achieving such straight line motions. The first method is a refinement of one developed in 1974 by R. Paul. Intermediate points are interpolated along the Cartesian straight line path at regular intervals during the motion, and the manipulator's kinematic equations are solved to produce the corresponding intermediate joint parameter values. The path interpolation functions developed here offer several advantages, including less computational cost and improved motion characteristics. The second method uses a motion planning phase to precompute enough intermediate points so that the manipulator may be driven by interpolation of joint parameter values while keeping the tool on an approximately straight line path. This technique allows a substantial reduction in real time computation and permits problems arising from degenerate joint alignments to be handled more easily. The planning is done by an efficient recursive algorithm which generates only enough intermediate points to guarantee that the tool's deviation from a straight line path stays within prespecified error bounds.