End Effector Path Generation

The path followed by a robotic manipulator is often defined by a sequence of Cartesian knots, i.e., position and orientation (location) of the end effector and the corresponding linear and angular velocity (speed) at each knot. The path location and speed in the interval between knots are not specified. Typically the control of robots is performed in terms of joint coordinates. Often, the joint coordinates corresponding to the path knots are splined together using lower degree polynomials. The actual path and speed followed by the end effector can be obtained by performing forward (direct) kinematics—a pointwise transformation. To obtain a good approximation of the actual path, many points must be used. In this paper an efficient first order approximation of the actual path using third order (cubic) interpolating polynomials is presented. The technique eliminates the need for repeatedly using the forward kinematics. The technique is illustrated by means of numerical examples.