High-Order Derivatives of Serial Manipulator Jacobians Using Multidual Differentiation Transform

The use of robots is continuously growing, from heavy-duty industries to nanotechnology. Exact multilink robot end effector control is required to withstand this tendency in modern robotics. Mapping between joint variables in joint-space coordinate and end effector configuration in task-space coordinate are provided by serial manipulator kinematics. A computation of higher-order Jacobian matrix derivatives is required for accurate trajectory tracking. With conventional numerical derivation, only approximate results can be obtained. Still, the computation of high-order derivatives of multi-DoF manipulators with high accuracy requires long time intervals and it is difficult. This paper investigates a novel derivation method for a multilink robot Jacobian. According to this method, an exact value of higher-order acceleration can be obtained using a multidual differentiation transform. Multidual functions for sine and cosine will be used to get the exact value of acceleration, jerk, and hyper-jerk (jounce) expressions, commonly used for accurate trajectory-tracking.