Simultaneous computation of robot kinematics and differential kinematics with automatic differentiation

Abstract

Describes the computation of derivatives of functions defined on a robot's kinematic quantities using the efficient adjoint technique for automatic differentiation. Implemented software called RAD (Robot Automated Differentiation), which can generate optimized C programs for computing these quantities from concise descriptions of the robot and the required kinematic quantities, is also described. In addition to automatic differentiation, the RAD software provides a symbolic formulation of the kinematics and simplification of trigonometric algebraic expressions using Mathematica and pattern matching. The authors illustrate the utility of the software with a 2-link robot and a PUMA robot.