Automatic Differentiation of Serial Manipulator Jacobians Using Multidual Algebra

Nowadays, the usage of robots is continuously growing and aims to replace human work in different areas as much as possible. Some places, like medicine or nanotechnology, require high-precision multilink robot end-effector control. Regarding accurate trajectory tracking, conventional computation methods for high-order derivatives of multi-Doff manipulators are highly time-consuming and offer only approximative results. Inaccurate results, in the end, reduce the performance of multi-Doff manipulators and re-strict utilization in the areas where high precision and response time are necessary. It is essential to employ an advanced technique for computing higher-order Jacobian matrix derivatives to achieve precise control. This paper explores a novel approach for deriving the Jacobian matrix of a multilink robot using multi-dual algebra. With multidual algebra and its automatic differentiation proprieties, obtaining an exact value for higher-order acceleration is possible. Combining multidual algebra and automatic differentiation enhances our ability to compute derivatives efficiently and accurately, improving performance and reliability in various applications. This method is applicable everywhere, for any lower-pair serial kinematic chain and any order of higher-order acceleration.