A new mathematical formulation of manipulator motion that simplifies dynamics and kinematics

Labbé, M. & Michaud, F., Comprehensive theory of differential kinematics and dynamics towards extensive motion optimization framework, The International Journal of Robotics Research First Published May 20, 2018 DOI: 10.1177/0278364918772893.

This paper presents a novel unified theoretical framework for differential kinematics and dynamics for the optimization of complex robot motion. By introducing an 18×18 comprehensive motion transformation matrix, the forward differential kinematics and dynamics, including velocity and acceleration, can be written in a simple chain product similar to an ordinary rotational matrix. This formulation enables the analytical computation of derivatives of various physical quantities (e.g. link velocities, link accelerations, or joint torques) with respect to joint coordinates, velocities and accelerations for a robot trajectory in an efficient manner (O(NJ), where NJ is the number of the robot’s degree of freedom), which is useful for motion optimization. Practical implementation of gradient computation is demonstrated together with simulation results of robot motion optimization to validate the effectiveness of the proposed framework.

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