@Article{ayusawa:ijrr:2018,
  author    = {Ayusawa, Ko and Yoshida, Eiichi},
  title     = {Comprehensive theory of differential kinematics and dynamics towards extensive motion optimization framework},
  journal   = {The International Journal of Robotics Research},
  year      = {2018},
  volume    = {37},
  pages     = {1--19},
  month     = {May},
  doi       = {10.1177/0278364918772893},
  url       = {https://staff.aist.go.jp/k.ayusawa/pdf/Ayusawa\_2018\_IJRR.pdf},
  keywords  = {motion optimization, forward kinematics, inverse dynamics, Jacobian matrix, gradient computation, comprehensive motion transformation matrix},
  abstract  = {This paper presents a novel unified theoretical framework for differential kinematics and dynamics for the optimization of complex robot motion. By introducing an 18\texttimes 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 ordi-nary 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 use-
ful 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.},
  publisher = {Sage Publications Ltd},
  address   = {1 Olivers Yard, 55 City Road, London EC1Y 1SP, England}
}