Real

To obtain real-time haptic interactions in virtual cockpit systems (VCSs), a real-time trajectory planning method based on kinematical optimization for haptic feedback manipulators (HFMs) is presented in this paper. Firstly, the control panel area is extracted in the workspace of the HFM, in which the interacting point is located. Then a feasible interacting configuration is calculated as the objective configuration of the trajectory encoded by a parametric representation. The trajectory planning problem is formulated as a non-linear optimization problem based on kinematics, which is solved in real-time by finding a good initial solution with machine learning methods. Simulations show that trajectories with a compromise between safety and rapidity can be calculated in real-time by this method, which provides a basis for haptic interaction in VCSs