To obtain real-time interactions in the virtual cockpit system (VCS), a real-time trajectory generation method based on dynamical nonlinear optimization and regression prediction for the haptic feedback manipulator (HFM) is presented in this paper. First, a haptic feedback system based on servoserial manipulator is constructed. Then, the trajectory planning problem for the HFM is formulated as a nonlinear optimization problem to balance the motion time and power consumption and ensure the safety of physical human–robot interactions (pHRI). Multiple optimization problems are solved to generate the optimal database off-line. Finally, the classified multivariate (CM) regression method is presented to learn the database and generate optimal trajectories with arbitrary initial and objective positions on-line. Results show that trajectories with rapidity, safety, and lower power consumption can be generated in real-time by this method, which lay a basis of haptic interactions in the VCS.

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