Optimum trajectory planning method for a system that includes passive joints - (Proposal of a function approximation method)

We have proposed a new optimal trajectory planning method for a system with nonholonomic constraints due to passive joints based on a function approximation method. The trajectory is approximated by a linear combination of Hermite functions and Fourier series. The combination variables are solved by a nonlinear programming method that considers the constraints in the same function space as that of the trajectory. We have examined the validity and features of this method by applying it to the optimal trajectory planning of a steady giant swing motion. We found that this method has efficient convergence characteristics in iteration calculations and can provide accurate solutions depending on the order number of the approximating functions. Optimal giant swings with no input torque can be obtained for various motion periods.