Kinodynamic planning - an analytical approximation with Cn polynomials for industrial application

The need for n-times continuously differentiable trajectories arises when high speed, high precision control of dynamical systems is intended. Especially in mechanics, dynamical systems are usually limited in speed, acceleration and jerk. This paper introduces a strictly analytical method for generating Cⁿ trajectories along given points under dynamic constraints and given maximum path deviations. Addressing the need for discrete time point evaluation in industrial application, a discrete time speed scheduling method is applied. By using higher order polynomials to interconnect given points along the trajectory it is shown that the resulting path complies with the given geometric and dynamic constraints. As an example, a trajectory for a given set of points is derived and the results are discussed in comparison to a computed time-optimal solution.