Efficient Approximation of Optimal High-Order Kinematic Trajectories

Abstract

A method for efficiently planning one-dimensional pop-limited trajectories is presented, along with a direct method for synchronizing trajectories across multiple dimensions. This heuristic is designed for a double integrator utilizing acceleration commands passed through a 4th-order cascaded filter, the model for which is presented along with the system solution for an arbitrary time step and derivative limits. Examples for trajectories generated in both one and two dimensions are shown, with comparison to an iterative solver which searches for the exact optimal solution. The presented algorithm shows drastically lower computational requirements than the iterative solver, with very little cost in accuracy. Benefits and limitations of this approach are discussed.