Multi-axis High-order Trajectory Planning

This paper presents a trajectory planning algorithm for multi-axis systems. It generates smooth trajectories of any order subject to general initial and final conditions, and constant state and control constraints. The algorithm is recursive, as it constructs a high order trajectory using lower order trajectories. Multi-axis trajectories are computed by synchronizing independent single-axis trajectories to reach their respective targets at the same time. The algorithm’s efficiency and ability to handle general initial and final conditions make it suitable for reactive real time applications. Its ability to generate high order trajectories makes it suitable for applications requiring high trajectory smoothness. The algorithm is demonstrated in several examples for single- and two-axis trajectories of order 2 − 6.