Near-Optimal Trajectory Generation for Flexible Motion Systems using Two-Boundary Approach

The dynamics of the supposedly known flexible motion system is given a voice in the making process of the desired trajectory signals it has to follow. In doing so, and according to the herein proposed approach, a singularly perturbed version of the system dynamics is obtained which allows the system to be treated as time-invariant despite any existing time dependency. Based on the nature of the system assigned task, the trajectory making process is subdivided into several intervals, where each interval has its own boundary conditions that need to be assigned by the motion designer. In this sense, the boundary conditions act as way-points that govern the smooth states evolution over time, and are used to build internal and self-driven optimal reference trajectories to fulfill the desired actual system motion profile. Despite its simplicity, the superiority of the proposed technique is compared to the 2(nd)-order, 3(rd)-order, and sinusoidal standard motion trajectories, and its performance is evaluated through simulation.