The problem of online trajectory generation is a common challenge when dealing with moving target tracking. Offline planning is often impractical when the target's intentions are not clear in advance.
When using model predictive control for the application of trajectory tracking control, the trajectory towards the target can be generated as part of the optimal control problem. This, however, often requires large control horizons and can lead to numerical divergence of the solver. To counteract these effects, simple first-order lag elements are commonly used in industry to create reference trajectories, which steadily approach the target set point. However, they typically do not take system limitations into account, which can lead to infeasible trajectories.
We present an approach utilizing higher-order lag elements with adaptive pole placement based on the tracking error to keep the generated trajectories smooth and feasible. We demonstrate the simplicity of this approach using a three dimensional double integrator example, which serves as a representative model for many feedback linearizable mechanical systems.
The adaptive lag elements can be used to quickly generate smooth and feasible trajectories while enforcing constraints on its derivatives. We show that the tracking performance of the presented approach corresponds to or even improves upon the direct use of the unfiltered target trajectory while at the same time improving the smoothness of the actuator commands.