The Pareto-frontier-based Stiffness of A Controller: Trade-off between Trajectory Plan and Controller Design

TL;DR

This paper investigates the trade-off between trajectory planning and controller design for UAVs, using Pareto fronts to analyze how dynamic state errors affect the optimality of control strategies in a second-order system model.

Contribution

It introduces a Pareto-frontier-based approach to quantify the trade-offs between trajectory accuracy and controller performance considering dynamic state errors.

Findings

Pareto fronts illustrate the trade-off between trajectory plan and control.

Analytical estimation of dynamic state error using Copenhagen Limit.

Relationship between controller design and pseudo Pareto fronts explored.

Abstract

Approaching a set goal for a UAV comprises a trajectory plan and a controller design (control after plan problems). The optimal trajectory (reference) is calculated before being tracked with a proper controller. It is believed that the quadrotor will follow the designed trajectory totally in the trajectory plan process. However, the dynamic state error usually, for a mismatched feed-forward, spoils this assumption, making the unwanted sacrifice in the objective function defined in the trajectory plan process. We base the target problem in this research on a second-order system model which widely exists in the dynamics of vehicles. Specially, the unavoidable dynamic state error is considered in the trajectory plan process, assuming the LQR without the feed-forward is applied in the subsequent control after plan problems. The Copenhagen Limit provides the possibility of estimating the dynamic state error in an analytical solution. The trade-off results are provided in multiobjective Pareto front solutions and the mapped pseudo Pareto fronts. We explore the relationship between the controller and the corresponding pseudo Pareto fronts.