Bounded Control for Double Integrator in Quadrotor Dynamics

TL;DR

This paper develops bounded control strategies for a double integrator system, applying these to improve trajectory tracking in quadrotor dynamics through coordinate transformations and Lyapunov-based stability guarantees.

Contribution

It introduces two new bounded controllers for double integrator systems along with their Lyapunov functions, enhancing quadrotor trajectory control methods.

Findings

Two alternative bounded controllers for double integrator systems.

Lyapunov functions guaranteeing stability of the controllers.

Application to quadrotor trajectory tracking.

Abstract

We construct a trajectory tracking controller for a quadrotor system by finding a coordinate change which transforms the quadrotor's vector field into that of a thrust propelled system. In a thrust propelled system, the goal is to stabilize its position around the origin, while the system is actuated by a one dimensional acceleration/thrust along a direction vector, by a time-varying gravity, and by the angular acceleration of the direction vector. For this system, a solution has been proposed in a companion article, submitted to ECC 2016, based on the implicit knowledge of a bounded controller for a double integrator system, and on the implicit knowledge of a Lyapunov function that guarantees the origin is asymptotically stable for the double integrator controlled by the bounded controller. We present two alternative bounded controllers for a double integrator system, and corresponding Lyapunov functions.