Flatness-based Quadcopter Trajectory Planning and Tracking with Continuous-time Safety Guarantees

TL;DR

This paper introduces a convex optimization framework leveraging differential flatness and B-splines for safe, continuous-time trajectory planning and tracking of quadcopters, validated through real-world experiments.

Contribution

It presents a novel convex optimization approach combining B-splines, differential flatness, and control barrier functions for safe quadcopter trajectory planning and tracking.

Findings

The framework guarantees continuous-time safety constraints.

The QP-based controller ensures bounded trajectory tracking.

Experimental validation on Crazyflie2.1 demonstrates effectiveness.

Abstract

This work presents a convex optimization framework for the planning and tracking of quadcopter trajectories with continuous-time safety guarantees. Using B-spline basis functions and the differential flatness property of quadcopters, a second-order cone program is formulated to generate optimal trajectories that respect safe state and input constraints in the continuous-time sense. A quadratic program (QP) based on control barrier functions is proposed to guarantee bounded trajectory tracking in continuous time by filtering a nominal controller, where the QP is shown to be always feasible. Furthermore, conditions that ensure the safe tracking controller respects thrust, roll angle, and pitch angle constraints are also proposed. The effectiveness of the proposed framework is demonstrated by real-world experiments using a Crazyflie2.1 nano quadcopter.