Piecewise Bézier curve trajectory generation and control for quadrotors

Abstract

Quadrotors have the capability of being immensely useful vehicles to aid humans in labor intensive tasks. The critical challenge of using quadrotors inside homes is the efficient navigation of these vehicles in tight spaces while avoiding obstacles. Although methods exists to generate collision free trajectories, they often do not account for the dynamics of quadrotor.

This thesis presents an approach for trajectory generation and control that can harness the complete dynamics of the quadrotor to achieve efficient navigation in cluttered spaces. First, the equations of motion for a quadrotor model is derived. It is also shown that the quadrotor system is differentially flat, which allows the analytical conversion of a time parameterized trajectory to states and outputs of the vehicle. Next, the thesis describes a control design approach in the non-Euclidean state space of quadrotors to achieve improved tracking performance for complex trajectories.

A novel trajectory generation method is presented to achieve smooth and graceful paths for quadrotors. The trajectory generation is formulated as an optimization problem that generates piecewise Bézier curves which minimize snap over the complete trajectory. The optimization method generates these trajectories from collision-free waypoints indicative of the constrained environment. Further, the Bézier curves are time parameterized to satisfy the dynamic constraints and ensure feasibility.