Trajectory Generation and Optimization Algorithm for Autonomous Aerial Robots

This paper presents a new trajectory generation and optimization algorithm (TGOA) for an agile and aggressive flight of quadrotor UAVs. The optimizer considered the constraints associated with robot dynamics, actuator inputs, and flying environment to produce collision-free dynamically feasible trajectories. The algorithm is developed based on time-par-ametrized polynomials trajectories consist of a predefined sequence of waypoints indicating the robot's desired state over time. This work is an extension of existing studies that utilized the differential flatness property and polynomial-based trajectories. Doing so will lead to eliminating the need for iterative searching and computationally intensive sampling in the high dimensional state space of the quadrotor system dynamics. The main advantage of the proposed algorithm lies in its numerical stability for a large number of waypoints and high-order polynomials. The TGOA addressed the ill-conditioned problem of Quadratic Programming (QP) based methods, by reformulating the trajectory generation and optimization problem into unconstrained quadratic programming (UCP). To do so, the numerically stable null-space factorization method is used. The Proposed TGOA produces minimum derivatives trajectories along with minimum waypoints' arrival times. Several scenarios and comparisons have been conducted to reveal the numerical stability and computational advantages of the proposed TGOA. They also demonstrate the variety of aggressive trajectories that can be rapidly generated so that utilizing the full maneuvering capabilities of quadrotor robots.