An alternating peak-optimization method for optimal trajectory generation of quadrotor drones (2312.02944v1)

Abstract: In this paper, we propose an alternating optimization method to address a time-optimal trajectory generation problem. Different from the existing solutions, our approach introduces a new formulation that minimizes the overall trajectory running time while maintaining the polynomial smoothness constraints and incorporating hard limits on motion derivatives to ensure feasibility. To address this problem, an alternating peak-optimization method is developed, which splits the optimization process into two sub-optimizations: the first sub-optimization optimizes polynomial coefficients for smoothness, and the second sub-optimization adjusts the time allocated to each trajectory segment. These are alternated until a feasible minimum-time solution is found. We offer a comprehensive set of simulations and experiments to showcase the superior performance of our approach in comparison to existing methods. A collection of demonstration videos with real drone flying experiments can be accessed at https://www.youtube.com/playlist?list=PLQGtPFK17zUYkwFT-fr0a8E49R8Uq712l .

• The paper presents a novel optimization approach that alternates between tuning polynomial coefficients and segment times for optimal quadrotor trajectories.
• The method effectively minimizes running time without compromising physical constraints, ensuring enhanced performance.
• Extensive simulations and experiments demonstrate that this strategy delivers faster, more efficient trajectories compared to conventional techniques.

Introduction to Trajectory Optimization for Quadrotor Drones

Quadrotor drones have risen to prominence due to their versatility, cost-effectiveness, and impressive maneuverability, making them valuable in a variety of applications, from environmental monitoring to search and rescue operations. However, their sophisticated dynamics and the requirement for multi-variable actuation present a substantial challenge in optimizing drone motion for efficiency and speed.

The Trajectory Optimization Challenge

Typically, trajectory optimization for quadrotors aims to push these drones to their performance limits, creating the most aggressive motion possible. This is often done using continuous-time polynomials, which simplify the drone's complex motion dynamics. However, a common issue with the prevailing optimization techniques is that they tend to predefine the total running time of the drone's trajectory, leading to suboptimal efficiency.

A Novel Time-Optimal Trajectory Approach

In contrast to traditional methods, the new approach introduced in the paper redefines trajectory optimization by focusing on minimizing the total running time of the drone's path without compromising the smoothness of the motion or violating the drone's physical limits. This is done by partitioning the optimization into two sub-problems: optimizing polynomial coefficients and adjusting segment times of the trajectory. These steps are alternated in what is termed an "alternating peak-optimization method," ensuring that the drone operates at peak efficiency over the entire trajectory.

Advantages and Implementation

Simulations and real-world experiments provide evidence that this new optimization strategy excels in generating time-optimal trajectories when compared to established methods. The technique's adaptability is evident by its ability to either aggressively minimize the running time or, alternatively, relax the constraints to ensure feasibility if the situation demands. Practical demonstrations deploying this method using standardized platforms underline its viability and superior performance in producing time-efficient quadrotor trajectories.

In summary, this paper presents a transformative step in quadrotor trajectory optimization, offering a methodology that outperforms existing solutions in speed without neglecting the drone's operational boundaries.