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research-article

An Efficient Approach of Time-optimal Trajectory Generation for the Fully Autonomous Navigation of the Quadrotor

[+] Author and Article Information
Wei Dong

State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering Shanghai Jiao Tong University,Shanghai, 200240, China
chengquess@sjtu.edu.cn

Ye Ding

State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering Shanghai Jiao Tong University,Shanghai, 200240, China
y.ding@sjtu.edu.cn

Jie Huang

State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering Shanghai Jiao Tong University,Shanghai, 200240, China
thk2dth@sjtu.edu.cn

Xiangyang Zhu

State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering Shanghai Jiao Tong University,Shanghai, 200240, China
mexyzhu@sjtu.edu.cn

Han Ding

State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering Shanghai Jiao Tong University,Shanghai, 200240, China
hding@sjtu.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4035453 History: Received May 12, 2016; Revised December 01, 2016

Abstract

In this work, a time-optimal trajectory generation approach is proposed for the multiple way-point navigation of the quadrotor based on the non-uniform rational B-spline (NURBS) curve and linear programming. To facilitate the development of the trajectory generation approach, the dynamic model of the quadrotor is formulated. Then the geometric trajectory regarding multiple way-point navigation is constructed based on the NURBS curve. With the constructed geometric trajectory, a time-optimal interpolation problem is imposed considering the velocity, acceleration and jerk constraints. This optimization problem is solved in two steps. At the first step, a preliminary result is obtained by solving a linear programming problem without jerk constraints. Then by introducing the properly relaxed jerk constraints, an additional linear programming problem is formulated based on the preliminarily obtained result and the time-optimal problem can be fully solved in this way. Subsequently, a nonlinear trajectory tracking controller is developed to track the generated trajectory. The feasibilities of the proposed trajectory generation approach as well as the tracking controller are verified through both simulations and real-time experiments. In the simulations, the advantages of the proposed approach compared to existing trajectory generation methods are well demonstrated with the efficient computation and significantly reduced flight time cost. The experimental results also show that with velocity, acceleration, and jerk constraints: Vmax = 1 m/s, Amax = 2 m/s2, and Jmax = 5 m/s3, the proposed approach can generate trajectory with the smooth acceleration profile and moderate velocity V ≈ 1 m/s. In such a case, the trajectory tracking controller can closely track the reference trajectory with cross-tracking error less than 0.05 m. All of these results show the superiorities of the proposed time-optimal trajectory generation approach for the fully autonomous navigation of the quadrotor.

Copyright (c) 2016 by ASME
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