基於分佈式共識控制與模型預測控制之四旋翼編隊與基於幾何關係與相對運動之防撞設計

Quadrotors Formation Strategies Based on Distributed Consensus and Model Predictive Controls and Collision Avoidance Based on Geometric Relationship and Relative Motion

張家瑋(Chia-Wei Chang)

指導教授 ： 蕭照焜

淡江大學/工學院/航空太空工程學系碩士班/碩士(2019年)

https://doi.org/10.6846/TKU.2019.00333

摘要

本研究主要分為兩個部分：四旋翼之編隊飛行與防撞設計。第一部分主要討論基於共識控制與模型預測控制之四旋翼編隊策略。首先，四旋翼之編隊問題可以分為水平方向與垂直方向之運動。在水平方向運動當中，長機以模型預測控制執行航點之追隨，並在自主飛行的同時根據自身的預測軌跡、速度方向與指定編隊隊形計算各個僚機的編隊飛行參考軌跡。另一方面，僚機以共識控制搭配模型預測控制來執行參考軌跡的追隨。在垂直方向運動當中，長機以模型預測控制執行高度與爬升率的追隨並計算各僚機之參考軌跡。僚機在垂直方向運動則單以模型預測控制來執行參考軌跡的追隨。最終在Matlab/Simulink的環境下進行非線性的模擬以驗證本研究所提出之編隊飛行策略的可行性。
本研究的第二部分主要在探討四旋翼彼此間的防撞問題。本研究依據幾何與相對運動關係提出兩架四旋翼間在水平上之防撞策略。防撞策略主要分為判斷與計算兩個部分。首先，防撞策略的第一部分根據幾何與相對運動關係判斷兩架四旋翼間是否有碰撞危險。在有碰撞危險的情況下，防撞策略的第二部分將介入並計算防撞控制。完整的防撞控制主要包含方向以及大小。防撞控制的方向之決定是依據當下的幾何與相對運動的情況，本研究根據其中一種幾何情況做推導，並引入一般化防撞控制將防撞控制拓展到所有幾何情況；防撞控制的大小是以一個從相對速度與視線向量(Line of sight, LOS)的內積所推導出的方程式計算之，此方程式包含四旋翼之狀態變數與四旋翼水平上之幾何夾角。最終根據不同飛行情況在Matlab/Simulink的環境下進行非線性的模擬以驗證本研究所提出之防撞策略的可行性。

關鍵字

四旋翼 ； 編隊飛行 ； 共識控制 ； 模型預測控制 ； 四旋翼防撞 ； 幾何方法 ； 相對運動

並列摘要

This study includes two parts. In the first part, the distributed consensus control and model predictive control (MPC)-based formation strategies for quadrotors are proposed. First, the formation-control problem is decoupled into horizontal and vertical motions. The distributed consensus control and MPC-based formation strategy are implemented in the follower's horizontal formation control. In the horizontal motion, the leader tracks the given waypoints by simply using the MPC, and generates the desired formation trajectory for each follower based on its flight information, predicted trajectory, and the given formation pattern. On the other hand, the followers carry out the formation flight based on the proposed horizontal formation strategy and the desired formation trajectories generated by the leader. In the vertical motion, formation control is carried out using only the MPC for both the leader and the follower. Likewise, the leader tracks the desired altitude/climb rate and generates the desired formation trajectories for the followers, and the followers track the desired formation trajectories generated by the leader using the MPC. The optimization problem considered in the MPC differs for the horizontal and vertical motions. The problem is formulated as a quadratic programming (QP) problem for the horizontal motion, and as a linear quadratic tracker (LQT) for the vertical motion. Simulation of a comprehensive maneuver was carried out under a Matlab/Simulink environment to examine the performance of the proposed formation strategies.
In the second part, a collision avoidance strategy based on the relative motions and horizontal geometric relationship between two quadrotors is proposed. The avoidance strategy includes two parts. The first part of the avoidance strategy determines the existence of the collision warning condition by using the line of sight (LOS), relative motions, and horizontal geometric relationship between two quadrotors. The second part of the avoidance strategy generates the avoidance control if the collision warning condition exists. A complete avoidance control includes two parts, the direction and the magnitude. The direction of the avoidance control for the quadrotor under consideration is determined based on the relative position between two quadrotors with respect to the translated frame of the quadrotor under consideration. The magnitude of the avoidance control for the quadrotor under consideration is derived based on the relative velocity, line of sight (LOS), and the quadrotor's dynamics model. Simulations were carried out under Matlab/Simulink environment to examine the performance of the proposed avoidance strategy.

並列關鍵字

Quadrotor formation control ； consensus control ； model predictive control ； linear quadratic tracker ； quadratic programming ； collision avoidance ； geometric approach ； collision cone ； relative motion

參考文獻

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