An optimal control problem for automatic air collision avoidance

Author(s):  
Y. Ikeda ◽  
J. Kay
Robotics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 9 ◽  
Author(s):  
Hamid Alturbeh ◽  
James F. Whidborne

The operation of Unmanned Aerial Vehicles (UAVs) in civil airspace is restricted by the aviation authorities, which require full compliance with regulations that apply for manned aircraft. This paper proposes control algorithms for a collision avoidance system that can be used as an advisory system or a guidance system for UAVs that are flying in civil airspace under visual flight rules. A decision-making system for collision avoidance is developed based on the rules of the air. The proposed architecture of the decision-making system is engineered to be implementable in both manned aircraft and UAVs to perform different tasks ranging from collision detection to a safe avoidance manoeuvre initiation. Avoidance manoeuvres that are compliant with the rules of the air are proposed based on pilot suggestions for a subset of possible collision scenarios. The proposed avoidance manoeuvres are parameterized using a geometric approach. An optimal collision avoidance algorithm is developed for real-time local trajectory planning. Essentially, a finite-horizon optimal control problem is periodically solved in real-time hence updating the aircraft trajectory to avoid obstacles and track a predefined trajectory. The optimal control problem is formulated in output space, and parameterized by using B-splines. Then the optimal designed outputs are mapped into control inputs of the system by using the inverse dynamics of a fixed wing aircraft.


Author(s):  
Yuhang Jiang ◽  
Shiqiang Hu ◽  
Christopher J Damaren

Flight collision between unmanned aerial vehicles (UAVs) in mid-air poses a potential risk to flight safety in low-altitude airspace. This article transforms the problem of collision avoidance between quadrotor UAVs into a trajectory-planning problem using optimal control algorithms, therefore achieving both robustness and efficiency. Specifically, the pseudospectral method is introduced to solve the raised optimal control problem, while the generated optimal trajectory is precisely followed by a feedback controller. It is worth noting that the contributions of this article also include the introduction of the normalized relative coordinate, so that UAVs can obtain collision-free trajectories more conveniently in real time. The collision-free trajectories for a classical scenario of collision avoidance between two UAVs are given in the simulation part by both solving the optimal control problem and querying the prior results. The scalability of the proposed method is also verified in the simulation part by solving a collision avoidance problem among multiple UAVs.


2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.


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