Collision-free guidance control of multiple UAVs with restricted communication networks

In this paper, collision-free guidance control of multiple small unmanned helicopters is designed. Collision avoidance of the helicopters should be considered in the control system design for safe operation, Therefore, a guidance control system using a distributed nonlinear model predictive control (DNMPC) is proposed te realize the collision avoidance, A constraint for the relative position vector between the each helicopter is considered in the design for eMcient ayoidance, Small single rotor helicopter is considered as controlled object, and the guiclanee control system is designed fbr the nonlinear translational model treated a helicopter as an ellipsoid. DNMPC is designed with three constraints, an input constraint, a state constraint, and a relative position yector constraint. An input constraint and a state constraint realize collision avoidance in input within the constant Iimits. If the moving path of the one helicopter is significantly affectecl by the moving path of other helicopter, the relative position vector constraint makes the helicopters exchange their relative position each other. By using these constraints, smooth collision avoidance is realized. The helicopters exchange information about current state and optimal input sequence each other for calculating the predictive trajectory of others, Based on the calculated trajectories, each helicopter solves its local optimization problem, Here, sharing the velocity information is diMcult because calculation processing capability of the small $ensor and communication capability between UiNVs are restricted, Therefore, a dynamic compensator for velocity compensation is introduced, By introducing the dynamic compensator, collision avoidance using only exchange on the position and the input sequence information is accomplished without exchanging velocity information. The effectiveness of the proposed control system is verified by numerical simulations, Kley words : Multiple small unmanned helicopters, Collision avoidance, Distributed nonlinear model predictive control, Resuicted comrnunication networks 1. lntroduction In recent years, great success of unmanned aerial vehicle (UAV) is expected (Howard and Kaminer, 199S, Nonami, 2007), UAY can operate cheaper and safer than manned aerial vehicle, and small unmanned helicopter could be used for various tasks under various environments, For example, it is used for information gathering at the time of a disaster, observation service in a height and many others. In addition, a fieet of the unmanned helicopters have a potential to be used for several missions that could not be achieved by using single helicopter. For exarnple, cooperative load carriage, wide range simultaneous aerial photography from multiple helicopters, Furthermore, it is also possible to improve the operational eficiency and the robustness of the systern, Therefore, simultaneous operation of multiple small unmanned helicopters is desired (Nakazawa, et al,, 2007, Nathan, et al., 2e11). Tb realize the above, constmction of the guidance control system in consideration of the collision avoidance of the helicopters become essential, Several collision avoidance methods between moving vehicles have been designed befere The Japan Society of Mechanical Engineers NII-Electronic Library Service heJapanSociety E echanical ngineeis now. For example, artificial potential functions method (Kim, et al,, 2004, Simakura, et al., 2009), virtual impedance method (Arai, et al., 1993), hybrid control method (Kogiso, et al., 2008). in general, artificial potential functions method is lilcely to local minima and hybrid control method is likely to destabilize when switching the controller. Moreover, the problem that oneself moving path is obstmcted by the moving path of other vehicle must be considered in collision avoidance between moving vehicles (Arai, et al., 1993). In this paper, we use Nonlinear Mode] Predictive Control (NMPC) for guidance co]tro] of the multiple Uirvs with collision avoidance. Although guidance control method considering collision avoidance using NMPC has been studied by many researchers in recent years (Shim, et al., 2003, Chung, et al,, 2006, Saffarian, et al, 2008, Shin et al, 2009), the approach which fOcuses oll trajectory generation during collision avoidance has not been studied. So in this paper, guidance control systern using NMPC considering a constraint for a relative position vector from oneself to other helicopter is presented, Based on the achievement of previous study (Ishii, et al., 2013), proposed guidance control system uses Distiibuted Nonlinear Model Predictive Control (DNMPC), each helicopter exchanges infOrmation rnutually and executes NMPC. Proposed guidance control system realizes smooth collision avoidance between multiple helicepters. The helicopters exchange information about current state and optimal input sequence each other, and calculate own and others' predictive trajectorles, Based on the calculated trajectories, each helicopter solves its local optimization problem, Although exchanged information i cludes current positioll, velocity, and optimal input sequence, but sharing the velocity information is diMcult because calculation processing capability of the small sensor and communication capability between UAVs are strongly restricted. Therefore, a dynamic compensator fbr velocity compensation is introduced. [lhe dynamic compensator works the filter which generates approximate velocity information from position information, Collision avoidance using only exchange on the position and the input sequence information is accomplished without exchanging velocity inforrnation, The rest of the paper is organized as fo11ows, Section 2 will introduce the problem statement The centrolled object and the control system of the helicopter will be shown, Section 3 will introduce the communicatioll structure and the dynamic compensator with which velocity infbrmation is compensated, Section 4 will introduce the design of DNMPC with collision avoidance, Section 5 will introduce the numerical simulation to verify the proposed DNMPC. Finally, conclusion of this work will be presented in section 6. 2. Problem Statement 2.1. Controlled Object in this paper, small single rotor helieopter is treated as controlled object such as Fig, 1. Figure 2 shows the overview of our proposed control system (Ishii, et al,, 2013), The contro! system is composed of attitude control loop (inner loop) and guidance control loop (outer loop), The attitude controller makes the attitude of the helicopter fo11ows desired attitucle, The guidance controller generates desired attitude and desired thrust force that is needed to guide the helicopter to target position. Fxref, Fy.ef, Fz..f are desired external force of each axis in the inertial frame; its origin is fixed at arbitrary point on the ground. di..f is desired angle of yaw axis in the body frame; its origin is fixed at the center of gravity of the helicopter. [ip,,f e.,f e.,f 7;.]T represents target angle of roll, pitch, yaw and target thrust fbrce, The control system consists of two feedback control loop. The outer feedback loep is the guidance control system for the rnode1 which Fig. 1 Overview ef small unmamed helicopter. The Japan Society of Mechanical Engineers NII-Electronic Library Service heJapanSociety EMechanical ngineeis Force Xlector' ?osition Reference lIFI.-,J FtJ,.-1 ATtitucle andF:T'['f g''rc.f]/'t Tllltust ReferenceiC',,f Or,f ,.'.,-f Yl,,IT Fig,2Control system of the helicopter, .Xttt,{/'.T'..Y.' ]L-tie[il)lel' 't-..f'''' .."・'f.tttf"'""ttttttt'ttlk.,'1'ji''/t y. i''' t.' /ttt/tttl・v,..・.t.t''r'''・}'tt /1ttf l, ,--''' + tet 'tb Fig. 3Ttanslational model of the helicopter, removed auitude dynamics. Therefore, the low dimension of the design model of NMPC is enabled, computational cost for NMPC could also be reduced, Next, mathematical model of translational motion of the helicopter is derived. We assume that the attitude of the helicopter is stabilized by the attitude control system and the helicopter perfbrrns hovering fiight or low-speed movement, Therefore, we use the translational model that ignores the attitude dynamics. Figure 3 shows the translational model which treated the helicopter as an ellipsoid. The equation of translation of the helicopter is obtained as mX(t)=-k.(di(t))k(t)?+F.(t) (1) mij(t)=-kij(ut(t))e(t)2+F,(t) (2) mZ(t)=-k22(t)2+mg+4(t) (3) Here, x[m] is heading, z[m] is downward, m[kg] denotes mass of the helicopter, g[rnls2] is gravitational acceleration, k., ky, k,[-] denote coeficients relates to air resistamce proportional to the square ef the velocity, Fl, 4,, F, are external forces generated by rotor thrust force, k., ky are considered as a function of di as foIIows: k.(di(t))=k.(in+lysinut(t)) (4) ig(0(t))=k.,(l.+lbcosW(t)) (5) Now, weconsider astatevectoras x(t) = [x(t), y(t), z(t), S(t), g(t), 2(t)]', andainput vectoras u(t) = [F.(t), F,(t), F,(t), then nonlinear state space equation could be obtained by using Eqs. (1)-(5) as S(t)=f(x(t),u(t)) ' (6) in this paper, each he!icopter shall be expressed by Eq, (6), -tr(t)]T, 3. Communication Structure and Design ofDynamic Compensator In this paper, we consider the condition that the helicopter could exchange the information between all helicopters. Figure 4 shows the communication structure. The helicopters exchange information about current position xp(t) = [x(t), y(t), z(t)]T and optimal input sequence U(t) each other, and calculate own and others' predictive trajectories, Based The Japan Society of Mechanical Engineers NII-Electronic Library Service heJapanSociety EMechanical ngineeis on the calculated trajectories, ach helicopter solves its local optimization problem, The aim of this paper is that multiple helicopters reach the target positions from different initial positions with avoid being in a collision, Then, velocity inforrnation f other helicopters is need for calculate the predictive trajecto