Geometric Mechanics And Optimal Control Of UAVs Formation

With the developments of modern control theory, there have been successful mil?itary and civilian applications of unmanned aerial vehicle (UAV). Later, the concept ofUAVs formation is developed for the complex environments and tasks. The researchof UAVs formation concerns with different topics. One hand is the pursuance of highprecision control technology of single UAV, the other hand is to build a framework offormation which can guarantee the coordinated motion of UAVs. With the help of ge?ometric mechanics, this thesis concerns in a study on the trajectory planning of singleUAV and the control strategy of formation preserving with its algorithm implement.The trajectory planning is the main content of the control technology of singleUAV, the optimality and real-time performances are required for the corresponding al?gorithms. The traditional theory of optimal control can achieve the optimality. How?ever, the optimal control in time domain is always contradictory with real-time perfor?mances for the situations of complex environments and huge scale problems. In suchsituations, the trajectory planning can be divided into two procedures. Firstly, globalplanning algorithms are used to ifnd a series of feasible way-points. Such algorithms areusually off-line methods with good performance on convergence. Then, optimal con?trols are used to generate the motion between the way-points. Algorithms of optimalcontrol with high precision are the main content for this section. Geometric mechanicfocuses on the geometric character of rigid body. By using the concept of Lie group,optimal controls with high precision are achieved. In the context, Lie group integratorof rigid body is derived by variational principle. The algorithms based on Lie groupintegrator results in a high precision optimal control of rigid body.A framework of UAVs formation is investigated based on artiifcial potential ifeld.The potential ifeld can support the motion character of formation preserving, and it iscombinable with the Lagrange mechanic system. The corresponding potential forcesstand for the real controls. The leader-follower formation of three agents in plane isa restricted three body problem, whose stability analysis is based on the equilibriumpoint of an error dynamic system. And the equilibrium point can be derived from thepotential ifeld. The equilibrium point of error dynamic system is only related to thestable structure of formation which is a triangle in plane and a tetrahedron in space. However, in the inertial frame, there are inifnite possible coordinates of formation cor?responding to the stable structure. The Jacobian matrix of error dynamic system at theequilibrium point is unsolvable, which makes the stability analysis to impossible.A methodology based on coordinates transformation and system reduction is pro?posed for the stability analysis. The methodology requires a coordinates transformationfrom inertial frame to a speciifc body frame, making the stability analysis focusing onthe stable structure of formation. In the new frame, the coordinates are limited andidentiifed for stable structure. So, the Jacobian matrix of error dynamic system at theequilibrium point is solvable. Meanwhile, there are dependences of variables. The re?duction of error dynamic system is necessary, which can help to remove the zero rootscaused by dependences of variables. In the context, the stability of reduced system isanalyzed according to Routh criterion. Then, the stability of error dynamic system isachieved.Variational integrator is used to construct a real-time algorithm of formation, be?cause of its character of long-time preserving for the precision. The variational inte?grator of formation is derived from the Lagrangian, parts of which are the potentialfunctions. The algorithm only requires to solve algebraic equations for every time stepin integration. Therefore, a real-time and coordinated performance can be achieved. Forconsideration of avoidance, the modiifed gyroscopic force is introduced by improvingthe time-varying turning radius of typical gyroscopic, resulting in algorithms which aresuitable for different situations.This work also discussed the consensus and formation controls of nonholonomicagents. The dynamic system of nonholonomic formation is highly nonlinear because ofthe coupling variables of the positions and orientations. The stabilization of nonholo?nomic agent achieved by sliding model control is proofed to be valid for the consensuscontrol of nonholonomic agents. The research is mainly about the switched conditionsof sliding model control and the convergence of such algorithm. It can be proofed thatthe switched conditions of different agents are equivalent for the given sliding modelcontrol, which means the consensus control is achievable. The control strategy of non?holonomic formation is then given based on the consensus control of nonholonomicagents.