A direct method for a real-time generation of near-optimal spatial trajectories of short-term maneuvers onboard a ying vehicle with predetermined thrust history is introduced. The paper starts with a survey about the founders of the direct methods of calculus of variations and their followers in ight mechanics, both in Russia and in the United States. It then describes a new direct method based on three cues: high-order polynomials from the virtual arc as a reference function for aircraft's coordinates, a preset history of one of the controls (thrust), and a few optimization parameters. The trajectory optimization problem is transformed into a nonlinear programming problem and then solved numerically using an appropriate algorithm in accelerated scale of time. A series of examples is presented. Calculated near-optimal trajectory is compared with real ight data, and with the solution obtainedby Pontryagin's maximumprinciple. Fast convergence of the numerical algorithm,which has been already implemented and tested onboard a real aircraft, is illustrated. Nomenclature a ik= polynomial coef cients g = acceleration due to gravity J = cost function j = quantity pertaining to the j th time node m = aircraft mass N = number of nodes n = polynomial order n = relative revolutions of engine's rotor n x , n z = tangential and normal projections of load factor, respectively Sh = penalty function T,T = total thrust and relative thrust (fraction of maximum thrust), respectively CONCEPT of the onboard pilot's support system (PSS; electronic copilot or pilot associate) assumes the presenceof a sub-

The paper proposes a complete real-time control algorithm for autonomous collision-free operations of the quadrotor UAV. As opposed to fixed wing vehicles the quadrotor is a small agile vehicle which might be more suitable for the variety of specific applications including search and rescue, surveillance and remote inspection. The developed control system incorporates both trajectory planning and path following. Using a differential flatness property the trajectory planning is posed as a constrained optimization problem in the output space (as opposed to the control space), which simplifies the problem. The trajectory and speed profile are parameterized to reduce the problem to a finite dimensional problem. To optimize the speed profile independently of the trajectory a virtual argument is used as opposed to time. A path following portion of the proposed algorithm uses a standard linear multi-variable control technique. The paper presents the results of simulations to demonstrate the suitability of the proposed control algorithm.

This paper develops a complete framework for coordinated control of multiple unmanned air vehicles (UAVs) that are tasked to execute collision-free maneuvers under strict spatial and temporal constraints in restricted airspace. The framework proposed includes strategies for deconflicted real-time path generation, nonlinear path following, and multiple vehicle coordination. Path following relies on the augmentation of existing autopilots with L1 adaptive output feedback control laws to obtain inner-outer loop control structures with guaranteed performance. Multiple vehicle coordination is achieved by enforcing temporal constraints on the speed profiles of the vehicles along their paths in response to information exchanged over a communication network. Again, L1 adaptive control is used to yield an inner-outer loop structure for vehicle coordination.A rigorous proof of stability and performance bounds of the combined path following and coordination strategies is given. Flight test results obtained at Camp Roberts, CA in 2007 demonstrate the benefits of using L1 adaptive control for path following of a single vehicle. Hardware-in-the-loop simulations for two vehicles are discussed and provide a proof of concept for time-critical coordination of multiple vehicles over communication networks with fixed topologies.

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This paper formulates and solves the problem of minimum-time and minimum-energy optimal trajectories of rendezvous of a powered chaser and a passive tumbling target, in a circular orbit. Both translational and rotational dynamics are considered. In particular, ending conditions are imposed of matching the positions and velocities of two points of interest onboard the vehicles. A collision-avoidance condition is imposed as well. The optimal control problems are analytically formulated through the use of the Pontryagin minimum principle. The problems are then solved numerically, by using a direct collocation method based on the Gauss pseudospectral approach. Finally, the obtained solutions are verified through the minimum principle, solved by a shooting method. The simulation results show that the pseudospectral solver provides solutions very close to the optimal ones, except in the case of presence of singular arcs when it may not provide a feasible solution. The computational time needed by the pseudospectral solver is a small fraction of the one needed by the indirect approach, but it is still considerably too large to allow for its use in real-time onboard guidance.