Oleg A. Yakimenko

Direct Method for Rapid Prototyping of Near-Optimal Aircraft Trajectories

Adirectmethod fora real-timegenerationofnear-optimal spatialtrajectoriesofshort-term maneuversonboard a e ying vehiclewith predetermined thrust history isintroduced. Thepaperstarts with a survey about the founders of the direct methods of calculus of variations and their followers in e 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 e ight data, and with the solution obtainedbyPontryagin’ smaximumprinciple.Fastconvergenceofthenumericalalgorithm,whichhasbeenalready implemented and tested onboard a real aircraft, is illustrated. Nomenclature aik = polynomial coefe cients g = acceleration due to gravity J = cost function j = quantity pertaining to the jth time node m = aircraft mass N = number of nodes n = polynomial order ¯ n = relative revolutions of engine’ s rotor nx, nz = tangential and normal projections of load factor, respectively Sh = penalty function T, ¯ T = total thrust and relative thrust (fraction of maximum thrust), respectively t = time t ¤

Coordinated Path Following for Time-Critical Missions of Multiple UAVs via L1 Adaptive Output Feedback Controllers

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 deconicted 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 proles 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 benets 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 xed topologies.

Path Generation, Path Following and Coordinated Control for TimeCritical Missions of Multiple UAVs

The paper proposes a solution to the problem of coordinated control of multiple unmanned air vehicle (UAV) to ensure collision-free maneuvers under strict spatial and temporal constraints. First, a set of feasible trajectories are generated for all UAVs using a new direct method of optimal control that takes into account rules for collision avoidance. A by-product of this step yields, for each vehicle, a spatial path to be followed together with a nominal desired speed profile. Each vehicle is then made to execute a pure path following maneuver in three-dimensional space by resorting to a novel 3D algorithm. Finally, the speed profile for each vehicle is adjusted to enforce the temporal constraints that must be met in order to coordinate the fleet of vehicles. Simulations illustrate the potential of the methodology developed

Unmanned aircraft navigation for shipboard landing using infrared vision

This paper addresses the problem of determining the relative position and orientation of an unmanned air vehicle with respect to a ship using three visible points of known separation. The, images of the points are obtained from an onboard infrared camera. The paper develops a numerical solution to this problem. Both simulation and flight test results are presented.

Development and Testing of the Miniature Aerial Delivery System Snowflake

Proceedings of the 20th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar, Seattle, WA, May 4-7, 2009.

Optimal Rendezvous Trajectories of a Controlled Spacecraft and a Tumbling Object

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.

Direct Method Based Control System for an Autonomous Quadrotor

This paper proposes a real time control algorithm for autonomous operation of a quadrotor unmanned air vehicle. The quadrotor is a small agile vehicle, which as well as being a excellent test bed for advanced control techniques could also be suitable for internal surveillance, search and rescue and remote inspection. The proposed control scheme incorporates two key aspects of autonomy; trajectory planning and trajectory following. Using the differentially-flat dynamics property of the system, the trajectory optimization is posed as a non-linear constrained optimization within the output space in the virtual domain, not explicitly related to the time domain. A suitable parameterization using a virtual argument as opposed to time is applied, which ensures initial and terminal constraint satisfaction. The speed profile is optimized independently, followed by the mapping to the time domain achieved using a speed factor. Trajectory following is achieved with a standard multi-variable control technique and a digital switch is used to re-optimize the reference trajectory in the event of infeasibility or mission change. The paper includes simulations using a full dynamic model of the quadrotor demonstrating the suitability of the proposed control scheme.

Linear parametrically varying systems with brief instabilities: an application to vision/inertial navigation

This paper addresses the problem of nonlinear filter design to estimate the relative position and velocity of an unmanned air vehicle (UAV) with respect to a point on a ship using infrared (IR) vision, inertial, and air data sensors. Sufficient conditions are derived for the existence of a particular type of complementary filters with guaranteed stability and performance in the presence of so-called out-of-frame events that arise when the vision system loses its target temporarily. The results obtained build upon new developments in the theory of linear parametrically varying systems (LPVs) with brief instabilities - also reported in the paper - and provide the proper framework to deal with out-of-frame events. Field tests with a prototype UAV illustrate the performance of the filter and the scope of applications of the new theory developed.

Computing short-time aircraft maneuvers using direct methods

This paper analyzes the applicability of direct methods to design optimal short-term spatial maneuvers for an unmanned vehicle in a faster than real-time scale. It starts by introducing different basic control schemes, which employ online trajectory generation. Next, it presents and analyzes the results obtained through two recently developed direct transcription (collocation) methods: the Gauss pseudospec-tral method and the Legendre-Gauss-Lobatto pseudosp ectral method. The achieved results are further compared with those found through the Pontryagin’s Maximum (Minimum) Principle, and the paper continues by providing another set of direct method simulations incorporating more realistic boundary conditions. Finally, the results obtained using the third direct method, based on inverse dynamics in the virtual domain, are presented and discussed.

Optimal Control for Terminal Guidance of Autonomous Parafoils

This paper deals with the development of guidance, navigation and control algorithms for a prototype of a miniature aerial delivery system capable of high-precision maneuvering and high touchdown accuracy. High accuracy enables use in precision troop resupply, sensor placement, urban warfare reconnaissance, and other similar operations. Specifically, this paper addresses the terminal phase, where uncertainties in winds cause most of the problems. The paper develops a six degree-offreedom model to adequately address dynamics and kinematics of the prototype delivery system and then reduces it to a two degrees-of-freedom model to develop a model predictive control algorithm for reference trajectory tracking during all stages. Reference trajectories are developed in the inertial coordinate frame associated with the target. The reference trajectory during terminal guidance, just prior to impact, is especially important to the final accuracy of the system. This paper explores an approach for generating reference trajectories based on the inverse dynamics in the virtual domain. The method results in efficient solution of a two-point boundary-value problem onboard the aerial delivery system allowing the trajectory to be generated at a high rate, mitigating effects of the unknown winds. This paper provides derivation of the guidance and control algorithms and present analysis through simulation.