This paper presents an end-to-end solution to the battlefield scenario where M unmanned air vehicles are assigned to strike N known targets, in the presence of dynamic threats. The problem is decomposed into the subproblems of (1) cooperative target assignment, (2) coordinated UAV intercept, (3) path planning, and (4) feasible trajectory generation. The design technique is based on a hierarchical approach to coordinated control. Detailed simulation results are presented.

Preliminary results of a new computational approach to generate aggressive trajectories in real-time for constrained mechanical systems are presented. The algorithm is based on a combination of nonlinear control theory, spline theory, and sequential quadratic programming. It is demonstrated that real-time trajectory generation for constrained mechanical systems is possible by mapping the problem to one of finding trajectory curves in a lower dimensional space. Performance of the algorithm is compared with existing optimal trajectory generation techniques. Numerical results are reported using the NTG software package. Keywords: Real-time optimization, nonlinear control design, optimal control, constrained trajectory generation, guidance. 1

This paper focuses on the problem of cooperatively searching, using a team of unmanned air vehicles (UAVs), an area of interest that contains regions of opportunity and regions of potential hazard. The objective of the UAV team is to visit as many opportunities as possible, while avoiding as many hazards as possible. To enable cooperation, the UAVs are constrained to stay within communication range of one another. Collision avoidance is also required. Algorithms for teamoptimal and individually-optimal/team-suboptimal solutions are developed and their computational complexity compared. Simulation results demonstrating the feasibility of the cooperative search algorithms are presented. 1

Autonomous unmanned air vehicle flight control systems require robust path generation to account for terrain obstructions, weather, and moving threats such as radar, jammers, and unfriendly aircraft. In this paper, we outline a feasible, hierarchal approach for real-time motion planning of small autonomous fixed-wing UAVs. The approach divides the trajectory generation into four tasks: waypoint path planning, dynamic trajectory smoothing, trajectory tracking, and low-level autopilot compensation. The waypoint path planner determines the vehicle 's route without regard for the dynamic constraints of the vehicle. This results in a significant reduction in the path search space, enabling the generation of complicated paths that account for pop-up and dynamically moving threats. Kinematic constraints are satisfied using a trajectory smoother which has the same kinematic structure as the physical vehicle. The third step of the approach uses a novel tracking algorithm to generate a feasible state trajectory that can be followed by a standard autopilot. Monte-Carlo simulations were done to analyze the performance and feasibility of the approach and determine real-time computation requirements. A planar version of the algorithm has also been implemented and tested in a low-cost micro-controller. The paper describes a custom UAV built to test the algorithms.

This paper presents a solution strategy for achieving cooperative timing among teams of vehicles. Based on the notion of coordination variables and coordination functions, the strategy facilitates cooperative timing by requiring acceptably low levels of communication and computation. The application of the coordination variable/function approach to trajectory planning problems for teams of unmanned air vehicles with timing constraints is described. Three types of timing constraints are considered: simultaneous arrival, tight sequenc- ing, and loose sequencing. Simulation results demonstrating the viability of the approach are presented.

: Acom92EU92622 approach to generatereal-timJ optimF trajectories for a flight control experim0 t is presented.Minim um tim trajectories arecom)#J0 for hover-to-hover and forward flightm296) ers. Instantaneous changes in the trajectory constraints thatm del obstacles and threats are also investigated. ExperimJ tal results using the Nonlinear Trajectory Generation software package show good closedloop performJEU for bothmhE20 ers and in the presence of obstacles. Success of the algorithm demithmUJ6 that high-confidencereal-tim trajectory generation is achievable in spite of the highly nonlinear and non-convex nature of the problem Keywords: Trajectory planning, real-timU optim9 control,optim#()EUJ2 nonlinear control, guidancesystem 1.

A technique is presented for creating continuously parameterized classes of feasible system trajectories. These classes, which are useful for higher-level vehicle motion planners, follow directly from a small collection of userprovided example motions. A dynamically feasible trajectory interpolation algorithm generates a continuous family of vehicle maneuvers across a range of boundary conditions while enforcing nonlinear system equations of motion as well as nonlinear equality and inequality constraints. The scheme is particularly useful for describing motions that deviate widely from the range of linearized dynamics and where satisfactory example motions may be found from off-line nonlinear programming solutions or motion capture of human-piloted flight. The interpolation algorithm is computationally efficient, making it a viable method for real-time maneuver synthesis, particularly when used in concert with a vehicle motion planner. Experimental application to a three-degree-of-freedom rotorcraft test bed demonstrates the essential features of system and trajectory modeling, maneuver example selection, maneuver class synthesis, and integration into a hybrid system path planner. Nomenclature ai = vehicle model coefficients Bi,k = ith B-spline basis function of order k b = binary variable

Abstract—This brief presents a real-time, feasible trajectory generation algorithm for unmanned air vehicles (UAVs) flying through a sequence of waypoints. The algorithm produces extremal trajectories that transition between straight-line path segments in a time-optimal fashion. In addition, the algorithm can be configured so that the dynamically feasible trajectory has the same path length as the straight-line waypoint path. Implementation issues associated with the algorithm are described in detail. Simulation studies show the effectiveness of the proposed method. Index Terms—Autonomous systems, optimal control, path planning, trajectory generation, unmanned air vehicles (UAVs). I.

Under appropriate conditions, the dynamics of a control system governed by ordinary differential equations can be formulated several ways: differential inclusion, control parameterization, flatness parameterization, higher-order inclusions and so on. A plethora of techniques have been proposed for each of these formulations but they are typically not portable across equivalent mathematical formulations. Further complications arise as a result of configuration and control constraints such as those imposed by obstacle avoidance or control saturation. In this paper, we present a unified framework for handling the computation of optimal controls where the description of the governing equations or that of the path constraint is not a limitation. In fact, our method exploits the advantages offered by coordinate transformations and harnesses any inherent smoothness present in the optimal system trajectories. We demonstrate how our computational framework can easily and efficiently handle different cost formulations, control sets and path constraints. We illustrate our ideas by formulating a robotics problem eight different ways that includes a differentially flat formulation subject to control saturation. This example establishes the loss of convexity in the flat formulation as well as its ramifications on computation and optimality. In addition, a numerical comparison of our unified approach to a recent technique tailored for control-affine systems reveals that we get about 30 % improvement in the performance index.

Efficient algorithms for collision-free energy sub-optimal path planning for formations of spacecraft flying in deep space are presented. The idea is to introduce a set of way-points through which the spacecraft are required to pass, combined with parameterizations of the trajectories which are energy-optimal for each spacecraft. The resulting constrained optimization problem is formulated as a quasiquadratic parameter optimization problem in terms of the way-points parameters. The mathematical structure of the problem is further exploited to develop gradient-based algorithms in which the gradients are computed analytically. The collision avoidance constraints are approximated such that closed form solutions are generated. This combination results in fast and robust numerical algorithms which work very well for scenarios involving a large number of spacecraft (e.g. 20).