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.

In this paper, we provide a graph theoretical framework that allows us to formally de ne formations of multiple vehicles and the issues arising in uniqueness of graph realizations and its connection to stability of formations. The notion of graph rigidity is crucial in identifying the shape variables of a formation and an appropriate potential function associated with the formation. This allows formulation of meaningful optimization or nonlinear control problems for formation stabilization/tacking, in addition to formal representation of split, rejoin, and recon guration maneuvers for multi-vehicle formations. We introduce an algebra that consists of performing some basic operations on graphs which allow creation of larger rigidby -construction graphs by combining smaller rigid subgraphs. This is particularly useful in performing and representing rejoin/split maneuvers of multiple formations in a distributed fashion.

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

n Automatic Control, pages 898 907, 1990. J. Shamma and M. Athans. Guaranteed properties of gain scheduled control for linear parameter-varying plants. Automatica, pages 559 564, 1991. J. Shamma and M. Athans. Gain-scheduling: Potential hazards and possible remedies. IEEE Control Systems Magazine, 12(3):101 107, June 1992. [Sch96] A. Schwartz. Theory and Implementation of Numerical Methods Based on Runge-Kutta Integration for Optimal Control Problems. PhD Disser- tation, University of California, Berkeley, 1996. [SCH+00] M. Sznaier, J. Cloutier, R. Hull, D. Jacques, and C. Mracek. Reced- ing horizon control lyapunov function approach to suboptimal regula- tion of nonlinear systems. Journal of Guidance, Control, and Dynamics, 23(3):399 405, 2000. [SD90] M. Sznaier and M. J. Damborg. Heuristically enhanced feedback con- trol of constrained discrete-time linear systems. Automatica, 26:521 532, 1990. [SMR99] P. Scokaert, D. Mayne, and J. Rawlings. Suboptimal model predictive cont

A generalized model predictive control (MPC) formulation is derived that extends the existing theory to a multi-vehicle formation stabilization problem. The vehicles are individually governed by nonlinear and constrained dynamics. The extension considers formation stabilization to a set of permissible equilibria, rather than a unique equilibrium. Simulations for three vehicle formations with input constrained dynamics on configuration space SE(2) are performed using a nonlinear trajectory generation (NTG) software package developed at Caltech. Preliminary results and an outline of future work for scaling/decentralizing the MPC approach and applying it to an emerging experimental testbed are given.

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.

A computationally efficient technique for the numerical solution of optimal

this paper show the success of this choice for V for stabilization. An inner-loop PD controller on #, # is implemented to stabilize to the receding horizon states # # T , # # T . The # dynamics are the fastest for this system and although most receding horizon controllers were found to be nominally stable without this inner-loop controller, small disturbances could lead to instability

We consider the control of interacting subsystems whose dynamics and constraints are uncoupled, but whose state vectors are coupled non-separably in a single centralized cost function of a finite horizon optimal control problem. For a given centralized cost structure, we generate distributed optimal control problems for each subsystem and establish that the distributed receding horizon implementation is asymptotically stabilizing. The communication requirements between subsystems with coupling in the cost function are that each subsystem obtain the previous optimal control trajectory of those subsystems at each receding horizon update. The key requirements for stability are that each distributed optimal control not deviate too far from the previous optimal control, and that the receding horizon updates happen su#ciently fast. The theory is applied in simulation for stabilization of a formation of vehicles.

We introduce a class of triangulated graphs for algebraic representation of formations that allows us to specify a mission cost for a group of vehicles. This representation plus the navigational information allows us to formally specify and solve tracking problems for groups of vehicles in formations using an optimizationbased approach. The approach is illustrated using a collection of six underactuated vehicles that track a desired trajectory in formation.