Gokhan Inalhan

Relative Dynamics and Control of Spacecraft Formations in Eccentric Orbits

Formation eying is a key technology for both deep-space and orbital applications that involve multiple spacecraft. Many future space applications will beneet from using formation e ying technologies to perform distributed observations (e.g., synthetic apertures for Earth mapping interferometry) and to provide improved coverage for communication and surveillance. Previous research has focused on designing passive apertures for these formation e ying missions assuming a circular reference orbit. Those design approaches are extended and a complete initialization procedure for a large e eet of vehicles with an eccentric reference orbit is presented. The main result is derived from the homogenous solutions of the linearized relative equations of motion for the spacecraft. These solutions are used to end the necessary conditions on the initial states that produce T-periodic solutions that have the vehicles returning to the initial relative states at the end of each orbit, that is, v(t0)=v(t0+T). This periodicity condition and the resulting initialization procedure are originally given (in compact form) at the reference orbit perigee, butthis is alsogeneralized to enable initialization atanypoint around thereference orbit. In particular, an algorithm is given that minimizes the fuel cost associated with initializingthe vehicle states (primarily the in-track and radial relative velocities) to values that are consistent with periodic relative motion. These algorithms extend and generalize previously published solutions for passive aperture forming with circular orbits. The periodicity condition and the homogenous solutions can also be used to estimate relative motion errors and the approximate fuel cost associated with neglecting the eccentricity in the reference orbit. The nonlinear simulations presented clearlyshowthatignoringthereferenceorbiteccentricitygeneratesanerrorthatiscomparabletothedisturbances caused by differential gravity accelerations.

Decentralized optimization, with application to multiple aircraft coordination

We present a decentralized optimization method for solving the coordination problem of interconnected nonlinear discrete-time dynamic systems with multiple decision makers. The optimization framework embeds the inherent structure in which each decision maker has a mathematical model that captures only the local dynamics and the associated interconnecting global constraints. A globally convergent algorithm based on sequential local optimizations is presented. Under assumptions of differentiability and linear independence constraint qualification, we show that the method results in global convergence to /spl epsiv/-feasible Nash solutions that satisfy the Karush-Kuhn-Tucker necessary conditions for Pareto-optimality. We apply this methodology to a multiple unmanned air vehicle system, with kinematic aircraft models, coordinating in a common airspace with separation requirements between the aircraft.

Decentralized overlapping control of a formation of unmanned aerial vehicles

Decentralized overlapping feedback laws are designed for a formation of unmanned aerial vehicles. The dynamic model of the formation with an overlapping information structure constraint is treated as an interconnected system with overlapping subsystems. Using the mathematical framework of the inclusion principle, the interconnected system is expanded into a higher dimensional space in which the subsystems appear to be disjoint. On a subsystem level, a static state feedback controller is designed to robustly stabilize the perturbed nominal dynamics of the subsystem. The design procedure is based on the hierarchical application of convex optimization tools involving linear matrix inequalities. As a final step, the decentralized controllers are contracted back to the original interconnected system for implementation.

Spacecraft formation flying control design for the Orion mission

Formation ying of multiple spacecraft is an enabling technology for many future space science missions. However, the coordination and control of such instruments present many design challenges. This paper addresses the formation ying spacecraft control problem at several levels. We present low-level, multi-vehicle, station keeping algorithms and a control architecture to keep the vehicles aligned in formation. We also present a high-level eet planner that creates trajectories (e.g. to re-size or re-target the formation) and takes into account the limited fuel onboard each vehicle. A coordinator is introduced at the highest-level to ensure that vehicle resources are expended equally within the eet. Algorithms are discussed for each level, with simulations to compare performance. The simulation results are then veri ed on a formation ying testbed. The control design is then discussed with a perspective on the upcoming Orion mission. 1

Formation control strategies for a separated spacecraft interferometer

Formation flying of multiple spacecraft is an enabling technology for future space science missions such as separated spacecraft interferometers. Controllers designed for these multi-vehicle fleets must address many high- and low-level tasks, and will become very complicated for large fleets. As such, this work describes ongoing research to investigate the precise sensing and control of a distributed spacecraft interferometer using a layered approach based on GPS and laser metrology. In particular, it focuses on the design of low-level controllers within several candidate control architectures, and analyzes how well these controllers perform on basic formations. Initial experimental results are presented on a three vehicle formation flying testbed executing station-keeping and rigid body maneuvers.

DragonFly: a versatile UAV platform for the advancement of aircraft navigation and control

The DragonFly experimental test bed is a platform that supports new research and innovations in navigation, fault tolerant control and multiple vehicle coordination. It consists of two UAVs with modular onboard avionics packages, which communicate through a wired and wireless network to the ground and lab development systems running QNX real-time OS. Its modularity and networked architecture is key in supporting such a wide range of concurrent research. This paper gives an overview of the DragonFly experimental test bed and the specific research goals that it currently supports.

Integration of Path/Maneuver Planning in Complex Environments for Agile Maneuvering UCAVs

In this work, we consider the problem of generating agile maneuver profiles for Unmanned Combat Aerial Vehicles in 3D Complex environments. This problem is complicated by the fact that, generation of the dynamically and geometrically feasible flight trajectories for agile maneuver profiles requires search of nonlinear state space of the aircraft dynamics. This work suggests a two layer feasible trajectory/maneuver generation system. Integrated Path planning (considers geometrical, velocity and acceleration constraints) and maneuver generation (considers saturation envelope and attitude continuity constraints) system enables each layer to solve its own reduced order dimensional feasibility problem, thus simplifies the problem and improves the real time implement ability. In Trajectory Planning layer, to solve the time depended path planning problem of an unmanned combat aerial vehicles, we suggest a two step planner. In the first step, the planner explores the environment through a randomized reachability tree search using an approximate line segment model. The resulting connecting path is converted into flight way points through a line-of-sight segmentation. In the second step, every consecutive way points are connected with B-Spline curves and these curves are repaired probabilistically to obtain a geometrically and dynamically feasible path. This generated feasible path is turned in to time depended trajectory with using time scale factor considering the velocity and acceleration limits of the aircraft. Maneuver planning layer is constructed upon multi modal control framework, where the flight trajectories are decomposed to sequences of maneuver modes and associated parameters. Maneuver generation algorithm, makes use of mode transition rules and agility metric graphs to derive feasible maneuver parameters for each mode and overall sequence. Resulting integrated system; tested on simulations for 3D complex environments, gives satisfactory results and promises successful real time implementation.

A probabilistic B-spline motion planning algorithm for unmanned helicopters flying in dense 3D environments

This paper presents a strategy for improving motion planning of an unmanned helicopter flying in a dense and complex city-like environment. Although Sampling Based Motion planning algorithms have shown success in many robotic problems, problems that exhibit ldquonarrow passagerdquo properties involving kinodynamic planning of high dimensional vehicles like aerial vehicles still present computational challenges. In this work, to solve the kinodynamic motion planning problem of an unmanned helicopter, we suggest a two step planner. In the first step, the planner explores the environment through a randomized reachability tree search using an approximate line segment model. The resulting connecting path is converted into flight way points through a line-of-sight segmentation. In the second step, every consecutive way points are connected with B-Spline curves and these curves are repaired probabilistically to obtain a dynamically feasible path. Numerical simulations in 3D indicate the ability of the method to provide real-time solutions in dense and complex environments.

8 – Cooperative Spacecraft Formation Flying: Model Predictive Control with Open- and Closed-Loop Robustness

This chapter discusses the cooperative spacecraft formation flying. Formation flying of multiple spacecraft is an enabling technology for many future space science missions including enhanced stellar optical interferometers and virtual platforms for Earth observations. Controlling a formation will require several considerations beyond those of a single spacecraft. Key among these is the increased emphasis on fuel savings for a fleet of vehicles because the spacecraft must typically be kept in an accurate formation for periods on the order of hours or days, and the performance of the formation should degrade gracefully as one or more of the spacecraft runs out of fuel. This chapter presents a model predictive controller that is particularly well-suited to formation flying spacecraft because it explicitly minimizes fuel use, exploits the well-known orbital dynamics environment, and naturally incorporates constraints.

A Probabilistic Algorithm for Mode Based Motion Planning of Agile Unmanned Air Vehicles in Complex Environments

Abstract In this work, we consider the design of a probabilistic trajectory planner for a highly maneuverable unmanned air vehicle flying in a dense and complex city-like environment. Our design hinges on the decomposition of the problem into a) flight controls of fundamental agile-maneuvering flight modes and b) trajectory planning using these controlled flight modes from which almost any aggressive maneuver (or a combination of) can be created. This allows significant decreases in control input space and thus search dimensions, resulting in a natural way to design controllers and implement trajectory planning using the closed-form flight modes. Focusing on the trajectory planning part, we provide a three-step probabilistic trajectory planner. In the first step, the algorithm rapidly explores the environment through a randomized reachability tree search using an approximate line segment models. The resulting connecting path is converted into flight milestones through a line-of-sight segmentation. This path and the corresponding milestones are refined with a single-query Probabilistic Road Map (PRM) implementation that creates dynamically feasible flight paths with distinct flight mode selections. We address the problematic issue of narrow passages through non-uniform distributed capture regions, which prefer state solutions that align the vehicle to enter the milestone region in line with the next milestone to come. Numerical simulations in 3D and 2D demonstrate the ability of the method to provide real-time solutions in dense and complex environments.