Jonathan P. How

Aircraft trajectory planning with collision avoidance using mixed integer linear programming

Describes a method for finding optimal trajectories for multiple aircraft avoiding collisions. Developments in spacecraft path-planning have shown that trajectory optimization including collision avoidance can be written as a linear program subject to mixed integer constraints, known as a mixed-integer linear program (MILP). This can be solved using commercial software written for the operations research community. In the paper, an approximate model of aircraft dynamics using only linear constraints is developed, enabling the MILP approach to be applied to aircraft collision avoidance. The formulation can also be extended to include multiple waypoint path-planning, in which each vehicle is required to visit a set of points in an order chosen within the optimization.

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.

Real-time indoor autonomous vehicle test environment

To investigate and develop unmanned vehicle systems technologies for autonomous multiagent mission platforms, we are using an indoor multivehicle testbed called real-time indoor autonomous vehicle test environment (RAVEN) to study long-duration multivehicle missions in a controlled environment. Normally, demonstrations of multivehicle coordination and control technologies require that multiple human operators simultaneously manage flight hardware, navigation, control, and vehicle tasking. However, RAVEN simplifies all of these issues to allow researchers to focus, if desired, on the algorithms associated with high-level tasks. Alternatively, RAVEN provides a facility for testing low-level control algorithms on both fixed- and rotary-wing aerial platforms. RAVEN is also being used to analyze and implement techniques for embedding the fleet and vehicle health state (for instance, vehicle failures, refueling, and maintenance) into UAV mission planning. These characteristics facilitate the rapid prototyping of new vehicle configurations and algorithms without requiring a redesign of the vehicle hardware. This article describes the main components and architecture of RAVEN and presents recent flight test results illustrating the applications discussed above.

Spacecraft trajectory planning with avoidance constraints using mixed-integer linear programming

A method for finding fuel-optimal trajectories for spacecraft subjected to avoidance requirements is introduced. These include avoidance of collisions with obstacles or other vehicles and prevention of thruster plumes from one spacecraft impinging on another spacecraft. The necessary logical constraints for avoidance are appended to a fuel-optimizing linear program by including binary variables in the optimization. The resulting problem is a mixed-integer linear program (MILP) that can be solved using available software. The logical constraints can also be used to express the configuration requirements for maneuvers where only the final relative alignment of the vehicles is important and the assignment of spacecraft within the fleet is not specified. The collision avoidance, trajectory optimization, and fleet assignment problems can be combined into a single MILP to obtain the optimal solution for these maneuvers. The MILP problem formulation, including these various avoidance constraints, is presented, and then several examples of their application to spacecraft maneuvers, including reconfiguration of a satellite formation and close inspection of the International Space Station by a microsatellite, are shown. These examples clearly show that the trajectory design methods presented are particularly well suited to proposed formation flying missions that involve multiple vehicles operating in close proximity.

COORDINATION AND CONTROL OF MULTIPLE UAVs

This paper addresses the problems of autonomous task allocation and trajectory planning for a fleet of UAVs. Two methods are compared for solving the optimization that combines task assignment, subjected to UAV capability constraints, and path planning, subjected to dynamics, avoidance and timing constraints. Both sub-problems are non-convex and the two are strongly-coupled. The first method expresses the entire problem as a single mixed-integer linear program (MILP) that can be solved using available software. This method is guaranteed to find the globally-optimal solution to the problem, but is computationally intensive. The second method employs an approximation for rapid computation of the cost of many different trajectories. This enables the assignment and trajectory problems to be decoupled and partially distributed, offering much faster computation. The paper presents several examples to compare the performance and computational results from these two algorithms.

Receding horizon control of autonomous aerial vehicles

This paper presents a new approach to trajectory optimization for autonomous fixed-wing aerial vehicles performing large-scale maneuvers. The main result is a planner which designs nearly minimum time planar trajectories to a goal, constrained by no-fly zones and the vehicles maximum speed and turning rate. Mixed-Integer Linear Programming (MILP) is used for the optimization, and is well suited to trajectory optimization because it can incorporate logical constraints, such as no-fly zone avoidance, and continuous constraints, such as aircraft dynamics. MILP is applied over a receding planning horizon to reduce the computational effort of the planner and to incorporate feedback. In this approach, MILP is used to plan short trajectories that extend towards the goal, but do not necessarily reach it. The cost function accounts for decisions beyond the planning horizon by estimating the time to reach the goal from the plans end point. This time is estimated by searching a graph representation of the environment. This approach is shown to avoid entrapment behind obstacles, to yield near-optimal performance when comparison with the minimum arrival time found using a fixed horizon controller is possible, and to work consistently on large trajectory optimization problems that are intractable for the fixed horizon controller.

Robust distributed model predictive control

This paper presents a formulation for distributed model predictive control (DMPC) of systems with coupled constraints. The approach divides the single large planning optimization into smaller sub-problems, each planning only for the controls of a particular subsystem. Relevant plan data is communicated between sub-problems to ensure that all decisions satisfy the coupled constraints. The new algorithm guarantees that all optimizations remain feasible, that the coupled constraints will be satisfied, and that each subsystem will converge to its target, despite the action of unknown but bounded disturbances. Simulation results are presented showing that the new algorithm offers significant reductions in computation time for only a small degradation in performance in comparison with centralized MPC.

A New Nonlinear Guidance Logic for Trajectory Tracking

A new nonlinear guidance logic, that has demonstrated superior performance in guiding unmanned air vehicles (UAVs) on curved trajectories, is presented. The logic approximates a proportional-derivative controller when following a straight line path, but the logic also contains an element of anticipatory control enabling tight tracking when following curved paths. The method uses inertial speed in the computation of commanded lateral acceleration and adds adaptive capability to the change of vehicle speed due to external disturbances, such as wind. Flight tests using two small UAVs showed that each aircraft was controlled to within 1.6 meters RMS when following circular paths. The logic was ultimately used for air rendezvous of the two aircraft, bringing them in close proximity to within 12 meters of separation, with 1.4 meters RMS relative position errors.

Performance and lyapunov stability of a nonlinear path-following guidance method

Performance and stability are demonstrated for a nonlinear path-following guidance method for unmanned air vehicles. The method was adapted from a pure pursuit-based path following, which has been widely used in ground based robot applications. The method is known to approximate a proportional-derivative controller when following a straight line path, but it is shown that there is also an element of anticipatory control that enables tight tracking when following curved paths. Ground speed is incorporated into the computation of commanded lateral acceleration, which adds an adaptive capability to accommodate vehicle speed changes due to external disturbances such as wind. Asymptotic Lyapunov stability of the nonlinear guidance method is demonstrated when the unmanned air vehicle is following circular paths. The adaptive nature of the guidance method makes its stability independent of vehicle velocity. The stability analysis is also extended to show robust stability of the guidance law in the presence of saturated lateral acceleration, which is an inherent limitation of flight vehicles. Flight tests of the algorithm, using two small unmanned air vehicles, showed that each aircraft was controlled to within 1.6 m root mean square when following circular paths. The method was used to perform a rendezvous of the two aircraft, bringing them into very close proximity, within 12 m of along track separation and 1.4 m root mean square relative position errors.

Cooperative path planning for multiple UAVs in dynamic and uncertain environments

This paper addresses the problem of cooperative path planning for a fleet of unmanned aerial vehicles (UAVs). The paths are optimized to account for uncertainty/adversaries in the environment by modeling the probability of UAV loss. The approach extends prior work by coupling the failure probabilities for each UAV to the selected missions for all other UAVs. In order to maximize the expected mission score, this stochastic formulation designs coordination plans that optimally exploit the coupling effects of cooperation between UAVs to improve survival probabilities. This allocation is shown to recover real-world air operations planning strategies, and to provide significant improvements over approaches that do not correctly account for UAV attrition. The algorithm is implemented in an approximate decomposition approach that uses straight-line paths to estimate the time-of-flight and risk for each mission. The task allocation for the UAVs is then posed as a mixed-integer linear program that can be solved using CPLEX.