This paper presents a new approach to fuel-optimal path planning of multiple vehicles using a combination of linear and integer programming. The basic problem formulation is to have the vehicles move from an initial dynamic state to a final state without colliding with each other, while at the same time avoiding other stationary and moving obstacles. It is shown that this problem can be rewritten as a linear program with mixed integer/linear constraints that account for the collision avoidance. A key benefit of this approach is that the path optimization can be readily solved using the CPLEX optimization software with an AMPL/Matlab interface. An example is worked out to show that the framework of mixed integer/linear programming is well suited for path planning and collision avoidance problems. Implementation issues are also considered. In particular, we compare receding horizon strategies with fixed arrival time approaches.

A method for nding 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 mixedinteger linear program (MILP) that can be solved using available software. The logical constraints can also be used to express the con guration requirements for maneuvers where only the nal relative alignment of the vehicles is important and the assignment of spacecraft within the eet is not speci ed. The collision avoidance, trajectory optimization, and eet 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 recon guration 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 ying missions that involve multiple vehicles operating in close proximity. Nomenclature

This paper extends a recently developed approach to optimal path planning of autonomous vehicles, based on mixed integer linear programming (MILP), to account for safety. We consider the case of a single vehicle navigating through a cluttered environment which is only known within a certain detection radius around the vehicle. A receding horizon strategy is presented with hard terminal constraints that guarantee feasibility of the MILP problem at all future time steps. The trajectory computed at each iteration is constrained to end in a so called basis state, in which the vehicle can safely remain for an indefinite period of time. The principle is applied to the case of a UAV with limited turn rate and minimum speed requirements, for which safety conditions are derived in the form of loiter circles. The latter need not be known ahead of time and are implicitly computed online. An example scenario is presented that illustrates the necessity of these safety constraints when the knowledge of the environment is limited and/or hard real-time restrictions are given.

No abstract

Abstract-This paper presents a decentralized robust Model Predictive Control algorithm for multi-vehicle trajectory optimization. The algorithm is an extension of a previous robust safe but knowledgeable (RSBK) algorithm that uses the constraint tightening technique to achieve robustness, an invariant set to ensure safety, and a cost-to-go function to generate an intelligent trajectory around obstacles in the environment. Although the RSBK algorithm was shown to solve faster than the previous robust MPC algorithms, the approach was based on a centralized calculation that is impractical for a large group of vehicles. This paper decentralizes the algorithm by ensuring that each vehicle always has a feasible solution under the action of disturbances. The key advantage of this algorithm is that it only requires local knowledge of the environment and the other vehicles while guaranteeing robust feasibility of the entire fleet. The new approach also facilitates a significantly more general implementation architecture for the decentralized trajectory optimization, which further decreases the delay due to computation time.

No abstract

This paper presents a receding horizon controller (RHC) that can be used to design trajectories for an aerial vehicle operating in an environment with disturbances. Various constraints are imposed in the problem, such as turning rate limits and bounds on the vehicle speed, and target regions and no-fly zones are included in the environment. The proposed algorithm modifies these constraints to ensure that the on-line RHC optimization remains feasible even when the vehicle is acted upon by unknown, but bounded, disturbances. The approach uses a robust control invariant admissible set as a terminal set that does not need to be a target set of the overall guidance problem. This result extends previous work in two ways: the vehicle is guaranteed to remain safe under the influence of disturbances; and much longer robust trajectories can be constructed on-line. The full algorithm is demonstrated in several numerical simulations.

No abstract