Mixed integer programming for multi-vehicle path planning

Abstract

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.

Unmanned aerial vehicle routing in the presence of threats

“…A single UAV and multiple targets were used in a paper by Dogan [28]. Papers that used multiple UAVs and a single target include Schouwenaars et al [20], Jun and D'Andrea [34], and Carlyle et al [39]. Few papers in the literature studied multiple UAVs and multiple targets.…”

“…[21] and [34]. Both moving and fixed threats were used in Schouwenaars et al [20]. Similarly, almost all papers used stationary targets.…”

“…The first method required intensive computations but gave optimal results, while the other was computationally efficient and suitable for real time applications but could give suboptimal solutions. In Schouwenaars et al [20], the paper's main goal was to find optimal fuel paths, while directly avoiding collision with obstacles as well as other vehicles. In addition, the paper accounted for the UAV's dynamics by directly imposing a combination of mixed integer and linear programing constraints in the formulation.…”

Generalized Conflict Learning for Hybrid Discrete/Linear Optimization

“…, n), the position, velocity and acceleration of the vehicle. f (x) is a linear cost function in terms of fuel use, and g(x) ≤ 0 is a conjunction of linear inequalities on vehicle dynamics, and the last constraint keeps the vehicle outside obstacle B, at each time step t. Note that HDLOPs can also be formulated in other ways: BIPs [17,15,14], MLLPs [13] and LCNF [16]. Our GCD-BB algorithm, though introduced in the context of DLPs, can be generalized to other formulations.…”

A decomposition approach to multi-vehicle cooperative control

“…The generation of such a policy has been the subject of a rich literature in cooperative control. A sample of the noteworthy work in this field includes a language for modeling and programming cooperative control systems [18], receding horizon control for multi-vehicle systems [9], non-communicative multi-robot coordination [21], hierarchical methods for target assignment and intercept [1], cooperative estimation for reconnaissance problems [28], mixed integer linear programming methods for cooperative control [33,13], the compilation on multi-robots in dynamics environments [22], and the compilation on cooperative control and optimization [26].…”