Differential flatness-based trajectory planning for multiple unmanned aerial vehicles using mixed-integer linear programming

This paper provides a method for planning fuel-optimal trajectories for multiple unmanned aerial vehicles to reconfigure and traverse between goal points in a dynamic environment in real-time. Recent developments in robot motion planning have shown that trajectory optimization of linear vehicle systems including collision avoidance can be written as a linear program subject to mixed integer constraints, known as a mixed integer linear program (MILP). This paper extends the trajectory optimization to a class of nonlinear systems: differentially flat systems using MILP. A polynomial basis for a Ritz approximation of the optimal solution reduces the optimization variables and computation time without discretizing the systems. Based on the differential flatness property of unmanned vehicle systems, the trajectory planner satisfies the kinematic constraints of the individual vehicles while accounting for inter-vehicle collision and path constraints. The analytical fuel-optimal trajectories are smooth and continuous. Illustrative trajectory planning examples of multiple unmanned aerial vehicles are presented.