Optimal control of robotic systems with logical constraints: Application to UAV path planning

Optimal control of robotic systems with logical constraints is an instance of a hybrid optimal control problem. It has been traditionally treated as a mixed-integer programming problem (MIP) which is of combinatorial complexity. This paper proposes a new approach for transforming logical constraints into inequality and equality constraints involving only continuous variables. In this way the hybrid optimal control problem is converted to a smooth optimal control problem that can in turn be solved using traditional nonlinear programming methods, thereby dramatically reducing the computational complexity of finding the solution. We illustrate the techniques by solving an optimal path planning problem for multiple unmanned aerial vehicles (UAVs) with collision avoidance. Simulation results are given to show the effectiveness of the approach.