Cooperative Motion Planning with Time, Energy and Active Navigation Constraints

One of the key elements for the successful execution of multiple AUV missions is the availability of reliable and efficient cooperative motion planning systems. In a representative mission, this system should have the capability to generate collision-free trajectories from the AUVs' initial positions to desired goal positions while optimizing some mission specific performance metric. The trajectories must also satisfy different constraints imposed by environmental conditions, AUV dynamics, and underwater communication limitations. This calls for the availability of algorithms that can deal with a large number of constraints and complex cost functions. In this paper we address the cooperative motion planning problem for a group of AUVs with time, energy, and active navigation constraints. We focus on two challenging problems. In the first problem the trajectories should guide the AUVs to a desired formation with minimum energy consumption, while in the second the information content of the path should be maximized for accurate single-beacon AUV positioning. We formulate the problems as optimal control problems to explicitly address the objectives and constraints. We employ the “direct multiple shooting” method along with a structure-exploiting optimization solver to efficiently solve the optimal control problem. Numerical results illustrate the efficacy of the methodology adopted for cooperative motion planning.