OPTIMAL TASK ALLOCATION AND DYNAMIC TRAJECTORY PLANNING FOR MULTI-VEHICLE SYSTEMS USING NONLINEAR HYBRID OPTIMAL CONTROL

摘要

Based on a nonlinear hybrid dynamical systems model a new planning method for optimal coordination and control of multiple unmanned vehicles is investigated. The time dependent hybrid state of the overall system consists of discrete (roles, actions) and continuous (e.g. position, orientation, velocity) state variables of the vehicles involved. The evolution in time of the system's hybrid state is described by a hybrid state automaton. The presented approach enables a tight and formal coupling of discrete and continuous state dynamics, i.e. of dynamic role and action assignment and sequencing as well as of the physical motion dynamics of a single vehicle modeled by nonlinear differential equations. The planning problem of determining optimal hybrid state trajectories that minimize a cost function as time or energy for optimal multi-vehicle cooperation subject to constraints including the vehicle's motion dynamics is transformed to a mixed-binary dynamic optimization problem being solved numerically. The numerical method consists of an inner iteration where multiphase optimal control problems are solved using a direct collocation method and an outer iteration based on a branch-and-bound search of the discrete solution space. The approach presented in this paper is applied to the scenarios of optimal simultaneous waypoint or target sequencing and dynamic trajectory planning for a team of unmanned aerial vehicles in a plane and to optimal role assignment and physics-based trajectories in robot soccer.