| This thesis develops a novel solution method for the problem of collision-free, optimal control of a robotic vehicle in an obstacle populated environment. The technique presented combines the well established approximate cell decomposition methodology with disjunctive programming in order to address both geometric and kinematic trajectory concerns. In this work, an algorithm for determining the shortest distance, collision-free path of a robot with unicycle kinematics is developed. In addition, the research defines a technique to discretize nonholonomic vehicle kinematics into a set of mixed integer linear constraints. Results obtained using the Tomlab/CPLEX mixed integer quadratic programming software exhibit that the method developed provides a powerful initial step in reconciling geometric path planning methods with optimal control techniques. |
