Multiobjective Kinematic Trajectory Planning An Application to the Captive Trajectory Simulation (CTS) System

In this thesis, a new approach to the resolution of multiobjective trajectory planning problems is proposed. Rather than providing a single solution with the weighting method, it is proposed to provide the entire Pareto optimal set, or more generally the entire minimal element set when the objective space is partially ordered by a cone. This approach is applied to the general class of multiobjective deterministic finite horizon optimal control problems to which many multiobjective trajectory planning problems, including the joint space trajectory planning problem arising from a wind-tunnel experimental setup called captive trajectory simulation (CTS) system, can be shown to belong. A new discrete dynamic programming (DDP) approximation method for the resolution of this class of problems is developed, from which an approximate minimal element set is obtained. Partial convergence results of this approximate set towards the original minimal element set is obtained using set convergence in the sense of Hausdorff. When the DDP approximation method is applied to the joint trajectory planning problem for the CTS system, the approximate Pareto optimal set is shown to provide a better representation of the Pareto optimal set than the set obtained with the weighting method. In order to improve the computational efficiency of the DDP approximation method, a clustering approach is introduced. With the application of clustering, the DDP approximation method is shown to have polynomial complexity, which yields a dramatic reduction in the resolution time. The resulting set is shown to still provide a better representation of the Pareto optimal set than the set obtained with the weighting method. The Hausdorff distance is proposed as a measure for comparison. Finally, the complete CTS trajectory planning problem is solved by sequentially solving the problem in the task and joint spaces. For the resolution of the task space problem, an algorithm based on the resolution of a rural postman problem is proposed. The proposed sequential approach for the resolution of the CTS trajectory planning problem allows for fast resolution times.