Path Planning for Multiple Marine Vehicles Andreas J. Häusler¹, Reza Ghabcheloo², Isaac Kaminer³ António M. Pascoal¹, A. Pedro Aguiar¹ ¹Instituto Superior Técnico, Lisbon, Portugal ²Tampere University of Technology, Tampere, Finland ³Naval Postgraduate School, Monterey, USA

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Motivation & Problem Statement Widening fields of application Increasing demand for autonomous robots Trend towards networked systems Presence of stringent limitations (dynamical constraints, energy, external disturbances) Robust path planning methods required

Mother Ship Current Introduction

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Introduction Multiple vehicle missions require the vehicles to be in formation An initial formation pattern must be established before the mission starts Lack of hovering capabilities  vehicles cannot be deployed and brought to formation separately Need to drive the vehicles to an initial formation pattern in a concerted manner.

Go-To-Formation Maneouvre

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Go-To-Formation Maneouvre Launch of multiple marine vehicles Formation to be reached before mission starts Simultaneous arrival time and equal speeds Collision avoidance & deconfliction clearance

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Spatial Deconfliction Vehicle 1 Vehicle 2 Initial positions Final positions (target formation)

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Temporal Deconfliction Final positions (target formation) Vehicle 1 Vehicle 2Initial positions Intermediate positions

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles MULTIPLE VEHICLE PATH PLANNING SYSTEM Initial Positions Initial Velocities Final Positions Final Velocities Vehicle dynamical constraints External constraints (e.g., obstacles) Cost criterion (e.g.weighted sum of energies, maneuvering time) Nominal Paths and Speed Profiles Vehicle collision avoidance constraints Path Planning System

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Path Planning: an overview Core methodology: based on the work on single vehicle path planning using direct methods (Yakimenko) Extension to multiple air vehicle path planning with spatial deconfliction ( Yakimenko, Kaminer, Pascoal) Extension to multiple marine vehicle path planning with temporal deconfliction (Aguiar, Ghabcheloo, Häusler, Kaminer, Pascoal)

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Decoupling of Space and Time Reduces number of opt. parameters  suitable for real-time implementation Single vehicle path Parameterized by Polynomial for each coordinate Degree determined by no. of boundary conditions Original work by Yakimenko and Kaminer

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Decoupling of Space and Time Optimization produces paths without time constraints, but with timing laws Evolution of with time is Temporal speedand acceleration

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Flexibility of Generated Paths Path shape can be changed by varying Simple choice Path geometry is “shaped” simply by varying

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Multiple Vehicle Path Generation Cost (Energy consumption) Constraints Optimize using zero order methods Spatial deconfliction: subject to

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Simulation Results Spatial Deconfliction in 2D

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Simulation Results Spatial Deconfliction in 3D

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Temporal Deconfliction Deconfliction constraint changes to Simultaneous arrival at time Time-coordinated path following using virtual time Cooperation to adjust vehicle motions in reaction to deviations from original plan (Ghabcheloo)

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Temporal Deconfliction Common path parametrization variable

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Simulation Results Temporal Deconfliction in 2D

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Conclusions Use of direct optimization methods (Yakimenko) Efficient and fast techniques for path generation first used for UAVs (Kaminer et al.) Extension to temporal deconfliction allows for equal times of arrival Decoupling of space and time, resulting in great flexibility for time-coordinated path following

May 13th, Oceans '09 IEEE Bremen Häusler et al. - Path Planning for Multiple Marine Vehicles Future Trends Incorporate effects of current fields Add obstacle avoidance Improve optimization techniques towards online re-planning Sea tests with multiple marine vehicles planned for the Fall of 2009

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