Motion Planning for an Autonomous Underwater Vehicle via Sampling Based Model Predictive Control Charmane V. Caldwell Department of Electrical and Computer Engineering CISCOR of the FAMU-FSU COE Tallahassee, FL. 32310 Email: cvcaldwe@eng.fsu.edu Damion D. Dunlap Naval Surface Warfare Center Panama City, FL. 32407 Email: damion.d.dunlap@navy.mil Emmanuel G. Collins Jr. Department of Mechanical Engineering CISCOR of the FAMU-FSU COE Tallahassee, FL. 32310 Email: ecollins@eng.fsu.edu Abstract— Unmanned Underwater Vehicles (UUVs) can be uti- lized to perform difficult tasks in cluttered environments such as harbor and port protection. However, since UUVs have nonlinear and highly coupled dynamics, motion planning and control can be difficult when completing complex tasks. Introducing models into the motion planning process can produce paths the vehicle can feasibly traverse. As a result, Sampling-Based Model Predictive Control (SBMPC) is proposed to simultaneously generate control inputs and system trajectories for an autonomous underwater vehicle (AUV). The algorithm combines the benefits of sampling- based motion planning with model predictive control (MPC) while avoiding some of the major pitfalls facing both traditional sampling-based planning algorithms and traditional MPC. The method is based on sampling (i.e., discretizing) the input space at each sample period and implementing a goal-directed optimiza- tion (e.g., A ⋆ ) in place of standard numerical optimization. This formulation of MPC readily applies to nonlinear systems and avoids the local minima which can cause a vehicle to become immobilized behind obstacles. The SBMPC algorithm is applied to an AUV in a cluttered environment and an AUV in a common local minima problem. I. INTRODUCTION The United States has over 360 ports that comprise more than 90% of the U.S. export and import industry [1]. These harbors pass through cargo and even passengers. A threat to the ports can produce an environmental and economic crisis [2]. A simple tactic a terrorist can use to cause havoc is employing mines or maritime improvised explosive devises (MIEDs) at a U.S. port. In this way a mine that cost no more than a few thousand dollars can cause great disruption. There have been non-mine related crises in the past that have caused setbacks at U.S. ports: the Exxon Valdez spill of 1989, which cost more than $2.5 billion to clean up, and the dock workers strike of 2002, which resulted in a loss of $1.9 billion dollars a day [2]. The effect of closing a port due to a mine explosion can also be catastrophic. Consequently, it is necessary to protect U.S. ports. The task of searching and destroying mines is a potentially harmful process that can be performed by a combination of surface vehicles, unmanned underwater vehicles (UUVs), and explo- sive ordinance divers (EODs) [1]. This paper will consider the use of an UUV, more specifically an autonomous underwater vehicle (AUV). Harbors and ports have naval ships, commer- cial vessels, fishing boats, piers and other articles that create a cluttered environment for AUV motion. For the inspection to be successful the AUV cannot collide with an obstacle, because this can obviously be very disruptive. In addition to the complex AUV mobility environment the nonlinear, tim- varying and highly coupled vehicle dynamics make motion planning and control difficult for harbor protection tasks since it is difficult to predict future paths for the vehicle as it moves through the environment. In addition, there are uncertainties in the hydrodynamic coefficients determined in a tank test, which effect the confidence in the fidelity of the dynamic model when the AUV maneuvers in the ocean. The vehicle is underdamped and easily perturbed, which is a challenge when there are external disturbances like ocean currents that cause the vehicle to deviate from its path. Furthermore, the center of gravity and buoyancy may change depending on the AUV payload. Consequently, an AUV requires robust motion planning and control to operate reliably in complex environments. Standard AUV motion planning and control first determines a trajectory that the AUV may not be physically able to follow, then applies a controller that may require the vehicle to follow this possibly infeasible trajectory. An approach that can help ensure robust motion planning is to incorporate a model of the AUV when planning the vehicle trajectory since this applies motion constraints that ensure feasible trajectories. In cluttered environments, the use of kinodynamic constraints in motion planning aid in determining a a collision free trajectory. The kinematics provides the turn rate constraint and side slip [3], while the dynamics can provide insight into an AUV’s movement and interaction with the water, providing limits on velocities, accelerations and applied forces. This paper presents preliminary results for motion planning with a kinematic model. A future paper will consider planning using an AUV dynamic model. There are researchers that have previously incorporated a