Optimal Direction-Dependent Path Planning for Autonomous Vehicles

The focus of this thesis is optimal path planning. The path planning problem is posed as an optimal control problem, for which the viscosity solution to the static Hamilton-Jacobi-Bellman (HJB) equation is used to determine the optimal path. The Ordered Upwind Method (OUM) has been previously used to numerically approximate the viscosity solution of the static HJB equation for direction-dependent weights. The contributions of this thesis include an analytical bound on the convergence rate of the OUM for the boundary value problem to the viscosity solution of the HJB equation. The convergence result provided in this thesis is to our knowledge the tightest existing bound on the convergence order of OUM solutions to the viscosity solution of the static HJB equation. Only convergence without any guarantee of rate has been previously shown. Navigation functions are often used to provide controls to robots. These functions can suffer from local minima that are not also global minima, which correspond to the inability to find a path at those minima. Provided the weight function is positive, the viscosity solution to the static HJB equation cannot have local minima. Though this has been discussed in literature, a proof has not yet appeared. The solution of the HJB equation is shown in this work to have no local minima that is not also global. A path can be found using this method. Though finding the shortest path is often considered in optimal path planning, safe and energy efficient paths are required for rover path planning. Reducing instability risk based on tip-over axes and maximizing solar exposure are important to consider in achieving these goals. In addition to obstacle avoidance, soil risk and path length on terrain are considered. In particular, the tip-over instability risk is a direction-dependent criteria, for which accurate approximate solutions to the static HJB equation cannot be found using the simpler Fast Marching Method. An extension of the OUM to include a bi-directional search for the source-point path planning problem is also presented. The solution is found on a smaller region of the environment, containing the optimal path. Savings in computational time are observed. A comparison is made in the path planning problem in both timing and performance between a genetic algorithm rover path planner and OUM. A comparison in timing and number of updates required is made between OUM and several other algorithms that approximate the same static HJB equation. Finally, the OUM algorithm solving the boundary value problem is shown to converge numerically with the rate of the proven theoretical bound

Decoupled Sampling-Based Motion Planning for Multiple Autonomous Marine Vehicles

There is increasing interest in the deployment and operation of multiple autonomous marine vehicles (AMVs) for a number of challenging scientific and commercial operational mission scenarios. Some of the missions, such as geotechnical surveying and 3D marine habitat mapping, require that a number of heterogeneous vehicles operate simultaneously in small areas, often in close proximity of each other. In these circumstances safety, reliability, and efficient multiple vehicle operation are key ingredients for mission success. Additionally, the deployment and operation of multiple AMVs at sea are extremely costly in terms of the logistics and human resources required for mission supervision, often during extended periods of time. These costs can be greatly minimized by automating the deployment and initial steering of a vehicle fleet to a predetermined configuration, in preparation for the ensuing mission, taking into account operational constraints. This is one of the core issues addressed in the scope of the Widely Scalable Mobile Underwater Sonar Technology project (WiMUST), an EU Horizon 2020 initiative for underwater robotics research. WiMUST uses a team of cooperative autonomous ma- rine robots, some of which towing streamers equipped with hydrophones, acting as intelligent sensing and communicat- ing nodes of a reconfigurable moving acoustic network. In WiMUST, the AMVs maintain a fixed geometric formation through cooperative navigation and motion control. Formation initialization requires that all the AMVs start from scattered positions in the water and maneuver so as to arrive at required target configuration points at the same time in a completely au- tomatic manner. This paper describes the decoupled prioritized vehicle motion planner developed in the scope of WiMUST that, together with an existing system for trajectory tracking, affords a fleet of vehicles the above capabilities, while ensuring inter- vehicle collision and streamer entanglement avoidance. Tests with a fleet of seven marine vehicles show the efficacy of the system planner developed.Peer reviewe

Human Motion Trajectory Prediction: A Survey

With growing numbers of intelligent autonomous systems in human environments, the ability of such systems to perceive, understand and anticipate human behavior becomes increasingly important. Specifically, predicting future positions of dynamic agents and planning considering such predictions are key tasks for self-driving vehicles, service robots and advanced surveillance systems. This paper provides a survey of human motion trajectory prediction. We review, analyze and structure a large selection of work from different communities and propose a taxonomy that categorizes existing methods based on the motion modeling approach and level of contextual information used. We provide an overview of the existing datasets and performance metrics. We discuss limitations of the state of the art and outline directions for further research.Comment: Submitted to the International Journal of Robotics Research (IJRR), 37 page

Optimal trajectory generation in ocean flows

In this paper it is shown that Lagrangian Coherent Structures (LCS) are useful in determining near optimal trajectories for autonomous underwater gliders in a dynamic ocean environment. This opens the opportunity for optimal path planning of autonomous underwater vehicles by studying the global flow geometry via dynamical systems methods. Optimal glider paths were computed for a 2-dimensional kinematic model of an end-point glider problem. Numerical solutions to the optimal control problem were obtained using Nonlinear Trajectory Generation (NTG) software. The resulting solution is compared to corresponding results on LCS obtained using the Direct Lyapunov Exponent method. The velocity data used for these computations was obtained from measurements taken in August, 2000, by HF-Radar stations located around Monterey Bay, CA