THE DUBINS TRAVELING SALESMAN PROBLEM WITH CONSTRAINED COLLECTING MANEUVERS

In this paper, we introduce a variant of the Dubins traveling salesman problem (DTSP) that is called the Dubins traveling salesman problem with constrained collecting maneuvers (DTSP-CM). In contrast to the ordinary formulation of the DTSP, in the proposed DTSP-CM, the vehicle is requested to visit each target by specified collecting maneuver to accomplish the mission. The proposed problem formulation is motivated by scenarios with unmanned aerial vehicles where particular maneuvers are necessary for accomplishing the mission, such as object dropping or data collection with sensor sensitive to changes in vehicle heading. We consider existing methods for the DTSP and propose its modifications to use these methods to address a variant of the introduced DTSP-CM, where the collecting maneuvers are constrained to straight line segments

Mutual Attraction Guided Search: a novel solution method to the Traveling Salesman Problem with vehicle dynamics

Traveling Salesman Problem (TSP) solution techniques are often used for route planning for automated vehicles. Most TSP solution methods focus on path length as the fitness reference, however in many cases, traversal time is of more practical importance. Mutual Attraction Guided Search (MAGS) is a novel solution method that uses an iterative process to simultaneously optimize both angle of travel through each target as well as the ordering of the targets in order to optimize path traversal time. MAGS deterministically locates a locally optimum solution quickly and can optimize for the acceleration limits of a specific vehicle rather than requiring a constant vehicle speed. Since the basic form of MAGS finds a solution deterministically, it has no mechanism for escaping local minima, therefore an evolutionary form is also developed that alternates between local search with MAGS and global search using evolutionary operators to combine and mutate solutions. This hybridization provides the necessary balance between local and global search that is required to locate a globally optimal solution. A fitness based on approximate travel time based on the maximum velocity achievable at each point on the path is calculated using the curvature of the path and the dynamic constraints of the vehicle. The performance of both the basic and evolutionary forms of MAGS are compared against path length based Euclidean and curvature constrained TSP methods --Abstract, page iii

Dynamic Vehicle Routing for Robotic Systems

Recent years have witnessed great advancements in the science and technology of autonomy, robotics, and networking. This paper surveys recent concepts and algorithms for dynamic vehicle routing (DVR), that is, for the automatic planning of optimal multivehicle routes to perform tasks that are generated over time by an exogenous process. We consider a rich variety of scenarios relevant for robotic applications. We begin by reviewing the basic DVR problem: demands for service arrive at random locations at random times and a vehicle travels to provide on-site service while minimizing the expected wait time of the demands. Next, we treat different multivehicle scenarios based on different models for demands (e.g., demands with different priority levels and impatient demands), vehicles (e.g., motion constraints, communication, and sensing capabilities), and tasks. The performance criterion used in these scenarios is either the expected wait time of the demands or the fraction of demands serviced successfully. In each specific DVR scenario, we adopt a rigorous technical approach that relies upon methods from queueing theory, combinatorial optimization, and stochastic geometry. First, we establish fundamental limits on the achievable performance, including limits on stability and quality of service. Second, we design algorithms, and provide provable guarantees on their performance with respect to the fundamental limits.United States. Air Force Office of Scientific Research (Award FA 8650-07-2-3744)United States. Army Research Office. Multidisciplinary University Research Initiative (Award W911NF-05-1-0219)National Science Foundation (U.S.) (Award ECCS-0705451)National Science Foundation (U.S.) (Award CMMI-0705453)United States. Army Research Office (Award W911NF-11-1-0092

The Cost of Bounded Curvature

We study the motion-planning problem for a car-like robot whose turning radius is bounded from below by one and which is allowed to move in the forward direction only (Dubins car). For two robot configurations $\sigma, \sigma'$, let $\ell(\sigma, \sigma')$ be the shortest bounded-curvature path from $\sigma$ to $\sigma'$. For $d \geq 0$, let $\ell(d)$ be the supremum of $\ell(\sigma, \sigma')$, over all pairs $(\sigma, \sigma')$ that are at Euclidean distance $d$. We study the function \dub(d) = \ell(d) - d, which expresses the difference between the bounded-curvature path length and the Euclidean distance of its endpoints. We show that \dub(d) decreases monotonically from \dub(0) = 7\pi/3 to \dub(\ds) = 2\pi, and is constant for d \geq \ds. Here \ds \approx 1.5874. We describe pairs of configurations that exhibit the worst-case of \dub(d) for every distance $d$

A projection algorithm for gradient waveforms design in Magnetic Resonance Imaging

International audienceCollecting the maximal amount of information in a given scanning time is a major concern in Magnetic Resonance Imaging (MRI) to speed up image acquisition. The hardware constraints (gradient magnitude, slew rate, ...), physical distortions (e.g., off-resonance effects) and sampling theorems (Shannon, compressed sensing) must be taken into account simultaneously, which makes this problem extremely challenging. To date, the main approach to design gradient waveform has consisted of selecting an initial shape (e.g. spiral, radial lines, ...) and then traversing it as fast as possible using optimal control. In this paper, we propose an alternative solution which first consists of defining a desired parameterization of the trajectory and then of optimizing for minimal deviation of the sampling points within gradient constraints. This method has various advantages. First, it better preserves the density of the input curve which is critical in sampling theory. Second, it allows to smooth high curvature areas making the acquisition time shorter in some cases. Third, it can be used both in the Shannon and CS sampling theories. Last, the optimized trajectory is computed as the solution of an efficient iterative algorithm based on convex programming. For piecewise linear trajectories, as compared to optimal control reparameterization, our approach generates a gain in scanning time of 10% in echo planar imaging while improving image quality in terms of signal-to-noise ratio (SNR) by more than 6 dB. We also investigate original trajectories relying on traveling salesman problem solutions. In this context, the sampling patterns obtained using the proposed projection algorithm are shown to provide significantly better reconstructions (more than 6 dB) while lasting the same scanning time