We consider a variant of the target defense problem where a single defender is tasked to capture a sequence of incoming intruders. Both the defender and the intruders have non-holonomic dynamics. The intruders' objective is to breach the target perimeter without being captured by the defender, while the defender's goal is to capture as many intruders as possible. After one intruder breaches or is captured, the next appears randomly on a fixed circle surrounding the target. Therefore, the defender's final position in one game becomes its starting position for the next. We divide an intruder-defender engagement into two phases, partial information and full information, depending on the information available to the players. We address the capturability of an intruder by the defender using the notions of Dubins path and guarding arc. We quantify the percentage of capture for both finite and infinite sequences of incoming intruders. Finally, the theoretical results are verified through numerical examples using Monte-Carlo-type random trials of experiments.

As UAV popularity soars, so does the mission planning associated with it. The classical approaches suffer from the triple problems of decoupled of task assignment and path planning, poor real-time performance and limited adaptability. Aiming at these challenges, this paper proposes a dynamic real-time multi-UAV collaborative mission planning algorithm based on Dubins paths under a distributed formation structure. Dubins path with multiple advantages bridges the gap between task assignment and path planning, leading to a coupled solution for mission planning. Then, a series of acceleration techniques, task clustering preprocessing, highly efficient distance cost functions, low-complexity and less iterative task allocation strategies, are employed to guarantee the real-time performance of the algorithms. To cope with different emergencies and their simultaneous extremes, real-time planning of emerging tasks and mission replanning due to the reduction of available UAVs are appropriately handled. Finally, the developed algorithm is comprehensively exemplified and studied through simulations, highlighting that the proposed method only sacrifices 9.57% of the path length, while achieving a speed improvement of 4-5 orders of magnitude over the simulated annealing method, with a single mission planning of about 0.0003s.

This paper addresses the Dubins path planning problem for vehicles in 3D space. In particular, we consider the problem of computing CSC paths -- paths that consist of a circular arc (C) followed by a straight segment (S) followed by a circular arc (C). These paths are useful for vehicles such as fixed-wing aircraft and underwater submersibles that are subject to lower bounds on turn radius. We present a new parameterization that reduces the 3D CSC planning problem to a search over 2 variables, thus lowering search complexity, while also providing gradients that assist that search. We use these equations with a numerical solver to explore numbers and types of solutions computed for a variety of planar and 3D scenarios. Our method successfully computes CSC paths for the large majority of test cases, indicating that it could be useful for future generation of robust, efficient curvature-constrained trajectories.

In this work, we propose a novel and efficient method for smoothing polylines in motion planning tasks. The algorithm applies to motion planning of vehicles with bounded curvature. In the paper, we show that the generated path: 1) has minimal length, 2) is $G^1$ continuous, and 3) is collision-free by construction, if the hypotheses are respected. We compare our solution with the state-of.the-art and show its convenience both in terms of computation time and of length of the compute path.

Abstract-- We present an analytic solution to the 3D Dubins path problem for paths composed of an initial circular arc, a straight component, and a final circular arc. These are commonly called CSC paths. By modeling the start and goal configurations of the path as the base frame and final frame of an RRPRR manipulator, we treat this as an inverse kinematics problem. The kinematic features of the 3D Dubins path are built into the constraints of our manipulator model. Furthermore, we show that the number of solutions is not constant, with up to seven valid CSC path solutions even in non-singular regions.

The paper develops a novel motion model, called Generalized Multi-Speed Dubins Motion Model (GMDM), which extends the Dubins model by considering multiple speeds. While the Dubins model produces time-optimal paths under a constant-speed constraint, these paths could be suboptimal if this constraint is relaxed to include multiple speeds. This is because a constant speed results in a large minimum turning radius, thus producing paths with longer maneuvers and larger travel times. In contrast, multi-speed relaxation allows for slower speed sharp turns, thus producing more direct paths with shorter maneuvers and smaller travel times. Furthermore, the inability of the Dubins model to reduce speed could result in fast maneuvers near obstacles, thus producing paths with high collision risks. In this regard, GMDM provides the motion planners the ability to jointly optimize time and risk by allowing the change of speed along the path. GMDM is built upon the six Dubins path types considering the change of speed on path segments. It is theoretically established that GMDM provides full reachability of the configuration space for any speed selections. Furthermore, it is shown that the Dubins model is a specific case of GMDM for constant speeds. The solutions of GMDM are analytical and suitable for real-time applications. The performance of GMDM in terms of solution quality (i.e., time/time-risk cost) and computation time is comparatively evaluated against the existing motion models in obstacle-free as well as obstacle-rich environments via extensive Monte Carlo simulations. The results show that in obstacle-free environments, GMDM produces near time-optimal paths with significantly lower travel times than the Dubins model while having similar computation times. In obstacle-rich environments, GMDM produces time-risk optimized paths with substantially lower collision risks.

AMR is widely used in factories to replace manual labor to reduce costs and improve efficiency. However, it is often difficult for logistics robots to plan the optimal trajectory and unreasonable trajectory planning can lead to low transport efficiency and high energy consumption. In this paper, we propose a method to directly calculate the optimal trajectory for short distance on the basis of the Dubins set, which completes the calculation of the Dubins path. Additionally, as an improvement of Dubins path, we smooth the Dubins path based on clothoid, which makes the curvature varies linearly. AMR can adjust the steering wheels while following this trajectory. The experiments show that the Dubins path can be calculated quickly and well smoothed.

This paper investigates the problem of planning a minimum-length tour for a three-dimensional Dubins airplane model to visually inspect a series of targets located on the ground or exterior surface of objects in an urban environment. Objects are 2.5D extruded polygons representing buildings or other structures. A visibility volume defines the set of admissible (occlusion-free) viewing locations for each target that satisfy feasible airspace and imaging constraints. The Dubins traveling salesperson problem with neighborhoods (DTSPN) is extended to three dimensions with visibility volumes that are approximated by triangular meshes. Four sampling algorithms are proposed for sampling vehicle configurations within each visibility volume to define vertices of the underlying DTSPN. Additionally, a heuristic approach is proposed to improve computation time by approximating edge costs of the 3D Dubins airplane with a lower bound that is used to solve for a sequence of viewing locations. The viewing locations are then assigned pitch and heading angles based on their relative geometry. The proposed sampling methods and heuristics are compared through a Monte-Carlo experiment that simulates view planning tours over a realistic urban environment.