Convex Tours of Bounded Curvature

We consider the motion planning problem for a point constrained to move along a smooth closed convex path of bounded curvature. The workspace of the moving point is bounded by a convex polygon with m vertices, containing an obstacle in a form of a simple polygon with $n$ vertices. We present an O(m+n) time algorithm finding the path, going around the obstacle, whose curvature is the smallest possible.Comment: 11 pages, 5 figures, abstract presented at European Symposium on Algorithms 199

Implications of Motion Planning: Optimality and k-survivability

We study motion planning problems, finding trajectories that connect two configurations of a system, from two different perspectives: optimality and survivability. For the problem of finding optimal trajectories, we provide a model in which the existence of optimal trajectories is guaranteed, and design an algorithm to find approximately optimal trajectories for a kinematic planar robot within this model. We also design an algorithm to build data structures to represent the configuration space, supporting optimal trajectory queries for any given pair of configurations in an obstructed environment. We are also interested in planning paths for expendable robots moving in a threat environment. Since robots are expendable, our goal is to ensure a certain number of robots reaching the goal. We consider a new motion planning problem, maximum k-survivability: given two points in a stochastic threat environment, find n paths connecting two given points while maximizing the probability that at least k paths reach the goal. Intuitively, a good solution should be diverse to avoid several paths being blocked simultaneously, and paths should be short so that robots can quickly pass through dangerous areas. Finding sets of paths with maximum k-survivability is NP-hard. We design two algorithms: an algorithm that is guaranteed to find an optimal list of paths, and a set of heuristic methods that finds paths with high k-survivability

Motion planning for rigid body robots

Given a non-holonomic disc model, D, its motion constraints in terms of maximum curvature (K (max)), a set W of rectilinear polygonal obstacles which assemble an office-like environment, and two configurations of S and G in free(W), this thesis investigates the planning of a smooth free path which satisfies the following condition: D is allowed backing up motions at the end portions of the path, but the middle is to be of class C(2) in its entirety. Although the motion planning problem of D amidst polygonal obstacles has been extensively studied, the paths considered are mostly class C(2) and piecewise C(2) only, and are subject only to the K(max) constraint. Typically, such paths consist of straight line segments and circular ars which have curvature discontinuity at the junction points. In order for D to follow such paths physically, D has to stop abruptly at each junction point to change curvature. The C(2) path investigated in this thesis allows non-stopping motion of D. It is also subject to a further K(mas) constraint to avoid turns that exceed the rate of change of curvature constraint. A class of smooth curves called cubic spirals are adopted for planning C(2) paths. Properties of the cubic spiral are examined in detail. A framework of layered motion planning approach is proposed to divide and conquer the motion planning problem. A novel sensor-oriented method is presented. It plans a spine net which facilitates D carry out deviation correction using sonar sensors while following a motion path.http://archive.org/details/motionplanningfo00tanlCivilian, Singapore Ministry of DefenseApproved for public release; distribution is unlimited

Path planning algorithms for autonomous navigation of a non-holonomic robot in unstructured environments

openPath planning is a crucial aspect of autonomous robot navigation, enabling robots to efficiently and safely navigate through complex environments. This thesis focuses on autonomous navigation for robots in dynamic and uncertain environments. In particular, the project aims to analyze the localization and path planning problems. A fundamental review of the existing literature on path planning algorithms has been carried on. Various factors affecting path planning, such as sensor data fusion, map representation, and motion constraints, are also analyzed. Thanks to the collaboration with E80 Group S.p.A., the project has been developed using ROS (Robot Operating System) on a Clearpath Dingo-O, an indoor mobile robot. To address the challenges posed by unstructured and dynamic environments, ROS follows a combined approach of using a global planner and a local planner. The global planner generates a high-level path, considering the overall environment, while the local planner handles real-time adjustments to avoid moving obstacles and optimize the trajectory. This thesis describes the role of the global planner in a ROS-framework. Performance benchmarking of traditional algorithms like Dijkstra and A*, as well as other techniques, is fundamental in order to understand the limits of these methods. In the end, the Hybrid A* algorithm is introduced as a promising approach for addressing the issues of unstructured environments for autonomous navigation of a non-holonomic robot. The core concepts and implementation details of the algorithm are discussed, emphasizing its ability to efficiently explore continuous state spaces and generate drivable paths.The effectiveness of the proposed path planning algorithms is evaluated through extensive simulations and real-world experiments using the mobile platform. Performance metrics such as path length, execution time, and collision avoidance are analyzed to assess the efficiency and reliability of the algorithms.Path planning is a crucial aspect of autonomous robot navigation, enabling robots to efficiently and safely navigate through complex environments. This thesis focuses on autonomous navigation for robots in dynamic and uncertain environments. In particular, the project aims to analyze the localization and path planning problems. A fundamental review of the existing literature on path planning algorithms has been carried on. Various factors affecting path planning, such as sensor data fusion, map representation, and motion constraints, are also analyzed. Thanks to the collaboration with E80 Group S.p.A., the project has been developed using ROS (Robot Operating System) on a Clearpath Dingo-O, an indoor mobile robot. To address the challenges posed by unstructured and dynamic environments, ROS follows a combined approach of using a global planner and a local planner. The global planner generates a high-level path, considering the overall environment, while the local planner handles real-time adjustments to avoid moving obstacles and optimize the trajectory. This thesis describes the role of the global planner in a ROS-framework. Performance benchmarking of traditional algorithms like Dijkstra and A*, as well as other techniques, is fundamental in order to understand the limits of these methods. In the end, the Hybrid A* algorithm is introduced as a promising approach for addressing the issues of unstructured environments for autonomous navigation of a non-holonomic robot. The core concepts and implementation details of the algorithm are discussed, emphasizing its ability to efficiently explore continuous state spaces and generate drivable paths.The effectiveness of the proposed path planning algorithms is evaluated through extensive simulations and real-world experiments using the mobile platform. Performance metrics such as path length, execution time, and collision avoidance are analyzed to assess the efficiency and reliability of the algorithms

Path Planning Based on Parametric Curves

Parametric curves are extensively used in engineering. The most commonly used parametric curves are, Bézier, B-splines, (NURBSs), and rational Bézier. Each and every one of them has special features, being the main difference between them the complexity of their mathematical definition. While Bézier curves are the simplest ones, B-splines or NURBSs are more complex. In mobile robotics, two main problems have been addressed with parametric curves. The first one is the definition of an initial trajectory for a mobile robot from a start location to a goal. The path has to be a continuous curve, smooth and easy to manipulate, and the properties of the parametric curves meet these requirements. The second one is the modification of the initial trajectory in real time attending to the dynamic properties of the environment. Parametric curves are capable of enhancing the trajectories produced by path planning algorithms adapting them to the kinematic properties of the robot. In order to avoid obstacles, the shape modification of parametric curves is required. In this chapter, an algorithm is proposed for computing an initial Bézier trajectory of a mobile robot and subsequently modifies it in real time in order to avoid obstacles in a dynamic environment