Geometric Path-Planning Algorithm in Cluttered 2D Environments Using Convex Hulls

Routing or path planning is the problem of finding a collision-free path in an environment usually scattered with multiple objects. Finding the shortest route in a planar (2D) or spatial (3D) environment has a variety of applications such as robot motion planning, navigating autonomous vehicles, routing of cables, wires, and harnesses in vehicles, routing of pipes in chemical process plants, etc. The problem often times is decomposed into two main sub-problems: modeling and representation of the workspace geometrically and optimization of the path. Geometric modeling and representation of the workspace are paramount in any path planning problem since it builds the data structures and provides the means for solving the optimization problem. The optimization aspect of the path planning involves satisfying some constraints, the most important of which is to avoid intersections with the interior of any object and optimizing one or more criteria. The most common criterion in path planning problems is to minimize the length of the path between a source and a destination point of the workspace while other criteria such as minimizing the number of links or curves could also be taken into account. Planar path planning is mainly about modeling the workspace of the problem as a collision-free graph. The graph is, later on, searched for the optimal path using network optimization techniques such as branch-and-bound or search algorithms such as Dijkstra\u27s. Previous methods developed to construct the collision-free graph explore the entire workspace of the problem which usually results in some unnecessary information that has no value but to increase the time complexity of the algorithm, hence, affecting the efficiency significantly. For example, the fastest known algorithm to construct the visibility graph, which is the most common method of modeling the collision-free space, in a workspace with a total of n vertices has a time complexity of order O(n2). In this research, first, the 2D workspace of the problem is modeled using the tessellated format of the objects in a CAD software which facilitates handling of any free-form object. Then, an algorithm is developed to construct the collision-free graph of the workspace using the convex hulls of the intersecting obstacles. The proposed algorithm focuses only on a portion of the workspace involved in the straight line connecting the source and destination points. Considering the worst case that all the objects of the workspace are intersecting, the algorithm yields a time complexity of O(nlog(n/f)), with n being the total number of vertices and f being the number of objects. The collision-free graph is later searched for the shortest path between the two given nodes using a search algorithm known as Dijkstra\u27s

A neural network methodology for path planning and coordination of car-like robots

A car-like indoor mobile robot is a kinematically constrained robot that can be modeled as a 2D object translating and rotating in the horizontal plane among well- defined obstacles. The kinematic constraints impose that the linear velocity of the robot is along its main axis (no sideways motion is possible) and restrict the range of admissible values for the steering angle. The goal of this study is to combine neural network techniques and motion planning algorithms to create a new methodology for coordinating the motion of multiple car-like robots avoiding collision with polygonal obstacles in a work environment. An incremental technique is used to develop this methodology. First, a strategy for planning the path of a point robot moving in the presence of obstacles is constructed. Second, this strategy is adapted to path planning for a polygonal robot. Third, holonomic and non-holonomic constraints are imposed on the robot and the method is further refined. Finally, a plan for the coordinated motion of multiple car-like robots is devised through use of the concept of coordination space --Abstract, page iii

Industrial manipulators collision detection algorithms

In this work we present some algorithms for detecting collisions between two robots. Firstly we estimate robot trajectories given via points and workcell configuration, then we develop the actual algorithm to detect collisions, providing multiple models of each link which differ in reliability and simplicity. The algorithm is then optimized for anthropomorphic robots, in order to be performed on-line. Finally some results are summarized, which show the effective behaviour in worst case

A study of mobile robot motion planning

This thesis studies motion planning for mobile robots in various environments. The basic tools for the research are the configuration space and the visibility graph. A new approach is developed which generates a smoothed minimum time path. The difference between this and the Minimum Time Path at Visibility Node (MTPVN) is that there is more clearance between the robot and the obstacles, and so it is safer. The accessibility graph plays an important role in motion planning for a massless mobile robot in dynamic environments. It can generate a minimum time motion in 0(n2»log(n)) computation time, where n is the number of vertices of all the polygonal obstacles. If the robot is not considered to be massless (that is, it requires time to accelerate), the space time approach becomes a 3D problem which requires exponential time and memory. A new approach is presented here based on the improved accessibility polygon and improved accessibility graph, which generates a minimum time motion for a mobile robot with mass in O((n+k)2»log(n+k)) time, where n is the number of vertices of the obstacles and k is the number of obstacles. Since k is much less than n, so the computation time for this approach is almost the same as the accessibility graph approach. The accessibility graph approach is extended to solve motion planning for robots in three dimensional environments. The three dimensional accessibility graph is constructed based on the concept of the accessibility polyhedron. Based on the properties of minimum time motion, an approach is proposed to search the three dimensional accessibility graph to generate the minimum time motion. Motion planning in binary image representation environment is also studied. Fuzzy logic based digital image processing has been studied. The concept of Fuzzy Principal Index Of Area Coverage (PIOAC) is proposed to recognise and match objects in consecutive images. Experiments show that PIOAC is useful in recognising objects. The visibility graph of a binary image representation environment is very inefficient, so the approach usually used to plan the motion for such an environment is the quadtree approach. In this research, polygonizing an obstacle is proposed. The approaches developed for various environments can be used to solve the motion planning problem without any modification. A simulation system is designed to simulate the approaches

Geometric-based Optimization Algorithms for Cable Routing and Branching in Cluttered Environments

The need for designing lighter and more compact systems often leaves limited space for planning routes for the connectors that enable interactions among the system’s components. Finding optimal routes for these connectors in a densely populated environment left behind at the detail design stage has been a challenging problem for decades. A variety of deterministic as well as heuristic methods has been developed to address different instances of this problem. While the focus of the deterministic methods is primarily on the optimality of the final solution, the heuristics offer acceptable solutions, especially for such problems, in a reasonable amount of time without guaranteeing to find optimal solutions. This study is an attempt to furthering the efforts in deterministic optimization methods to tackle the routing problem in two and three dimensions by focusing on the optimality of final solutions. The objective of this research is twofold. First, a mathematical framework is proposed for the optimization of the layout of wiring connectors in planar cluttered environments. The problem looks at finding the optimal tree network that spans multiple components to be connected with the aim of minimizing the overall length of the connectors while maximizing their common length (for maintainability and traceability of connectors). The optimization problem is formulated as a bi-objective problem and two solution methods are proposed: (1) to solve for the optimal locations of a known number of breakouts (where the connectors branch out) using mixed-binary optimization and visibility notion and (2) to find the minimum length tree that spans multiple components of the system and generates the optimal layout using the previously-developed convex hull based routing. The computational performance of these methods in solving a variety of problems is further evaluated. Second, the problem of finding the shortest route connecting two given nodes in a 3D cluttered environment is considered and addressed through deterministically generating a graphical representation of the collision-free space and searching for the shortest path on the found graph. The method is tested on sample workspaces with scattered convex polyhedra and its computational performance is evaluated. The work demonstrates the NP-hardness aspect of the problem which becomes quickly intractable as added components or increase in facets are considered

Point seeking: a family of dynamic path finding algorithms

In the field of Artificial Intelligence, calculating the best route from one point to another, known as “path finding,” has become a common problem. If an agent cannot effectively navigate through an environment – be it real or virtual – it will often not be able to perform even the most routine tasks. For example, a Martian rover can\u27t collect samples if it can\u27t get to them; meanwhile, a computer game is not much of a challenge if your opponents can\u27t find their way around. The problem of path finding has three basic aspects: map representation, path generation, and locomotion. First, the environment must be interpreted into a form which can be processed algorithmically. Afterward, a path through this environment is planned out. A list of movement instructions or locations to travel to are then produced in order to guide the agent. During both the planning and movement of the agent, an algorithm may consider the agent\u27s limitations with regards to changes in velocity and orientation. Together, these steps serve to move an agent from its initial position to the desired location