Proving Path Non-Existence Using Sampling and Alpha Shapes

In this thesis, we address the problem of determining the connectivity of a robot's free configuration space. Our method iteratively builds a constructive proof that two configurations lie in disjoint components of the free configuration space. Our algorithm first generates samples that correspond to configurations for which the robot is in collision with an obstacle. These samples are then weighted by their generalized penetration distance and used to construct alpha shapes. The alpha shape defines a collection of simplices that are fully contained within the configuration space obstacle region. These simplices can be used to quickly solve connectivity queries, which in turn can be used to define termination conditions for sampling-based planners. Such planners, while typically either resolution complete or probabilistically complete, are not able to determine when a path does not exist, and therefore would otherwise rely on heuristics to determine when the search for a free path should be abandoned. An implementation of the algorithm is provided for the case of a 3D Euclidean configuration space, and a proof of correctness is provided.NSFunpublishednot peer reviewedU of I OnlyUndergraduate senior thesis not recommended for open acces

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

Integrated Task and Motion Planning of Multi-Robot Manipulators in Industrial and Service Automation

Efficient coordination of several robot arms in order to carry out some given independent/cooperative tasks in a common workspace, avoiding collisions, is an appealing research problem that has been studied in different robotic fields, with industrial and service applications. Coordination of several robot arms in a shared environment is challenging because complexity of collision free path planning increases with the number of robots sharing the same workspace. Although research in different aspects of this problem such as task planning, motion planning and robot control has made great progress, the integration of these components is not well studied in the literature. This thesis focuses on integrating task and motion planning multi-robot-arm systems by introducing a practical and optimal interface layer for such systems. For a given set of speci fications and a sequence of tasks for a multi-arm system, the studied system design aims to automatically construct the necessary waypoints, the sequence of arms to be operated, and the algorithms required for the robots to reliably execute manipulation tasks. The contributions of the thesis are three-fold. First, an algorithm is introduced to integrate task and motion planning layers in order to achieve optimal and collision free task execution. Representation via shared space graph (SSG) is introduced to check whether two arms share certain parts of the workspace and to quantify cooperation of such arm pairs, which is essential in selection of arm sequence and scheduling of each arm in the sequence to perform a task or a sub-task. The introduced algorithm allows robots to autonomously reason about a structured environment, performs the sequence planning of robots to operate, and provides robots and objects path for each task to succeed a set of goals. Secondly, an integrated motion and task planning methodology is introduced for systems of multiple mobile and fixed base robot arms performing different tasks simultaneously in a shared workspace. We introduce concept of dynamic shared space graph (D-SSG) to continuously check whether two arms sharing certain parts of the workspace at different time steps and quantify cooperation of such arm pairs, which is essential to the selection of arm sequences and scheduling of each arm in the sequence to perform a task or a sub-task. The introduced algorithm allows robots to autonomously reason about complex human involving environments to plan the high level decisions (sequence planning) of robots to operate and calculates robots and objects path for each task to succeed a set of goals. The third contribution is design of an integration algorithm between low-level motion planning and high-level symbolic task planning layers to produce alternate plans in case of kinematic and geometric changes in the environment to prevent failure in the high-level task plan. In order to verify the methodological contributions of the thesis with a solid implementation basis, some implementations and tests are presented in the open-source robotics planning environments ROS, Moveit and Gazebo. Detailed analysis of these implementations and test results are provided as well