Dynamic Region RRT Application to Kinodynamic Systems

In the general motion planning problem the robot must satisfy basic constraints such as avoiding obstacles and remaining within the boundary of the environment. Kinodynamic motion planning is a type of planning where additional constraints must be satisfied. Kinodynamic planning is a more realistic planning problem as the robot must operate under constraints such as friction, gravity, velocity, and acceleration while avoiding obstacles as well. Sampling-based methods are often used to solve these types of problems. These methods generate robot configurations throughout the environment in order to eventually connect them to form a valid path from the start position to the goal. Rapidly-exploring Random Trees (RRT) are types of sampling-based methods that grow a tree from the start to goal. One important problem with these types of methods appears when planning in an environment with a narrow passage or cluttered space. In these problems it is unlikely to generate a sample in the narrow spaces and the robot does not explore these locations. Dynamic Region-biased Rapidly-exploring Random Trees (DRRRT) is a method that addresses these issues by guiding an RRT with dynamic sampling regions along an embedded graph of the workspace. DRRRT is effective in general motion planning problems, but faces issues in kinodynamic problems. Oftentimes, a sample is generated near an obstacle that is valid, but is found to be unrecoverable because if the robot were to move from that state with any of the available controls it would collide with an obstacle. This often occurs in environments with narrow spaces and tight turns such as a maze. In this work, we aim to address the problems DRRRT faces in kinodynamic problems with a series of improvements. The resulting method is compared with other motion planning techniques on two kinodynamic problems consisting of a car-like robot navigating a grid-like city and a maze, simulating narrow paths with numerous turns

Clearance Map for the Application of Workspace Skeleton-biased Motion Planning

Motion planning is the problem of finding a valid path for a moveable object from a start to a goal state. Current state-of-the-art sampling based planners are able to solve a variety of problems. Sometimes, it is difficult for them to find a collision-free path if the solution path is highly related to the workspace geometry and the free space is relatively restricted. Recent works have indicated that the planner can benefit from the inherent topological information in the workspace. These algorithms capture the topology of the free workspace in form of a graph called workspace skeleton. Nevertheless, they do not allow preferential selection of solution path if multiple paths exists. For example, some of the paths might not be feasible for robot of certain size. In this work, we address the preferential selection of paths based on the clearance requirements of the planning problem. To achieve this, we annotate the workspace skeleton with clearance information. Given the clearance requirements of the problem in form of a filter function, we generate a subgraph that only contains the edges from the original skeleton satisfying the function. This saves time in planning unnecessarily in regions of the workspace that are infeasible based on the clearance requirements of the problem. We study the impact of the annotated skeleton on the performance of one of the recent sampling based motion planner that uses workspace skeleton. We use two kind of filter function : one that filters edges based on the size of the robot, and other that forces following a specific route. Our results show improvement in planning time (6.5% in some cases) and in number of robot placements sampled before finding the solution path.This project is presented to refine embedded graph dynamically to prune out unfeasible paths in the environment that robot is struggling to go through and guide robot to more feasible paths with a algorithm called hierarchical aggregation

Dynamic Region RRT Application to Kinodynamic Systems

In the general motion planning problem the robot must satisfy basic constraints such as avoiding obstacles and remaining within the boundary of the environment. Kinodynamic motion planning is a type of planning where additional constraints must be satisfied. Kinodynamic planning is a more realistic planning problem as the robot must operate under constraints such as friction, gravity, velocity, and acceleration while avoiding obstacles. Sampling-based methods are often used to solve these types of problems. These methods generate robot configurations throughout the environment in order to eventually connect them to form a valid path from the start position to the goal. Rapidly-exploring Random Trees (RRT) are types of sampling-based methods that grow a tree from the start to goal. One important problem with these types of methods appears when planning in an environment with a narrow passage or cluttered space. In these problems it is unlikely to generate a sample in the narrow spaces and the robot does not explore these locations. Dynamic Region-biased Rapidly-exploring Random Trees (DRRRT) is a method that addresses these issues by guiding an RRT with dynamic sampling regions along an embedded graph of the workspace. DRRRT is effective in general motion planning problems, but faces issues in kinodynamic problems. Oftentimes, a sample is generated near an obstacle that is valid, but is found to be unrecoverable because if the robot were to move from that state with any of the available controls it would collide with an obstacle. This often occurs in environments with narrow spaces and tight turns such as a maze. In this work, we address the address the problems DRRRT faces in the kinodynamic problem with a series of improvements. First, we use the embedded graph to bias the direction that the tree extends to keep the robot moving along the graph. Second, also using the embedded graph we limit the candidates while neighborhood finding so that the entire tree is not searched each time a sample is chosen. Lastly, instead of uniformly selecting which region to be sampled, a bias is applied to the regions according to a heuristic designed to promote more successful regions. ii

2017 Faculty Accomplishments Reception

Program for the 2017 Faculty Accomplishments ReceptionIn Honor of University of Richmond Faculty Contributions to Scholarship, Research and Creative Work, January 2016 - December 2016March 17, 2017, 3:00 - 4:30 p.m.Boatwright Memorial Library, Research & Collaborative Study Area, First Floorhttps://scholarship.richmond.edu/far-programs/1002/thumbnail.jp

Silhouette-Informed Trajectory Generation Through a Wire Maze for Small UAS

Current rapidly-exploring random tree (RRT) algorithms rely on proximity query packages that often include collision checkers, tolerance verification, and distance computation algorithms for the generation of safe paths. In this paper, we broaden the information available to the path-planning algorithm by incorporating silhouette information of nearby obstacles in conflict. A silhouette-informed tree (SIT) is generated through the flight-safe region of a wire maze for a single unmanned aerial system (UAS). The silhouette is used to extract local geometric information of nearby obstacles and provide path alternatives around these obstacles. Thus, focusing the search for the generation of new tree branches near these obstacles, and decreasing the number of samples required to explore the narrow corridors within the wire maze. The SIT is then processed to extract a path that connects the initial location of the UAS with the goal, reduce the number of line segments in this path if possible, and smooth the resulting path using Pythagorean Hodograph Bezier curves. To ensure that the smoothed path remains in the flight-safe region of the configuration space, a tolerance verification algorithm for Bezier curves and convex polytopes in three dimensions is proposed. Lastly, temporal specifications are imposed on the smoothed path in the shape of an arbitrary speed profile

Improving Sampling-Based Motion Planning Using Library of Trajectories

Plánování pohybu je jedním z podstatných problémů robotiky. Tato práce kombinuje pokroky v plánování pohybu a hodnocení podobnosti objektů za účelem zrychlení plánování ve statických prostředích. První část této práce pojednává o současných metodách používaných pro hodnocení podobnosti objektů a plánování pohybu. Prostřední část popisuje, jak jsou tyto metody použity pro zrychlení plánování s využitím získaných znalostí o prostředí. V poslední části jsou navržené metody porovnány s ostatními plánovači v nezávislém testu. Námi navržené algoritmy se v experimentech ukázaly být často rychlejší v porovnání s ostatními plánovači. Také často nacházely cesty v prostředích, kde ostatní plánovače nebyly schopny cestu nalézt.Motion planning is one of the fundamental problems in robotics. This thesis combines the advances in motion planning and shape matching to improve planning speeds in static environments. The first part of this thesis covers current methods used in object similarity evaluation and motion planning. The middle part describes how these methods are used together to improve planning speeds by utilizing prior knowledge about the environment, along with additional modifications. In the last part, the proposed methods are tested against other state-of-the-art planners in an independent benchmarking facility. The proposed algorithms are shown to be faster than other planners in many cases, often finding paths in environments where the other planners are unable to

Multilevel Motion Planning: A Fiber Bundle Formulation

Motion planning problems involving high-dimensional state spaces can often be solved significantly faster by using multilevel abstractions. While there are various ways to formally capture multilevel abstractions, we formulate them in terms of fiber bundles, which allows us to concisely describe and derive novel algorithms in terms of bundle restrictions and bundle sections. Fiber bundles essentially describe lower-dimensional projections of the state space using local product spaces. Given such a structure and a corresponding admissible constraint function, we can develop highly efficient and optimal search-based motion planning methods for high-dimensional state spaces. Our contributions are the following: We first introduce the terminology of fiber bundles, in particular the notion of restrictions and sections. Second, we use the notion of restrictions and sections to develop novel multilevel motion planning algorithms, which we call QRRT* and QMP*. We show these algorithms to be probabilistically complete and almost-surely asymptotically optimal. Third, we develop a novel recursive path section method based on an L1 interpolation over path restrictions, which we use to quickly find feasible path sections. And fourth, we evaluate all novel algorithms against all available OMPL algorithms on benchmarks of eight challenging environments ranging from 21 to 100 degrees of freedom, including multiple robots and nonholonomic constraints. Our findings support the efficiency of our novel algorithms and the benefit of exploiting multilevel abstractions using the terminology of fiber bundles.Comment: Submitted to IJR

Tractable POMDP-planning for robots with complex non-linear dynamics

Planning under partial observability is an essential capability of autonomous robots. While robots operate in the real world, they are inherently subject to various uncertainties such a control and sensing errors, and limited information regarding the operating environment.Conceptually these type of planning problems can be solved in a principled manner when framed as a Partially Observable Markov Decision Process (POMDP). POMDPs model the aforementioned uncertainties as conditional probability functions and estimate the state of the system as probability functions over the state space, called beliefs. Instead of computing the best strategy with respect to single states, POMDP solvers compute the best strategy with respect to beliefs. Solving a POMDP exactly is computationally intractable in general.However, in the past two decades we have seen tremendous progress in the development of approximately optimal solvers that trade optimality for computational tractability. Despite this progress, approximately solving POMDPs for systems with complex non-linear dynamics remains challenging. Most state-of-the-art solvers rely on a large number of expensive forward simulations of the system to find an approximate-optimal strategy. For systems with complex non-linear dynamics that admit no closed-form solution, this strategy can become prohibitively expensive. Another difficulty in applying POMDPs to physical robots with complex transition dynamics is the fact that almost all implementations of state-of-the-art on-line POMDP solvers restrict the user to specific data structures for the POMDP model, and the model has to be hard-coded within the solver implementation. This, in turn, severely hinders the process of applying POMDPs to physical robots.In this thesis we aim to make POMDPs more practical for realistic robotic motion planning tasks under partial observability. We show that systematic approximations of complex, non-linear transition dynamics can be used to design on-line POMDP solvers that are more efficient than current solvers. Furthermore, we propose a new software-framework that supports the user in modeling complex planning problems under uncertainty with minimal implementation effort