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This dissertation introduces a novel path planning algorithm for robotics, known as Informed SRRT#. Our algorithm integrates a local planner from SRRT, accommodating both external and internal constraints. We introduce two extra lines at the Bézier spline's endpoints, which facilitates the rewiring process. A minimum of three state connections need adjustment during rewiring to meet kinematic constraints. The effectiveness of the proposed method is demonstrated through various channels: Python-based simulations, Gazebo/Rviz -- a robot simulator and visualization tool in Robot Operating System, and real-world scenarios. In real-world experiments, the algorithm successfully maneuvered TurtleBot3 past obstacles in the physical map, leading to a smooth, streamlined and optimal navigation approach. Our results reveal that the new algorithm identifies shorter paths than SRRT while achieving the same number of node sampling iterations. However, these enhancements come with a trade-off, as the computational time of this method is slightly higher compared to traditional methods.
Sampling-based motion planning received increasing attention during the last decade. In particular, some of the leading paradigms, such the Probabilistic RoadMap (PRM) and the Rapidly-exploring Random Tree (RRT) algorithms, have been demonstrated on several robotic platforms, and found applications well outside the robotics domain. However, a large portion of this research effort has been limited to the classical feasible path planning problem, which asks for finding a path that starts from an initial configuration and reaches a goal configuration while avoiding collision with obstacles. The main contribution of this dissertation is a novel class of algorithms that extend the application domain of sampling-based methods to two new directions: optimal path planning and path planning with complex task specifications. Regarding the optimal path planning problem, we first show that the existing algorithms either lack asymptotic optimality, i. e., almost-sure convergence to optimal solutions, or they lack computational efficiency: on one hand, neither the RRT nor the k-nearest PRM (for any fixed k) is asymptotically optimal; on the other hand, the simple PRM algorithm, where the connections are sought within fixed radius balls, is not computationally as efficient as the RRT or the efficient PRM variants. Subsequently, we propose two novel algorithms, called PRM* and RRT*, both of which guarantee asymptotic optimality without sacrificing computational efficiency. In fact, the proposed algorithms and the most efficient existing algorithms, such as the RRT, have the same asymptotic computational complexity. Regarding the path planning problem with complex task specifications, we propose an incremental sampling-based algorithm that is provably correct and probabilistically complete, i.e., it generates a correct-by-design path that satisfies a given deterministic pt-calculus specification, when such a path exists, with probability approaching to one as the number of samples approaches infinity. For this purpose, we develop two key ingredients. First, we propose an incremental sampling-based algorithm, called the RRG, that generates a representative set of paths in the form of a graph, with guaranteed almost-sure convergence towards feasible paths. Second, we propose an incremental local model-checking algorithm for the deterministic p-calculus. Moreover, with the help of these tools and the ideas behind the RRT*, we construct algorithms that also guarantee almost sure convergence to optimal solutions.
Asymptotically optimal planners, such as PRM*, guarantee that solutions approach optimal as iterations increase. Roadmaps with this property, however, may grow too large. If optimality is relaxed, asymptotically near-optimal solutions produce sparser graphs by not including all edges. The idea stems from graph spanner algorithms, which produce sparse subgraphs that guarantee near-optimal paths. Existing asymptotically optimal and near-optimal planners, however, include all sampled configurations as roadmap nodes. Consequently, only infinite graphs have the desired properties. This work proposes an approach that provides the following asymptotic properties: (a) completeness, (b) near-optimality and (c) the probability of adding nodes to the spanner roadmap converges to zero as iterations increase. Thus, the method suggests that finite-size data structures might have near-optimality properties. The method brings together ideas from various planners but deviates from existing integrations of PRM* with graph spanners. Simulations for rigid bodies show that the method indeed provides small roadmaps and results in faster query resolution. The rate of node addition is shown to decrease over time and the quality of solutions satisfies the theoretical bounds. Smoothing provides a more favorable comparison against alternatives with regards to path length.
Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. Written for computer scientists and engineers with interests in artificial intelligence, robotics, or control theory, this is the only book on this topic that tightly integrates a vast body of literature from several fields into a coherent source for teaching and reference in a wide variety of applications. Difficult mathematical material is explained through hundreds of examples and illustrations.
Vehicle Dynamics and Control provides a comprehensive coverage of vehicle control systems and the dynamic models used in the development of these control systems. The control system applications covered in the book include cruise control, adaptive cruise control, ABS, automated lane keeping, automated highway systems, yaw stability control, engine control, passive, active and semi-active suspensions, tire-road friction coefficient estimation, rollover prevention, and hybrid electric vehicles. In developing the dynamic model for each application, an effort is made to both keep the model simple enough for control system design but at the same time rich enough to capture the essential features of the dynamics. A special effort has been made to explain the several different tire models commonly used in literature and to interpret them physically. In the second edition of the book, chapters on roll dynamics, rollover prevention and hybrid electric vehicles have been added, and the chapter on electronic stability control has been enhanced. The use of feedback control systems on automobiles is growing rapidly. This book is intended to serve as a useful resource to researchers who work on the development of such control systems, both in the automotive industry and at universities. The book can also serve as a textbook for a graduate level course on Vehicle Dynamics and Control.
By virtue of their special algebraic structures, Pythagorean-hodograph (PH) curves offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and self-contained treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications. It emphasizes the interplay of ideas from algebra and geometry and their historical origins and includes many figures, worked examples, and detailed algorithm descriptions.
Selected contributions to the Workshop WAFR 2002, held December 15-17, 2002, Nice, France. This fifth biannual Workshop on Algorithmic Foundations of Robotics focuses on algorithmic issues related to robotics and automation. The design and analysis of robot algorithms raises fundamental questions in computer science, computational geometry, mechanical modeling, operations research, control theory, and associated fields. The highly selective program highlights significant new results such as algorithmic models and complexity bounds. The validation of algorithms, design concepts, or techniques is the common thread running through this focused collection.
This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.
Programmable graphics shaders, programs that can be downloaded to a graphics processor (GPU) to carry out operations outside the fixed-function pipeline of earlier standards, have become a key feature of computer graphics. This book is designed to open computer graphics shader programming to the student, whether in a traditional class or on their own. It is intended to complement texts based on fixed-function graphics APIs, specifically OpenGL. It introduces shader programming in general, and specifically the GLSL shader language. It also introduces a flexible, easy-to-use tool, glman, that helps you develop, test, and tune shaders outside an application that would use them.