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Motion Planning with Dynamic Constraints Through Pose Graph Optimization

Motion Planning with Dynamic Constraints Through Pose Graph Optimization
Author: Nadya L. Balabanska
Publisher:
Total Pages: 27
Release: 2020
Genre:
ISBN:

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This contribution is an optimization-based method for robotic path-planning that is able to recover vehicle controls in addition to discovering an optimized, feasible trajectory from start to goal for vehicles with arbitrary dynamics. The motion planner extends the application of factor-graph optimization commonly used in simultaneous localization and mapping tasks to the path-planning task, specifically the “timed elastic band” trajectory optimization approach [1] for control input extraction functionality. This is achieved by the introduction of control input-dependent vertices into the factor-graph along with a way to systematically design dynamics violation costs without relying on hand-picked geometric parameters. An implementation of the planner successfully recovers vehicle control inputs and produces feasible trajectories in simulation testing.


Multi-modal Motion Planning Using Composite Pose Graph Optimization

Multi-modal Motion Planning Using Composite Pose Graph Optimization
Author: Lukas C. Lao Beyer
Publisher:
Total Pages: 31
Release: 2021
Genre:
ISBN:

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This work presents a motion planning framework for multi-modal vehicle dynamics. An approach for transcribing cost function, vehicle dynamics, and state and control constraints into a sparse factor graph is introduced. By formulating the motion planning problem in pose graph form, the motion planning problem can be addressed using efficient optimization techniques, similar to those already widely applied in dual estimation problems, e.g., pose graph optimization for simultaneous localization and mapping (SLAM). Optimization of trajectories for vehicles under various dynamics models is demonstrated. The motion planner is able to optimize the location of mode transitions, and is guided by the pose graph optimization process to eliminate unnecessary mode transitions, enabling efficient discovery of optimized mode sequences from rough initial guesses. This functionality is demonstrated by using our planner to optimize multi-modal trajectories for vehicles such as an airplane which can both taxi on the ground or fly. Extensive experiments validate the use of the proposed motion planning framework in both simulation and real-life flight experiments using a vertical take-off and landing (VTOL) fixed-wing aircraft that can transition between hover and horizontal flight modes.


Optimized-Motion Planning

Optimized-Motion Planning
Author: Cherif Ahrikencheikh
Publisher: Wiley-Interscience
Total Pages: 400
Release: 1994-10-14
Genre: Science
ISBN:

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The first handbook to the practical specifics of motion planning, Optimized-Motion Planning offers design engineers methods and insights for solving real motion planning problems in a 3-dimensional space. Complete with a disk of software programs, this unique guide allows users to design, test, and implement possible solutions, useful in a host of contexts, especially tool path planning. Beginning with a brief overview of the general class of problems examined within the book as well as available solution techniques, Part 1 familiarizes the reader with the conceptual threads that underlie each approach. This early discussion also considers the specific applications of each technique as well as its computational efficiency. Part 2 illustrates basic problem-solving methodology by considering the case of a point moving between stationary polygons in a plane. This section features algorithms for data organization and storage, the concepts of passage networks and feasibility charts, as well as the path optimization algorithm. Elaborating on the problematic model described in Part 2, Part 3 develops an algorithm for optimizing the motion of a point between stationary polyhedra in a 3-dimensional space. This algorithm is first applied to the case of nonpoint objects moving between obstacles that can be stationary or moving with known patterns. It's then used in connection with the extensively investigated problem of motion planning for multilink manipulators.


On Motion Planning Using Numerical Optimal Control

On Motion Planning Using Numerical Optimal Control
Author: Kristoffer Bergman
Publisher: Linköping University Electronic Press
Total Pages: 91
Release: 2019-05-28
Genre:
ISBN: 9176850579

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During the last decades, motion planning for autonomous systems has become an important area of research. The high interest is not the least due to the development of systems such as self-driving cars, unmanned aerial vehicles and robotic manipulators. In this thesis, the objective is not only to find feasible solutions to a motion planning problem, but solutions that also optimize some kind of performance measure. From a control perspective, the resulting problem is an instance of an optimal control problem. In this thesis, the focus is to further develop optimal control algorithms such that they be can used to obtain improved solutions to motion planning problems. This is achieved by combining ideas from automatic control, numerical optimization and robotics. First, a systematic approach for computing local solutions to motion planning problems in challenging environments is presented. The solutions are computed by combining homotopy methods and numerical optimal control techniques. The general principle is to define a homotopy that transforms, or preferably relaxes, the original problem to an easily solved problem. The approach is demonstrated in motion planning problems in 2D and 3D environments, where the presented method outperforms both a state-of-the-art numerical optimal control method based on standard initialization strategies and a state-of-the-art optimizing sampling-based planner based on random sampling. Second, a framework for automatically generating motion primitives for lattice-based motion planners is proposed. Given a family of systems, the user only needs to specify which principle types of motions that are relevant for the considered system family. Based on the selected principle motions and a selected system instance, the algorithm not only automatically optimizes the motions connecting pre-defined boundary conditions, but also simultaneously optimizes the terminal state constraints as well. In addition to handling static a priori known system parameters such as platform dimensions, the framework also allows for fast automatic re-optimization of motion primitives if the system parameters change while the system is in use. Furthermore, the proposed framework is extended to also allow for an optimization of discretization parameters, that are are used by the lattice-based motion planner to define a state-space discretization. This enables an optimized selection of these parameters for a specific system instance. Finally, a unified optimization-based path planning approach to efficiently compute locally optimal solutions to advanced path planning problems is presented. The main idea is to combine the strengths of sampling-based path planners and numerical optimal control. The lattice-based path planner is applied to the problem in a first step using a discretized search space, where system dynamics and objective function are chosen to coincide with those used in a second numerical optimal control step. This novel tight combination of a sampling-based path planner and numerical optimal control makes, in a structured way, benefit of the former method’s ability to solve combinatorial parts of the problem and the latter method’s ability to obtain locally optimal solutions not constrained to a discretized search space. The proposed approach is shown in several practically relevant path planning problems to provide improvements in terms of computation time, numerical reliability, and objective function value.


Exploiting Direct Optimal Control for Motion Planning in Unstructured Environments

Exploiting Direct Optimal Control for Motion Planning in Unstructured Environments
Author: Kristoffer Bergman
Publisher: Linköping University Electronic Press
Total Pages: 60
Release: 2021-03-16
Genre: Electronic books
ISBN: 9179296777

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During the last decades, motion planning for autonomous systems has become an important area of research. The high interest is not the least due to the development of systems such as self-driving cars, unmanned aerial vehicles and robotic manipulators. The objective in optimal motion planning problems is to find feasible motion plans that also optimize a performance measure. From a control perspective, the problem is an instance of an optimal control problem. This thesis addresses optimal motion planning problems for complex dynamical systems that operate in unstructured environments, where no prior reference such as road-lane information is available. Some example scenarios are autonomous docking of vessels in harbors and autonomous parking of self-driving tractor-trailer vehicles at loading sites. The focus is to develop optimal motion planning algorithms that can reliably be applied to these types of problems. This is achieved by combining recent ideas from automatic control, numerical optimization and robotics. The first contribution is a systematic approach for computing local solutions to motion planning problems in challenging unstructured environments. The solutions are computed by combining homotopy methods and direct optimal control techniques. The general principle is to define a homotopy that transforms, or preferably relaxes, the original problem to an easily solved problem. The approach is demonstrated in motion planning problems in 2D and 3D environments, where the presented method outperforms a state-of-the-art asymptotically optimal motion planner based on random sampling. The second contribution is an optimization-based framework for automatic generation of motion primitives for lattice-based motion planners. Given a family of systems, the user only needs to specify which principle types of motions that are relevant for the considered system family. Based on the selected principle motions and a selected system instance, the framework computes a library of motion primitives by simultaneously optimizing the motions and the terminal states. The final contribution of this thesis is a motion planning framework that combines the strengths of sampling-based planners with direct optimal control in a novel way. The sampling-based planner is applied to the problem in a first step using a discretized search space, where the system dynamics and objective function are chosen to coincide with those used in a second step based on optimal control. This combination ensures that the sampling-based motion planner provides a feasible motion plan which is highly suitable as warm-start to the optimal control step. Furthermore, the second step is modified such that it also can be applied in a receding-horizon fashion, where the proposed combination of methods is used to provide theoretical guarantees in terms of recursive feasibility, worst-case objective function value and convergence to the terminal state. The proposed motion planning framework is successfully applied to several problems in challenging unstructured environments for tractor-trailer vehicles. The framework is also applied and tailored for maritime navigation for vessels in archipelagos and harbors, where it is able to compute energy-efficient trajectories which complies with the international regulations for preventing collisions at sea.


Algorithmic Foundations of Robotics V

Algorithmic Foundations of Robotics V
Author: Jean-Daniel Boissonnat
Publisher: Springer Science & Business Media
Total Pages: 600
Release: 2003-09-11
Genre: Technology & Engineering
ISBN: 9783540404767

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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.


Motion Planning in Dynamic Environments

Motion Planning in Dynamic Environments
Author: Kikuo Fujimura
Publisher: Springer Science & Business Media
Total Pages: 190
Release: 2012-12-06
Genre: Computers
ISBN: 4431681655

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Computer Science Workbench is a monograph series which will provide you with an in-depth working knowledge of current developments in computer technology. Every volume in this series will deal with a topic of importance in computer science and elaborate on how you yourself can build systems related to the main theme. You will be able to develop a variety of systems, including computer software tools, computer graphics, computer animation, database management systems, and computer-aided design and manufacturing systems. Computer Science Workbench represents an important new contribution in the field of practical computer technology. TOSIYASU L. KUNII To my parents Kenjiro and Nori Fujimura Preface Motion planning is an area in robotics that has received much attention recently. Much of the past research focuses on static environments - various methods have been developed and their characteristics have been well investigated. Although it is essential for autonomous intelligent robots to be able to navigate within dynamic worlds, the problem of motion planning in dynamic domains is relatively little understood compared with static problems.


Planning Algorithms

Planning Algorithms
Author: Steven M. LaValle
Publisher: Cambridge University Press
Total Pages: 844
Release: 2006-05-29
Genre: Computers
ISBN: 9780521862059

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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.


Implementation and Experimentation with Motion Planning Algorithms

Implementation and Experimentation with Motion Planning Algorithms
Author:
Publisher:
Total Pages: 13
Release: 1990
Genre:
ISBN:

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The main charter of this contract is the implementation and experimentation with motion planning algorithms that emphasize the exact combinatorial and purely geometric approach. Motion planning is considered to be one of the major research areas in robotics, and is one of the main stages in the design and implementation of autonomous intelligent systems, which is an important long-range goal in robotics research. Motion planning is one of the basic capabilities that such a system must possess. In purely geometric terms, the simplest version of the problem can be stated as follows. The system is given complete information about the geometry of the environment in which it is to operate (and of its own structure), and has to process it so that, when commanded to move from its current position to some target position, it can determine whether it can do so without colliding with any of the obstacles around it, and if so plan (and execute) such a motion. These are many variants of the problem. A few of those are: motion planning in environments that are only partially known to the system, compliant motion planning that allows contact with obstacles, which might be unavoidable due to measurement errors, optimal motion planning, motion planning with kino-dynamic constraints, and motion planning amidst moving obstacles. Still, even the simplest, static, and purely geometric version stated above is far from being simple, and poses serious challenges in the design of efficient and robust algorithms.