Optimal Trajectory Planning for a Space Robot Docking with a Moving Target via Homotopy Algorithms

The mathematical formulation of optimal trajectory planning for a space robot docking with a moving target is derived. The calculus of variations is applied to the problem so that the optimal robot trajectory can be obtained directlt from the target information without first planning the trajectory of the end-effector. The nonlinear two-point boundary value problem resulting from the problem formulation is solved numerically by a globally convergent homotopy algorithm. The algorithm guarantees convergence to a solution for an arbitrarily chosen initial guess. Numerical simulation for three examples demonstrates the approach

Near-Optimal Motion Planning Algorithms Via A Topological and Geometric Perspective

Motion planning is a fundamental problem in robotics, which involves finding a path for an autonomous system, such as a robot, from a given source to a destination while avoiding collisions with obstacles. The properties of the planning space heavily influence the performance of existing motion planning algorithms, which can pose significant challenges in handling complex regions, such as narrow passages or cluttered environments, even for simple objects. The problem of motion planning becomes deterministic if the details of the space are fully known, which is often difficult to achieve in constantly changing environments. Sampling-based algorithms are widely used among motion planning paradigms because they capture the topology of space into a roadmap. These planners have successfully solved high-dimensional planning problems with a probabilistic-complete guarantee, i.e., it guarantees to find a path if one exists as the number of vertices goes to infinity. Despite their progress, these methods have failed to optimize the sub-region information of the environment for reuse by other planners. This results in re-planning overhead at each execution, affecting the performance complexity for computation time and memory space usage. In this research, we address the problem by focusing on the theoretical foundation of the algorithmic approach that leverages the strengths of sampling-based motion planners and the Topological Data Analysis methods to extract intricate properties of the environment. The work contributes a novel algorithm to overcome the performance shortcomings of existing motion planners by capturing and preserving the essential topological and geometric features to generate a homotopy-equivalent roadmap of the environment. This roadmap provides a mathematically rich representation of the environment, including an approximate measure of the collision-free space. In addition, the roadmap graph vertices sampled close to the obstacles exhibit advantages when navigating through narrow passages and cluttered environments, making obstacle-avoidance path planning significantly more efficient. The application of the proposed algorithms solves motion planning problems, such as sub-optimal planning, diverse path planning, and fault-tolerant planning, by demonstrating the improvement in computational performance and path quality. Furthermore, we explore the potential of these algorithms in solving computational biology problems, particularly in finding optimal binding positions for protein-ligand or protein-protein interactions. Overall, our work contributes a new way to classify routes in higher dimensional space and shows promising results for high-dimensional robots, such as articulated linkage robots. The findings of this research provide a comprehensive solution to motion planning problems and offer a new perspective on solving computational biology problems

Social navigation of autonomous robots in populated environments

Programa de Doctorado en Biotecnología, Ingeniería y Tecnología QuímicaLínea de Investigación: Ingeniería InformáticaClave Programa: DBICódigo Línea: 19Today, more and more mobile robots are coexisting with us in our daily lives. As a result, the behavior of robots that share space with humans in dynamic environments is a subject of intense investigation in robotics. Robots must re- spect human social conventions, guarantee the comfort of surrounding people, and maintain the legibility so that humans can understand the robot¿s intentions. Robots that move in humans¿ vicinity should navigate in a socially compliant way; this is called human-aware navigation. These social behaviors are not easy to frame in mathematical expressions. Consequently, motion planners with pre- programmed constraints and hard-coded functions can fail in acquiring proper behaviors related to human-awareness. All in all, it is easier to demonstrate socially acceptable behaviors than mathematically defining them. Therefore, learning these social behaviors from data seems a more principled approach. This thesis aims at endowing mobile robots with new social skills for au- tonomous navigation in spaces populated with humans. This work makes use of learning from demonstration (LfD) approaches to solve the problem of human- aware navigation. Different techniques and algorithms are explored and devel- oped in order to transfer social navigation behaviors to a robot by using demon- strations of human experts performing the proposed tasks. The contributions of this thesis are in the field of Learning from Demonstra- tion applied to human-aware navigation tasks. First, a LfD technique based on Inverse Reinforcement Learning (IRL) is employed to learn a policy for ¿social¿ local motion planning. Then, a novel learning algorithm combining LfD concepts and sampling-based path planners is presented. Finally, other novel approaches combining different LfD techniques, like deep learning among others, and path planners are investigated. The methods proposed are compared against state- of-the-art approaches and tested in different experiments with the real robots employed in the European projects FROG and TERESA.Universidad Pablo de Olavide de Sevilla. Departamento de Deporte e InformáticaPostprin

Mobile robots and vehicles motion systems: a unifying framework

Robots perform many different activities in order to accomplish their tasks. The robot motion capability is one of the most important ones for an autonomous be- havior in a typical indoor-outdoor mission (without it other tasks can not be done), since it drastically determines the global success of a robotic mission. In this thesis, we focus on the main methods for mobile robot and vehicle motion systems and we build a common framework, where similar components can be interchanged or even used together in order to increase the whole system performance

Parallel software for nonlinear systems of equations. Final report, February 28, 1995--June 30, 1997

The nonlinear systems of equations arising in circuit simulation, structural optimization, closed loop optimal control, chemical engineering of distillation systems, combustion chemistry, CAD/CAM modeling, robotics, computer vision, and orbital mechanics have several properties that make them especially amenable to homotopy methods. Even so, the homotopy zero curves are not trivial to track, and sophisticated curve tracking techniques are sometimes required. The size of typical engineering problems also presents some interesting numerical linear algebra challenges, and the supported work has been geared toward developing parallel sparse matrix techniques specifically tailored to the sparsity structures corresponding to the mentioned problem areas, in the context of homotopy algorithms. There are many different algorithms for tracking the zero curve {gamma}; the previous proposal discussed three such algorithms: ordinary differential equation based, normal flow, and augmented Jacobian matrix. The descriptions of these algorithms are now in the literature for the software package HOMPACK, so will not be repeated here. The development of sparse homotopy algorithms within HOMPACK specifically tailored for various parallel machines (e.g., distributed memory, shared memory, and vector) and problem areas (e.g., circuit simulation, structural optimization, optimal control, and combustion chemistry) was the central theme of this research

Fast Marching Methods in path and motion planning: improvements and high-level applications

Mención Internacional en el título de doctorPath planning is defined as the process to establish the sequence of states a system must go through in order to reach a desired state. Additionally, motion planning (or trajectory planning) aims to compute the sequence of motions (or actions) to take the system from one state to another. In robotics path planning can refer for instance to the waypoints a robot should follow through a maze or the sequence of points a robotic arm has to follow in order to grasp an object. Motion planning is considered a more general problem, since it includes kinodynamic constraints. As motion planning is a more complex problem, it is often solved in a two-level approach: path planning in the first level and then a control layer tries to drive the system along the specified path. However, it is hard to guarantee that the final trajectory will keep the initial characteristics. The objective of this work is to solve different path and motion planning problems under a common framework in order to facilitate the integration of the different algorithms that can be required during the nominal operation of a mobile robot. Also, other related areas such as motion learning are explored using this framework. In order to achieve this, a simple but powerful algorithm called Fast Marching will be used. Originally, it was proposed to solve optimal control problems. However, it has became very useful to other related problems such as path and motion planning. Since Fast Marching was initially proposed, many different alternative approaches have been proposed. Therefore, the first step is to formulate all these methods within a common framework and carry out an exhaustive comparison in order to give a final answer to: which algorithm is the best under which situations? This Thesis shows that the different versions of Fast Marching Methods become useful when applied to motion and path planning problems. Usually, high-level problems as motion learning or robot formation planning are solved with completely different algorithms, as the problem formulation are mixed. Under a common framework, task integration becomes much easier bringing robots closer to everyday applications. The Fast Marching Method has also inspired modern probabilistic methodologies, where computational cost is enormously improved at the cost of bounded, stochastic variations on the resulting paths and trajectories. This Thesis also explores these novel algorithms and their performance.Programa Oficial de Doctorado en Ingeniería Eléctrica, Electrónica y AutomáticaPresidente: Carlos Balaguer Bernaldo de Quirós.- Secretario: Antonio Giménez Fernández.- Vocal: Isabel Lobato de Faria Ribeir

Technology for large space systems: A bibliography with indexes (supplement 22)

This bibliography lists 1077 reports, articles, and other documents introduced into the NASA Scientific and Technical Information System between July 1, 1989 and December 31, 1989. Its purpose is to provide helpful information to the researcher or manager engaged in the development of technologies related to large space systems. Subject areas include mission and program definition, design techniques, structural and thermal analysis, structural dynamics and control systems, electronics, advanced materials, assembly concepts, and propulsion

Technology for large space systems: A bibliography with indexes (supplement 19)

This bibliography lists 526 reports, articles, and other documents introduced into the NASA scientific and technical information system between January 1, 1988 and June 30, 1988. Its purpose is to provide helpful information to the researcher, manager, and designer in technology development and mission design according to system, interactive analysis and design, structural and thermal analysis and design, structural concepts and control systems, electronics, advanced materials, assembly concepts, propulsion, and solar power satellite systems