Completeness of Randomized Kinodynamic Planners with State-based Steering

Probabilistic completeness is an important property in motion planning. Although it has been established with clear assumptions for geometric planners, the panorama of completeness results for kinodynamic planners is still incomplete, as most existing proofs rely on strong assumptions that are difficult, if not impossible, to verify on practical systems. In this paper, we focus on an important class of kinodynamic planners, namely those that interpolate trajectories in the state space. We provide a proof of probabilistic completeness for these planners under assumptions that can be readily verified from the system's equations of motion and the user-defined interpolation function. Our proof relies crucially on a property of interpolated trajectories, termed second-order continuity (SOC), which we show is tightly related to the ability of a planner to benefit from denser sampling. We analyze the impact of this property in simulations on a low-torque pendulum. Our results show that a simple RRT using a second-order continuous interpolation swiftly finds solution, while it is impossible for the same planner using standard Bezier curves (which are not SOC) to find any solution.Comment: 21 pages, 5 figure

Kinematic Modeling And Path Planning With Collision Avoidance For Multiple Cartesian Arms

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2006Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2006Kartezyen robotlar, endüstride geniş kullanım alanı bulmaktadır. Birden fazla kartezyen robotun ortak bir iş yapmasına gerek duyulan durumlar vardır. Bu tezde yapılan çalışmanın temeli, aynı çalışma uzayındaki kartezyen robotların çarpışma olmaksızın yörünge planlamasıdır. Bu çalışmanın amacı, aynı çalışma uzayındaki kartezyen robotların konumlandırılması için gerekli algoritmaları bulmak veya türetmektir. Çarpışma sakınımlı yörünge planlaması algoritmalarını kullanarak istenen işin başarılması uzaysal işlem cebriyle kinematik olarak modellenmiş robotik sisteme dayanır. Yörünge planlaması metodları kartezyen robotlara uygulanarak çarpışma olmayan yörüngenin bulunması için algoritmalar geliştirilir.Cartesian robots are already being widely used in industry and their use will substantially increase as the developing technology brings the prices down of high payload and high precision linear motors. There are applications where more than one cartesian robots are required to perform a common task. The focus of the research presented in this thesis is the collision free path planning for multiple cartesian robots sharing the same task space. The objective of this research is to obtain or derive necessary algorithms to coordinate multiple cartesian robots sharing the same workspace. Using path planning algorithms with collision avoidance, the desired task is achieved based on the kinematic model of the complete robotic system which is rooted in the spatial operator algebra. Path planning methods are applied to the cartesian robots and the algorithms to find collision-free path for the cartesian robots are developed.Yüksek LisansM.Sc

Real time sensor based motion planning

Master'sMASTER OF ENGINEERIN

Minimum Jerk Trajectory Planning for Trajectory Constrained Redundant Robots

In this dissertation, we develop an efficient method of generating minimal jerk trajectories for redundant robots in trajectory following problems. We show that high jerk is a local phenomenon, and therefore focus on optimizing regions of high jerk that occur when using traditional trajectory generation methods. The optimal trajectory is shown to be located on the foliation of self-motion manifolds, and this property is exploited to express the problem as a minimal dimension Bolza optimal control problem. A numerical algorithm based on ideas from pseudo-spectral optimization methods is proposed and applied to two example planar robot structures with two redundant degrees of freedom. When compared with existing trajectory generation methods, the proposed algorithm reduces the integral jerk of the examples by 75% and 13%. Peak jerk is reduced by 98% and 33%. Finally a real time controller is proposed to accurately track the planned trajectory given real-time measurements of the tool-tip\u27s following error

A Predictive Technique for the Real-Time Trajectory Scaling under High-Order Constraints

Modern robotic systems must be able to react to unexpected environmental events. To this purpose, planning techniques for the real-time generation/modification of trajectories have been developed in recent times. In the frequent case of applications which require following a predefined path, the assigned time-law must be inspected in real time so as to verify whether it satisfies the system constraints or, conversely, if it must be scaled in order to obtain a feasible trajectory. The problem has been addressed in several ways in the literature. One of the known approaches, based on the use of nonlinear filters, is revised in this paper in order to return feasible solutions under any circumstances. Differently from alternative strategies, it manages constraints up to the torque derivatives and has evaluation times compatible with the ones required by modern control systems. The proposed technique is validated through simulations and real experiments. Comparisons are proposed with an algorithm based on a model predictive technique and with an alternative scaling system

Reinforcement Learning and Planning for Preference Balancing Tasks

Robots are often highly non-linear dynamical systems with many degrees of freedom, making solving motion problems computationally challenging. One solution has been reinforcement learning (RL), which learns through experimentation to automatically perform the near-optimal motions that complete a task. However, high-dimensional problems and task formulation often prove challenging for RL. We address these problems with PrEference Appraisal Reinforcement Learning (PEARL), which solves Preference Balancing Tasks (PBTs). PBTs define a problem as a set of preferences that the system must balance to achieve a goal. The method is appropriate for acceleration-controlled systems with continuous state-space and either discrete or continuous action spaces with unknown system dynamics. We show that PEARL learns a sub-optimal policy on a subset of states and actions, and transfers the policy to the expanded domain to produce a more refined plan on a class of robotic problems. We establish convergence to task goal conditions, and even when preconditions are not verifiable, show that this is a valuable method to use before other more expensive approaches. Evaluation is done on several robotic problems, such as Aerial Cargo Delivery, Multi-Agent Pursuit, Rendezvous, and Inverted Flying Pendulum both in simulation and experimentally. Additionally, PEARL is leveraged outside of robotics as an array sorting agent. The results demonstrate high accuracy and fast learning times on a large set of practical applications

Trajectory planning for industrial robot using genetic algorithms

En las últimas décadas, debido la importancia de sus aplicaciones, se han propuesto muchas investigaciones sobre la planificación de caminos y trayectorias para los manipuladores, algunos de los ámbitos en los que pueden encontrarse ejemplos de aplicación son; la robótica industrial, sistemas autónomos, creación de prototipos virtuales y diseño de fármacos asistido por ordenador. Por otro lado, los algoritmos evolutivos se han aplicado en muchos campos, lo que motiva el interés del autor por investigar sobre su aplicación a la planificación de caminos y trayectorias en robots industriales. En este trabajo se ha llevado a cabo una búsqueda exhaustiva de la literatura existente relacionada con la tesis, que ha servido para crear una completa base de datos utilizada para realizar un examen detallado de la evolución histórica desde sus orígenes al estado actual de la técnica y las últimas tendencias. Esta tesis presenta una nueva metodología que utiliza algoritmos genéticos para desarrollar y evaluar técnicas para la planificación de caminos y trayectorias. El conocimiento de problemas específicos y el conocimiento heurístico se incorporan a la codificación, la evaluación y los operadores genéticos del algoritmo. Esta metodología introduce nuevos enfoques con el objetivo de resolver el problema de la planificación de caminos y la planificación de trayectorias para sistemas robóticos industriales que operan en entornos 3D con obstáculos estáticos, y que ha llevado a la creación de dos algoritmos (de alguna manera similares, con algunas variaciones), que son capaces de resolver los problemas de planificación mencionados. El modelado de los obstáculos se ha realizado mediante el uso de combinaciones de objetos geométricos simples (esferas, cilindros, y los planos), de modo que se obtiene un algoritmo eficiente para la prevención de colisiones. El algoritmo de planificación de caminos se basa en técnicas de optimización globales, usando algoritmos genéticos para minimizar una función objetivo considerando restricciones para evitar las colisiones con los obstáculos. El camino está compuesto de configuraciones adyacentes obtenidas mediante una técnica de optimización construida con algoritmos genéticos, buscando minimizar una función multiobjetivo donde intervienen la distancia entre los puntos significativos de las dos configuraciones adyacentes, así como la distancia desde los puntos de la configuración actual a la final. El planteamiento del problema mediante algoritmos genéticos requiere de una modelización acorde al procedimiento, definiendo los individuos y operadores capaces de proporcionar soluciones eficientes para el problema.Abu-Dakka, FJM. (2011). Trajectory planning for industrial robot using genetic algorithms [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/10294Palanci

The statistical properties and coding of handwriting and hand-drawn graphics in tutorial classes

This research investigates compression techniques as applied to input from a digitizing tablet. The representations we consider are either drawn from the literature or developed within this thesis; they involve selecting relevant points along the trajectory of the writing pen, and using an interpolating function for reconstruction. The two dimensional parametric polynomial interpolator (e.g linear, quadratic, cubic ) is used for regenerating the trajectory of the pen. Several techniques for selecting relevant points , i.e control points are discussed. We determine our best representation by weighting the criteria, analyzing the experimental results, examining the theoretical considerations and, making where necessary, justifiable tradeoffs. The techniques tested are objectively evaluated in terms of accuracy, efficiency and compactness. The information characteristics (i.e signal entropy) of the handwriting and drawing signals, are estimated from the original and approximated data. Results are discussed and conclusions drawn. The research has been carried out on static data