Multi-Criteria Optimization Manipulator Trajectory Planning

In the last twenty years genetic algorithms (GAs) were applied in a plethora of fields such as: control, system identification, robotics, planning and scheduling, image processing, and pattern and speech recognition (Bäck et al., 1997). In robotics the problems of trajectory planning, collision avoidance and manipulator structure design considering a single criteria has been solved using several techniques (Alander, 2003). Most engineering applications require the optimization of several criteria simultaneously. Often the problems are complex, include discrete and continuous variables and there is no prior knowledge about the search space. These kind of problems are very more complex, since they consider multiple design criteria simultaneously within the optimization procedure. This is known as a multi-criteria (or multiobjective) optimization, that has been addressed successfully through GAs (Deb, 2001). The overall aim of multi-criteria evolutionary algorithms is to achieve a set of non-dominated optimal solutions known as Pareto front. At the end of the optimization procedure, instead of a single optimal (or near optimal) solution, the decision maker can select a solution from the Pareto front. Some of the key issues in multi-criteria GAs are: i) the number of objectives, ii) to obtain a Pareto front as wide as possible and iii) to achieve a Pareto front uniformly spread. Indeed, multi-objective techniques using GAs have been increasing in relevance as a research area. In 1989, Goldberg suggested the use of a GA to solve multi-objective problems and since then other researchers have been developing new methods, such as the multi-objective genetic algorithm (MOGA) (Fonseca & Fleming, 1995), the non-dominated sorted genetic algorithm (NSGA) (Deb, 2001), and the niched Pareto genetic algorithm (NPGA) (Horn et al., 1994), among several other variants (Coello, 1998). In this work the trajectory planning problem considers: i) robots with 2 and 3 degrees of freedom (dof ), ii) the inclusion of obstacles in the workspace and iii) up to five criteria that are used to qualify the evolving trajectory, namely the: joint traveling distance, joint velocity, end effector / Cartesian distance, end effector / Cartesian velocity and energy involved. These criteria are used to minimize the joint and end effector traveled distance, trajectory ripple and energy required by the manipulator to reach at destination point. Bearing this ideas in mind, the paper addresses the planning of robot trajectories, meaning the development of an algorithm to find a continuous motion that takes the manipulator from a given starting configuration up to a desired end position without colliding with any obstacle in the workspace. The chapter is organized as follows. Section 2 describes the trajectory planning and several approaches proposed in the literature. Section 3 formulates the problem, namely the representation adopted to solve the trajectory planning and the objectives considered in the optimization. Section 4 studies the algorithm convergence. Section 5 studies a 2R manipulator (i.e., a robot with two rotational joints/links) when the optimization trajectory considers two and five objectives. Sections 6 and 7 show the results for the 3R redundant manipulator with five goals and for other complementary experiments are described, respectively. Finally, section 8 draws the main conclusions

Reitinsuunnittelu määrätyssä järjestyksessä tehtäville peltotöille usean työkoneen yhteistyönä

Coverage path planning is the task of finding a collision free path that passes over every point of an area or volume of interest. In agriculture, the coverage task is encountered especially in the process of crop cultivation. Several tasks are performed on the field, one after the other, during the cultivation cycle. Cooperation means that multiple agents, in this case vehicles, are working together towards a common goal. Several studies consider the problem where a single task is divided and assigned among the agents. In this thesis, however, the vehicles have different tasks that are sequentially dependent, that is, the first task must be completed before the other. The tasks are performed simultaneously on the same area. The literature review suggests that there is a lack of previous research on this topic. The objective of this thesis was to develop an algorithm to solve the cooperative coverage path planning problem for sequentially dependent tasks. A tool chain that involves Matlab, Simulink and Visual Studio was adapted for the development and testing of the solution. A development and testing architecture was designed including a compatible interface to a simulation and a real-life test environment. Two different algorithms were implemented based on the idea of computing short simultaneous paths at a time and scheduling them in real-time. The results were successfully demonstrated in a real-life test environment with two tractors equipped with a disc cultivator and a seeder. The objective was to sow the test area. The test drives show that with the algorithms that were developed in this thesis it is possible to perform two sequentially dependent agricultural coverage tasks simultaneously on the same area.Kattavassa reitinsuunnittelussa yritetään löytää polku, jonka aikana määritelty ala tai tilavuus tulee käytyä läpi niin että alueen jokainen piste on käsitelty. Maataloudessa tämä tehtävä on merkityksellinen erityisesti peltoviljelyssä. Useita peltotöitä suoritetaan yksi toisensa jälkeen samalla alueella viljelyvuoden aikana. Useissa tutkimuksissa käsitellään yhteistyönä tehtävää reitinsuunnittelua, jossa yksi tehtävä on jaettu osiin ja osat jaetaan useiden tekijöiden kuten robottien kesken. Tässä diplomityössä peltotyökoneilla on kuitenkin omat erilliset tehtävänsä, joilla on määrätty järjestys, eli niiden suorittaminen riippuu työjärjestyksestä. Työkoneet työskentelevät samanaikaisesti samalla alueella. Diplomityössä tehty kirjallisuuskatsaus viittaa siihen, että vastaavaa aihetta ei ole aiemmin tutkittu. Tämän diplomityön tavoitteena on kehittää algoritmi, jolla voidaan toteuttaa reitinsuunnittelu määrätyssä järjestyksessä tehtäville peltotöille usean peltotyökoneen yhteistyönä. Algoritmikehitystä ja testausta varten suunniteltiin yhtenäinen rajapinta, jolla algoritmia voitaisiin testata sekä simulaatiossa että todellisessa testitilanteessa. Algoritmikehityksessä käytettiin työkaluina Matlab, Simulink ja Visual Studio -ohjelmia. Työssä toteutettiin kaksi algoritmia, jotka perustuvat samaan ideaan: suunnitellaan kerrallaan kaksi lyhyttä samanaikaista polkua, jotka ajoitetaan reaaliajassa. Algoritmeja testattiin todellisessa testiympäristössä kahden työkoneen yhteistyönä, kun tavoitteena on kylvää koko testialue. Ensimmäinen työvaihe suoritettiin lautasmuokkaimella ja toinen kylvökoneella. Testiajot osoittavat, että diplomityössä kehitetyillä algoritmeilla voidaan ohjata kahden toisistaan riippuvaisen peltotyön toteutus samanaikaisesti samalla peltoalueella

Exploratory Path Planning for Mobile Robots in Dynamic Environments with Ant Colony Optimization

In the path planning task for autonomous mobile robots, robots should be able to plan their trajectory to leave the start position and reach the goal, safely. There are several path planning approaches for mobile robots in the literature. Ant Colony Optimization algorithms have been investigated for this problem, giving promising results. In this paper, we propose the Max-Min Ant System for Dynamic Path Planning algorithm for the exploratory path planning task for autonomous mobile robots based on topological maps. A topological map is an environment representation whose focus is the main reference points of the environment and their connections. Based on this representation, the path can be composed by a sequence of state/actions pairs, which facilitates the navigability of the path, with no need to have the information of the complete map. The proposed algorithm was evaluated in static and dynamic envi- ronments, showing promising results in both of them. Experiments in dynamic environments show the adaptability of our proposal