A Real-Time Optimization for 2R Manipulators

This work proposes a real-time algorithm to generate a trajectory for a 2 link planar robotic manipulator. The objective is to minimize the space/time ripple and the energy requirements or the time duration in the robot trajectories. The proposed method uses an off line genetic algorithm to calculate every possible trajectory between all cells of the workspace grid. The resultant trajectories are saved in several trees. Then any trajectory requested is constructed in real-time, from these trees. The article presents the results for several experiments

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

Structure and trajectory optimization for redundant manipulators

This paper proposes a genetic algorithm to generate a robot structure and the required manipulating trajectories. The objective is to minimize the space/time ripple in the trajectory without colliding with any obstacles in the workspace, while optimizing the mechanical structure.N/

Fractional order dynamics in a Genetic Algorithm

This work addresses the fractional-order dynamics during the evolution of a Genetic Algorithm population (GA) for generating a robot manipulator trajectory. The GA objective is to minimize the trajectory space/time ripple without exceeding the torque requirements. In order to investigate the phenomena involved in the GA population evolution, the mutation is exposed to excitation perturbations and the corresponding fitness variations are evaluated. The input/output signals are studied revealing a fractional-order dynamic evolution, characteristic of a long-term system memory.N/

Robotic Manipulator Synthesis using a Hierarchical Multi-objective Genetic Algorithm

Robotic manipulator synthesis considering the simultaneous optimization of several design objectives is a NP-hard problem. This paper proposes a hierarchical multi-objective genetic algorithm to generate a robot structure and the required manipulating trajectories. The aim is to minimize the trajectory space ripple, the initial and final binary torques, while optimizing the mechanical structure. Simulations results are presented from solving a structure synthesis problem which considers the optimization of three simultaneous objectives.N/

Fractional dynamics in genetic algorithms

This paper investigate the fractional-order dynamics during the evolution of a Genetic Algorithm (GA). In order to study the phenomena involved in the GA population evolution, themutation is exposed to excitation perturbations during some generations and the corresponding fitness variations are evaluated. Three similar functions are tested to measure its influence in GA dynamics. The input and output signals are studied revealing a fractional-order dynamic evolution.N/

Particle Swarm Optimization: Dynamical Analysis through Fractional Calculus

This chapter considers the particle swarm optimization algorithm as a system, whose dynamics is studied from the point of view of fractional calculus. In this study some initial swarm particles are randomly changed, for the system stimulation, and its response is compared with a non-perturbed reference response. The perturbation effect in the PSO evolution is observed in the perspective of the fitness time behaviour of the best particle. The dynamics is represented through the median of a sample of experiments, while adopting the Fourier analysis for describing the phenomena. The influence upon the global dynamics is also analyzed. Two main issues are reported: the PSO dynamics when the system is subjected to random perturbations, and its modelling with fractional order transfer functions

Fractional Dynamics in Particle Swarm Optimization

This paper studies the fractional dynamics during the evolution of a Particle Swarm Optimization (PSO). Some swarm particles of the initial population are randomly changed for stimulating the system response. After the result is compared with a reference situation. The perturbation effect in the PSO evolution is observed in the perspective of the time behavior of the fitness of the best individual position visited by the replaced particles. The dynamics is investigated through the median of a sample of experiments, while adopting the Fourier analysis for describing the phenomena. The influence of the PSO parameters upon the global dynamics is also analyzed by performing several experiments for distinct values.N/

A support tool for teaching grafcet : engineering students' perceptions

Modeling discrete event systems with sequential behavior can be a very hard and complex task. Some formalisms are used in this context, such as: Petri Nets, Statecharts, Finite automata, Grafcet and others. Among these, Grafcet seems to be a good choice because it is easy: to learn, to understand and to use. Teaching Grafcet is then relevant within engineering courses concerned with Industrial Automation. A virtual laboratory, e-GRAFCET, developed and first tested in UTAD University; it is a new, easy-to-use multimedia e-educational tool to support the self-learning process of Grafcet. This paper, reports a study of e-GRAFCET use by the students of University of Minho. A questionnaire was prepared and students asked to fulfill it in a volunteer basis. The results were statistically analyzed and the scores compared. The overall objective is to understand how the tool helps students in their study, and consequently improve their learning off Grafcet, independently of their engineering background