Point trajectory planning of flexible redundant robot manipulators using genetic algorithms

The paper focuses on the problem of point-to-point trajectory planning for flexible redundant robot manipulators (FRM) in joint space. Compared with irredundant flexible manipulators, a FRM possesses additional possibilities during point-to-point trajectory planning due to its kinematics redundancy. A trajectory planning method to minimize vibration and/or executing time of a point-to-point motion is presented for FRMs based on Genetic Algorithms (GAs). Kinematics redundancy is integrated into the presented method as planning variables. Quadrinomial and quintic polynomial are used to describe the segments that connect the initial, intermediate, and final points in joint space. The trajectory planning of FRM is formulated as a problem of optimization with constraints. A planar FRM with three flexible links is used in simulation. Case studies show that the method is applicable

An evolutionary approach for the motion planning of redundant and hyper-redundant manipulators

The trajectory planning of redundant robots is an important area of research and efficient optimization algorithms are needed. The pseudoinverse control is not repeatable, causing drift in joint space which is undesirable for physical control. This paper presents a new technique that combines the closed-loop pseudoinverse method with genetic algorithms, leading to an optimization criterion for repeatable control of redundant manipulators, and avoiding the joint angle drift problem. Computer simulations performed based on redundant and hyper-redundant planar manipulators show that, when the end-effector traces a closed path in the workspace, the robot returns to its initial configuration. The solution is repeatable for a workspace with and without obstacles in the sense that, after executing several cycles, the initial and final states of the manipulator are very close

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

An evolutionary approach to the trajectory planning of redundant robots

Several kinematic techniques for the trajectory optimization of redundant manipulators control the gripper using the pseudoinverse of the Jacobian. Nevertheless, these algorithms lead to a kind of chaotic motion with unpredictable arm configurations. This paper presents a new technique for solving the inverse kinematics problem for redundant manipulators that combines the closed-loop pseudoinverse method with genetic algorithms.N/

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

Optimization Approach for Inverse Kinematic Solution

Inverse kinematics of serial or parallel manipulators can be computed from given Cartesian position and orientation of end effector and reverse of this would yield forward kinematics. Which is nothing but finding out end effector coordinates and angles from given joint angles. Forward kinematics of serial manipulators gives exact solution while inverse kinematics yields number of solutions. The complexity of inverse kinematic solution arises with the increment of degrees of freedom. Therefore it would be desired to adopt optimization techniques. Although the optimization techniques gives number of solution for inverse kinematics problem but it converses the best solution for the minimum function value. The selection of suitable optimization method will provides the global optimization solution, therefore, in this paper proposes quaternion derivation for 5R manipulator inverse kinematic solution which is later compared with teachers learner based optimization (TLBO) and genetic algorithm (GA) for the optimum convergence rate of inverse kinematic solution. An investigation has been made on the accuracies of adopted techniques and total computational time for inverse kinematic evaluations. It is found that TLBO is performing better as compared GA on the basis of fitness function and quaternion algebra gives better computational cost

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

Manipulability in trajectory tracking for constrained redundant manipulators via sequential quadratic programming

Trajectory tracking methods for constrained redundant manipulators are presented in this thesis, where the end-effector of a redundant serial manipulator has to track a desired trajectory while some points on its kinematic chain satisfy one or more constraints. In addition, two manipulability indexes are taken into account in order to optimize the trajectory. The first index is defined in terms of the geometric Jacobian of the manipulator in the constrained configuration. The second index is based on the constrained Jacobian, which maps velocities from joint space to task space, taking into account the holonomic constraints. Three methods for solving the trajectory tracking problem are discussed. The first two, kinematic control (KC) and quadratic programming (QP), are widely discussed in literature. The third, sequential quadratic programming (SQP), is a new approach, unlike KC or QP, has as advantages (despite some shortcomings) not explicitly depend on pseudoinverse Jacobian, derivative from the desired trajectory and linearization of indexes or constraints. A discussion of these three methods is presented in terms of tracking error, constraint violation, singularity distance, among others through experiments performed on a Baxter collaborative robot.Métodos de rastreamento de trajetória para manipuladores redundantes restritos são apresentados nesta tese, onde o efetuador de um manipulador serial redundante tem que rastrear uma trajetória desejada enquanto alguns pontos em sua cadeia cinemática satisfazem uma ou mais restrições. Além disso, dois índices de manipulabilidade são levados em consideração a fim de otimizar a trajetória para evitar singularidades. O primeiro índice é definido em função do jacobiano geométrico do manipulador na configuração restrita. O segundo índice é baseado no Jacobiano restrito, o qual mapeia velocidades no espaço das juntas para a espaço da tarefa, levando em conta as restrições holonômicas. Três métodos para resolver o problema de rastreamento de trajetória são discutidos. Os dois primeiros, controle cinemático e programação quadrática (QP), são amplamente discutidos na literatura. O terceiro, programação quadrática sequencial (SQP), é uma nova abordagem, diferentemente do controle cinemático ou QP, tem como vantagens (apesar de algumas deficiências) não depender explicitamente da pseudo-inversa de jacobianos, derivadas da trajetória desejada e linearização de índices ou restrições. Uma discussão desses três métodos é apresentada em termos de erro de rastreamento, violação da restrição, distância de singularidades, entre outros através de experimentos realizados em um robô colaborativo Baxter