Inverse kinematic solution for a 7 DOF robot with minimal computational complexity and singularity avoidance

Kirćanski, Manja; Petrovic, T.

doi:10.1109/robot.1991.132032

Cited by 15 publications

(2 citation statements)

References 10 publications

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“…Shimizu and Kakuya proposed the method of arm angle [4] , which is not universal enough, and obtained the geometric solution of redundant manipulators. Kircanski first proposed the method of pseudo-inverse of the Jacobian matrix [5] , which obtained the least square, and the numerical solution of the norm does not involve the optimization problem. Dubey et al put forward the gradient projection method [6] and optimized the result with the optimal time as the optimization goal.…”

Section: Introductionmentioning

confidence: 99%

Inverse Kinematics Solution and Trajectory Planning of Redundant Manipulator Based on Improved Gradient Projection Method

Chang

Sun

et al. 2022

J. Phys.: Conf. Ser.

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With the rapid development of high-speed railways, the water injection way for the train is developing in the direction of full automation. To enable the water-carrying robot arm on the train to cope with various emergencies during the operation, it is necessary to keep the robot arm more flexible. In this paper, the improved gradient projection algorithm (IGPM) is combined with the rapidly expanding random tree algorithm (RRT), and the optimal goal is to maximize the manipulator’s degradation operability and obtain a path with the best fault tolerance under the continuous joint angle. Finally, with the 4R redundant manipulator serving as an example, the feasibility and superiority of the algorithm in this paper are compared and verified through the numerical simulation method.

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Section: Introductionmentioning

confidence: 99%

Inverse Kinematics Solution and Trajectory Planning of Redundant Manipulator Based on Improved Gradient Projection Method

Chang

Sun

et al. 2022

J. Phys.: Conf. Ser.

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“…To handle these two situations, J −1 G is replaced by a generalized inverse. The most well-known ones are the pseudoinverse J † G (that can be calculated using the identity (A.21)), the transpose J T G and the damped least-squares Baillieul, 1986;Buss, 2009;Buss and Kim, 2005;Hsu et al, 1988;Kircanski and Petrovic, 1991;Lau and Wai, 2002;Nenchev, 1989;Pozna et al, 2016;Sung et al, 1996;Wang et al, 2012;Wampler, 1986). Other Jacobian-based methods include the use of the augmented Jacobian (Fratu et al, 2010), the so-called {1}-inverse (Lovass-Nagy and Schilling, 1987) or other generalized inverses based on the pseudoinverse J † G (Manocha and Canny, 1994;Aspragathos and Dimitros, 1998).…”

Section: Methodsmentioning

confidence: 99%

Solving robotic kinematic problems : singularities and inverse kinematics

Zaplana Agut

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Kinematics is a branch of classical mechanics that describes the motion of points, bodies, and systems of bodies without considering the forces that cause such motion. For serial robot manipulators, kinematics consists of describing the open chain geometry as well as the position, velocity and/or acceleration of each one of its components. Rigid serial robot manipulators are designed as a sequence of rigid bodies, called links, connected by motor-actuated pairs, called joints, that provide relative motion between consecutive links. Two kinematic problems of special relevance for serial robots are: - Singularities: are the configurations where the robot loses at least one degree of freedom (DOF). This is equivalent to: (a) The robot cannot translate or rotate its end-effector in at least one direction. (b) Unbounded joint velocities are required to generate finite linear and angular velocities. Either if it is real-time teleoperation or off-line path planning, singularities must be addressed to make the robot exhibit a good performance for a given task. The objective is not only to identify the singularities and their associated singular directions but to design strategies to avoid or handle them. - Inverse kinematic problem: Given a particular position and orientation of the end-effector, also known as the end-effector pose, the inverse kinematics consists of finding the configurations that provide such desired pose. The importance of the inverse kinematics relies on its role in the programming and control of serial robots. Besides, since for each given pose the inverse kinematics has up to sixteen different solutions, the objective is to find a closed-form method for solving this problem, since closed-form methods allow to obtain all the solutions in a compact form. The main goal of the Ph.D. dissertation is to contribute to the solution of both problems. In particular, with respect to the singularity problem, a novel scheme for the identification of the singularities and their associated singular directions is introduced. Moreover, geometric algebra is used to simplify such identification and to provide a distance function in the configuration space of the robot that allows the definition of algorithms for avoiding them. With respect to the inverse kinematics, redundant robots are reduced to non-redundant ones by selecting a set of joints, denoted redundant joints, and by parameterizing their joint variables. This selection is made through a workspace analysis which also provides an upper bound for the number of different closed-form solutions. Once these joints have been identified, several closed-form methods developed for non-redundant manipulators can be applied to obtain the analytical expressions of all the solutions. One of these methods is a novel strategy developed using again the conformal model of the spatial geometric algebra. To sum up, the Ph.D dissertation provides a rigorous analysis of the two above-mentioned kinematic problems as well as novel strategies for solving them. To illustrate the different results introduced in the Ph.D. memory, examples are given at the end of each of its chapters. La cinemática es una rama de la mecánica clásica que describe el movimiento de puntos, cuerpos y sistemas de cuerpos sin considerar las fuerzas que causan dicho movimiento. Para un robot manipulador serie, la cinemática consiste en la descripción de su geometría, su posición, velocidad y/o aceleración. Los robots manipuladores serie están diseñados como una secuencia de elementos estructurales rígidos, llamados eslabones, conectados entres si por articulaciones actuadas, que permiten el movimiento relativo entre pares de eslabones consecutivos. Dos problemas cinemáticos de especial relevancia para robots serie son: - Singularidades: son aquellas configuraciones donde el robot pierde al menos un grado de libertad (GDL). Esto equivale a: (a) El robot no puede trasladar ni rotar su elemento terminal en al menos una dirección. (b) Se requieren velocidades articulares no acotadas para generar velocidades lineales y angulares finitas. Ya sea en un sistema teleoperado en tiempo real o planificando una trayectoria, las singularidades deben manejarse para que el robot muestre un rendimiento óptimo mientras realiza una tarea. El objetivo no es solo identificar las singularidades y sus direcciones singulares asociadas, sino diseñar estrategias para evitarlas o manejarlas. - Problema de la cinemática inversa: dada una posición y orientación del elemento terminal (también conocida como la pose del elemento terminal), la cinemática inversa consiste en obtener las configuraciones asociadas a dicha pose. La importancia de la cinemática inversa se basa en el papel que juega en la programación y el control de robots serie. Además, dado que para cada pose la cinemática inversa tiene hasta dieciséis soluciones diferentes, el objetivo es encontrar un método cerrado para resolver este problema, ya que los métodos cerrados permiten obtener todas las soluciones en una forma compacta. El objetivo principal de la tesis doctoral es contribuir a la solución de ambos problemas. En particular, con respecto al problema de las singularidades, se presenta un nuevo método para su identificación basado en el álgebra geométrica. Además, el álgebra geométrica permite definir una distancia en el espacio de configuraciones del robot que permite la definición de distintos algoritmos para evitar las configuraciones singulares. Con respecto a la cinemática inversa, los robots redundantes se reducen a robots no-redundantes mediante la selección de un conjunto de articulaciones, las articulaciones redundantes, para después parametrizar sus variables articulares. Esta selección se realiza a través de un análisis de espacio de trabajo que también proporciona un límite superior para el número de diferentes soluciones en forma cerrada. Una vez las articulaciones redundantes han sido identificadas, varios métodos en forma cerrada desarrollados para robots no-redundantes pueden aplicarse a fin de obtener las expresiones analíticas de todas las soluciones. Uno de dichos métodos es una nueva estrategia desarrollada usando el modelo conforme del álgebra geométrica tridimensional. En resumen, la tesis doctoral proporciona un análisis riguroso de los dos problemas cinemáticos mencionados anteriormente, así como nuevas estrategias para resolverlos. Para ilustrar los diferentes resultados presentados en la tesis, la memoria contiene varios ejemplos al final de cada uno de sus capítulos.

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An Optimization-Based Approach for Redundancy Resolution of Spatial Robots in Realistic Working Environments

Chembuly

Voruganti

2023

J. Inst. Eng. India Ser. C

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Inverse kinematic solution for a 7 DOF robot with minimal computational complexity and singularity avoidance

Cited by 15 publications

References 10 publications

Inverse Kinematics Solution and Trajectory Planning of Redundant Manipulator Based on Improved Gradient Projection Method

Inverse Kinematics Solution and Trajectory Planning of Redundant Manipulator Based on Improved Gradient Projection Method

Solving robotic kinematic problems : singularities and inverse kinematics

An Optimization-Based Approach for Redundancy Resolution of Spatial Robots in Realistic Working Environments

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