Redundant robot manipulator control with obstacle avoidance using extended Jacobian method
23 Jun 2010-pp 371-376
TL;DR: In this article, a self-motion vector is introduced at the level of the inverse kinematic solution in order to produce the obstacle avoidance (the secondary task), thus, robot avoids obstacles without influencing the main task (trajectory tracking).
Abstract: In this paper, we develop a control of a redundant robot manipulator. That has to carry out a trajectory tracking in operational space while avoiding an obstacle. For this purpose, extended Jacobian method is used. The Self-motion vector is introduced at the level of the inverse kinematic solution in order to produce the obstacle avoidance (the secondary task). Thus, robot avoids obstacles without influencing the main task (trajectory tracking). The self-motion is computed from the optimization of scalar function depending on an anti collision constraint. Finally, this control method has leaded to a trajectory tracking in Cartesian space while avoiding the obstacle.
Citations
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TL;DR: An online adaptive strategy based on the Lyapunov stability theory is presented to solve the inverse kinematics of redundant manipulators using neural networks to obtain joint angles of the robot using the Cartesian coordinate of the end-effector.
58 citations
Cites background or methods from "Redundant robot manipulator control..."
...As comparing with other methods in the literature, such as the Jacobian’s inverse approaches [1–3,5], which require defining penalty functions for the constraints, the proposed method in this paper only needs simple formulation of constraints....
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...These issues include joint physical limitations [2,4,8,19,22], obstacles in the workspace of the robot [1,3,16,17], singularity [13,25], repeatability [18,26], reliability [27], minimum energy [15,20], maximum manipulability [7] and minimum efforts [25]....
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...have considered a task-space augmentation method to describe the self-motion of the robot [3]....
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...Several methods have been presented in the literature to solve the redundancy such as gradient projection methods [2,3,6,7], task augmentation methods [1,5], decomposition-based methods [14,15], neural networks [17,18,22,23], neuro-fuzzy methods [19], and evolutionary algorithms [26]....
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TL;DR: An improved clamping weighted least-norm method is proposed that adds an elastic field function into the original method for the sake of sustaining the constraints of joint angular velocity limits.
Abstract: A general method is presented for the inverse kinematics resolution of redundant manipulators with joint limits. The success of avoiding joint angular position limits of the original clamping weighted least-norm method is ascribable to the strength of the repulsive potential field function. However, the repulsive potential field function may lead to excessive joint angular velocities that can exceed the corresponding limits. We propose an improved clamping weighted least-norm method that adds an elastic field function into the original method for the sake of sustaining the constraints of joint angular velocity limits. Moreover, for hierarchical task-level construction, the priority of avoiding joint angular velocity limits is lower than that of avoiding joint angular position limits. To adequately illustrate the effectiveness of the proposed method, case studies were performed in comparison with other methods in singular configurations of a redundant manipulator.
27 citations
TL;DR: A hybrid trajectory tracking controller is designed for redundant robot manipulators, consisting of RBF neural network and an adaptive bound on disturbances and proved to be asymptotically stable in the sense of Lyapunov.
Abstract: In this paper, a hybrid trajectory tracking controller is designed for redundant robot manipulators, consisting of RBF neural network and an adaptive bound on disturbances. The controller is composed of computed torque type part, RBF neural network and an adaptive controller. The controller achieves end-effector trajectory tracking as well as subtask tracking effectively. The controller is able to learn the existing structured and unstructured uncertainties in the system in online manner. The RBF network learns the unknown part of the robot dynamics with no requirement of the offline training. The adaptive controller is used to estimate the unknown bounds on unstructured uncertainties and neural network reconstruction error. The overall system is proved to be asymptotically stable in the sense of Lyapunov. Finally, numerical simulation studies are performed on a 3R planar robot manipulator to show the effectiveness of the control scheme.
21 citations
Cites background from "Redundant robot manipulator control..."
...Benzaoui et al.10 developed a control of a redundant robot manipulator to carry out a trajectory tracking in operational space while avoiding an obstacle....
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TL;DR: A backward quadratic search algorithm (BQSA) is developed as another option for solving IK problems in obstacle avoidance by utilizing a hybrid IK scheme, incorporating the damped least-squares method, the weighted least-norm method and the gradient projection method.
Abstract: Obstacle avoidance can be achieved as a secondary task by appropriate inverse kinematics (IK) resolution of redundant manipulators. Most prior literature requires the time-consuming determination of the closest point to the obstacle for every calculation step. Aiming at the relief of computational burden, this paper develops what is termed a backward quadratic search algorithm (BQSA) as another option for solving IK problems in obstacle avoidance. The BQSA detects possible collisions based on the root property of a category of quadratic functions, which are derived from ellipse-enveloped obstacles and the positions of each link's end-points. The algorithm executes a backward search for possible obstacle collisions, from the end-effector to the base, and avoids obstacles by utilizing a hybrid IK scheme, incorporating the damped least-squares method, the weighted least-norm method and the gradient projection method. Some details of the hybrid IK scheme, such as values of the damped factor, weights and the c...
9 citations
Cites methods from "Redundant robot manipulator control..."
...Thus, prior literature [9] has proposed abundant methods, including damped least-squares (DLS) [10], gradient projection (GP) [11], weighted least-norm (WLN) [1] and augmented, or extended, Jacobian matrix (AJM or EJM) [7, 12] methods to cope with these difficulties....
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01 Dec 2011
TL;DR: In this paper, a numerical method based on neural network is presented to solve inverse kinematics problem of redundant manipulators subject to joint angle limits and obstacles in the workspace of the robot.
Abstract: In this paper, a numerical method based on neural network is presented to solve inverse kinematics problem of redundant manipulators subject to joint angle limits and obstacles in the workspace of the robot. The proposed method is performed in real time, where radial-basis function neural network is used to obtain joint angles of the robot. In order to satisfy constrains, a method called Nonlinear Quadratic Programming (NQP) is applied to update NN's weights. Moreover, it will be shown that if the Kuhn-Tucker conditions are satisfied, then convergence of NN's weights is guaranteed. Since the process is performed on-line, the computational time of obtaining the inverse kinematics solution must be suitable for real-time applications such as control of the robot manipulators. Moreover, since the convergence rate of the problem depends on the initial weights of the neural network, several initial weights are used relative to suitable factors such as feasibility of the solution and vicinity of the desired point. Simulations are carried out on the PA-10 redundant manipulator to show effectiveness of the proposed algorithm.
7 citations
References
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01 Jan 1985
TL;DR: Methods for resolving kinematic redundancies of manipulators by the effect on joint torque are examined, and a whiplash action develops over time that thrusts the endpoint off the intended path, and extremely high torques are required to overcome these natural movement dynamics.
Abstract: Methods for resolving kinematic redundancies of manipulators by the effect on joint torque are examined. When the generalized inverse is formulated in terms of accelerations and incorporated into the dynamics, the effect of redundancy resolution on joint torque can be directly reflected. One method chooses the joint acceleration null-space vector to minimize joint torque in a least squares sense; when the least squares is weighted by allowable torque range, the joint torques tend to be kept within their limits. Contrasting methods employing only the pseudoinverse with and without weighting by the inertia matrix are presented. The results show an unexpected stability problem during long trajectories for the null-space methods and for the inertia-weighted pseudoinverse method, but more seldom for the unweighted pseudoinverse method. Evidently, a whiplash action develops over time that thrusts the endpoint off the intended path, and extremely high torques are required to overcome these natural movement dynamics.
744 citations
07 Apr 1986
TL;DR: To provide COSMOS, a dynamic model based manipulator control system, with an improved dynamic model, a PUMA 560 arm was disassembled; the inertial properties of the individual links were measured; and an explicit model incorporating all of the non-zero measured parameters was derived.
Abstract: To provide COSMOS, a dynamic model based manipulator control system, with an improved dynamic model, a PUMA 560 arm was disassembled; the inertial properties of the individual links were measured; and an explicit model incorporating all of the non-zero measured parameters was derived. The explicit model of the PUMA arm has been obtained with a derivation procedure comprised of several heuristic rules for simplification. A simplified model, abbreviated from the full explicit model with a 1% significance criterion, can be evaluated with 805 calculations, one fifth the number required by the recursive Newton-Euler method. The procedure used to derive the model is laid out; the measured inertial parameters are presented, and the model is included in an appendix.
507 citations
"Redundant robot manipulator control..." refers background or methods in this paper
...Using, computed torque algorithm to obtain the trajectory tracking, the control law is calculated as follows [9]: ) , ( ) ....
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...One suitable solution is the use of Kinematic redundancy [1]-[9]....
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...So, the 1 θ , 4 θ and 6 θ joints are locked so only the three other joints are free (n=3) [9]....
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...The actuator torques vector τ is related to the robot dynamic by [9]: ) q , q ( Q q ) q ( A & & & + = τ (5) With ) q ( G ) q , q ( C ) q , q ( B ) q , q ( Q + + = & & & Where: A: the inertia matrix of the robot B: Vectors of the Coriolis forces C: Vectors of the centrifugal forces G: Vector of the gravitational forces....
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01 Feb 2004
TL;DR: A recurrent neural network is developed and applied for kinematic control of redundant manipulators with obstacle avoidance capability and an improved problem formulation is proposed that the collision-avoidance requirement is represented by dynamically-updated inequality constraints.
Abstract: One important issue in the motion planning and control of kinematically redundant manipulators is the obstacle avoidance. In this paper, a recurrent neural network is developed and applied for kinematic control of redundant manipulators with obstacle avoidance capability. An improved problem formulation is proposed in the sense that the collision-avoidance requirement is represented by dynamically-updated inequality constraints. In addition, physical constraints such as joint physical limits are also incorporated directly into the formulation. Based on the improved problem formulation, a dual neural network is developed for the online solution to collision-free inverse kinematics problem. The neural network is simulated for motion control of the PA10 robot arm in the presence of point and window-shaped obstacle.
179 citations
"Redundant robot manipulator control..." refers methods in this paper
...One suitable solution is the use of Kinematic redundancy [1]-[9]....
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01 Feb 1995
TL;DR: A new formulation of the extended Jacobian method is described that is well suited numerically for systems with multiple degrees of redundancy and for more general choices of the secondary criterion.
Abstract: The extended Jacobian method resolves the redundancy of a kinematically redundant manipulator such that a secondary criterion is kept at an optimal value. This paper describes a new formulation of this algorithm that is well suited numerically for systems with multiple degrees of redundancy and for more general choices of the secondary criterion. This formulation is used here for tracing algorithmic singularities, which mark a boundary of operation for any algorithm using the same secondary criterion to resolve the redundancy. Examples of tracing algorithmic singularities are presented for both planar and spatial systems. >
80 citations
TL;DR: The singularities of 3-joint manipu lators operating in 2-dimensional work spaces are classified, and an analysis is performed for case studies, with various manipulator designs.
Abstract: A robot arm is redundant if it has extra degrees offreedom. In such cases the kinematic function is a mapping from a higher-dimensional joint space to a lower-dimensional work space. The manipulator may have singular configurations, which are singularities of the kinematic function. At or near the singularities, the robot may be difficult to control. The redundancy may help to avoid some singularities, but other singularities may be unavoidable. To help in the robot design and in order to devise a controlling strategy that would avoid singularities, it is important to know analytically which singularities are avoidable. This paper gives some tools for classifying singularities. The singularities of 3-joint manipu lators operating in 2-dimensional work spaces are classified, and an analysis is performed for case studies, with various manipulator designs.
72 citations