Kinematic Control of Redundant Manipulators Using Neural Networks
TL;DR: This paper identifies two limitations of the existing RNN solutions for manipulator control, i.e., position error accumulation and the convex restriction on the projection set, and overcomes them by proposing two modified neural network models.
Abstract: Redundancy resolution is a critical problem in the control of robotic manipulators. Recurrent neural networks (RNNs), as inherently parallel processing models for time-sequence processing, are potentially applicable for the motion control of manipulators. However, the development of neural models for high-accuracy and real-time control is a challenging problem. This paper identifies two limitations of the existing RNN solutions for manipulator control, i.e., position error accumulation and the convex restriction on the projection set, and overcomes them by proposing two modified neural network models. Our method allows nonconvex sets for projection operations, and control error does not accumulate over time in the presence of noise. Unlike most works in which RNNs are used to process time sequences, the proposed approach is model-based and training-free, which makes it possible to achieve fast tracking of reference signals with superior robustness and accuracy. Theoretical analysis reveals the global stability of a system under the control of the proposed neural networks. Simulation results confirm the effectiveness of the proposed control method in both the position regulation and tracking control of redundant PUMA 560 manipulators.
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TL;DR: The use of long short-term memory recurrent neural network (LSTM-RNN) to accurately forecast the output power of PV systems and offers a further reduction in the forecasting error compared with the other methods.
Abstract: Photovoltaic (PV) is one of the most promising renewable energy sources. To ensure secure operation and economic integration of PV in smart grids, accurate forecasting of PV power is an important issue. In this paper, we propose the use of long short-term memory recurrent neural network (LSTM-RNN) to accurately forecast the output power of PV systems. The LSTM networks can model the temporal changes in PV output power because of their recurrent architecture and memory units. The proposed method is evaluated using hourly datasets of different sites for a year. We compare the proposed method with three PV forecasting methods. The use of LSTM offers a further reduction in the forecasting error compared with the other methods. The proposed forecasting method can be a helpful tool for planning and controlling smart grids.
443 citations
Additional excerpts
...Recently, recurrent neural networks have been used in various applications, such as optimal demand response in smart grids [54], control of single-phase converters [17], manipulator control [27, 28, 30, 31], modeling crack growth of aluminum alloy [56], distributed task allocation of multiple robots [26], text recognition [43], and localization of wireless sensor networks [29]....
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TL;DR: Computer simulations are conducted and show that, compared to the existing methods, the proposed scheme can raise the manipulability almost 40% on average, which substantiates the efficacy, accuracy, and superiority of the proposed manipulable optimization scheme.
Abstract: For solving the singularity problem arising in the control of manipulators, an efficient way is to maximize its manipulability. However, it is challenging to optimize manipulability effectively because it is a nonconvex function to the joint angles of a robotic arm. In addition, the involvement of an inversion operation in the expression of manipulability makes it even hard for timely optimization due to the intensively computational burden for matrix inversion. In this paper, we make progress on real-time manipulability optimization by establishing a dynamic neural network for recurrent calculation of manipulability-maximal control actions for redundant manipulators under physical constraints in an inverse-free manner. By expressing position tracking and matrix inversion as equality constraints, physical limits as inequality constraints, and velocity-level manipulability measure, which is affine to the joint velocities, as the objective function, the manipulability optimization scheme is further formulated as a constrained quadratic program. Then, a dynamic neural network with rigorously provable convergence is constructed to solve such a problem online. Computer simulations are conducted and show that, compared to the existing methods, the proposed scheme can raise the manipulability almost 40% on average, which substantiates the efficacy, accuracy, and superiority of the proposed manipulability optimization scheme.
296 citations
Cites background or methods from "Kinematic Control of Redundant Mani..."
...By contrast, as shown in the table, even without the ability to maximize the manipulability during the task execution process, these QP-based schemes presented in [12], [29], [30] could generate an approximated solution with no feasible solution at the cost of large position errors....
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...9 s 1029 s NA§ Scheme (19) in [29] Any No No Velocity Yes 0....
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...1 s Scheme (41) in [29] Any No No Velocity Yes 0....
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...It is also noteworthy that as the benefit of manipulability optimization, the proposed scheme can quickly solve the control action while others without optimizing manipulability have to update control actions very frequently when their Jacobian reaches singular, resulting the fact that the proposed scheme consumes less time than those without manipulability optimization [12], [29], [30]....
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TL;DR: The problem foundation of manipulator control and the theoretical ideas on using neural network to solve this problem are analyzed and then the latest progresses on this topic in recent years are described and reviewed in detail.
209 citations
TL;DR: T theoretical analyses show that the proposed neural-dynamic distributed scheme is able to execute a given task with exponentially convergent position errors and numerical comparisons substantiate the superiority, effectiveness, and accuracy of the proposed distributed scheme.
Abstract: In this paper, a neural-dynamic distributed scheme is proposed for the cooperative control of multiple redundant manipulators with limited communications. It is guaranteed that, with the communication network being connected, all manipulators can jointly reach the same desired motion. The proposed distributed scheme is rearranged as a time-varying quadratic program and solved online by a Zhang neural network. Then, theoretical analyses show that, without noise, the proposed distributed scheme is able to execute a given task with exponentially convergent position errors. Moreover, an explicit bound relationship between the control input noise and the end-effector position error is analytically derived. Furthermore, numerical comparisons substantiate the superiority, effectiveness, and accuracy of the proposed distributed scheme.
157 citations
Additional excerpts
...and various related schemes and methods have been proposed and investigated [28]–[30], [32], [33]....
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TL;DR: Simulation studies including comparisons and tests substantiate the efficacy and superiority of the proposed JMA method for the tracking control of robot manipulators subject to unknown models.
Abstract: Tracking control of robot manipulators is a fundamental and significant problem in robotic industry. As a conventional solution, the Jacobian-matrix-pseudo-inverse (JMPI) method suffers from two major limitations: one is the requirement on known information of the robot model such as parameter and structure; the other is the position error accumulation phenomenon caused by the open-loop nature. To overcome such two limitations, this paper proposes a novel Jacobian-matrix-adaption (JMA) method for the tracking control of robot manipulators via the zeroing dynamics. Unlike existing works requiring the information of the known robot model, the proposed JMA method uses only the input-output information to control the robot with unknown model. The solution based on the JMA method transforms the internal, implicit, and unmeasurable model information to the external, explicit, and measurable input-output information. Moreover, simulation studies including comparisons and tests substantiate the efficacy and superiority of the proposed JMA method for the tracking control of robot manipulators subject to unknown models.
151 citations
Cites background or methods from "Kinematic Control of Redundant Mani..."
...Its corresponding parameters and structure can be found in [31], [32]....
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...In addition, the corresponding robot structure can also be found in [31] and [32]....
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...tors with 6 independently controlled joints, and is widely used in robotic researches [31], [32]....
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...words, the type of the used robot, the length of each link, and the Denavit–Hartenberg (DH) parameters should be precisely known for the control design [31], [32]....
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References
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Book•
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TL;DR: In this article, the focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them, and a comprehensive introduction to the subject is given. But the focus of this book is not on the optimization problem itself, but on the problem of finding the appropriate technique to solve it.
Abstract: Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.
33,341 citations
Book•
20 Sep 1994
1,720 citations
"Kinematic Control of Redundant Mani..." refers background in this paper
...cannot be characterized in terms of any convex projection operators [24] and thus cannot be implemented using the...
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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
"Kinematic Control of Redundant Mani..." refers methods in this paper
...In the early work [1], control solutions were directly found using the pseudoinverse of the Jacobian matrix of a manipulator....
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TL;DR: This paper proposes a complete solution to solve multiple least-square quadratic problems of both equality and inequality constraints ordered into a strict hierarchy using a generic solver used to resolve the redundancy of humanoid robots while generating complex movements in constrained environments.
Abstract: Hierarchical least-square optimization is often used in robotics to inverse a direct function when multiple incompatible objectives are involved. Typical examples are inverse kinematics or dynamics. The objectives can be given as equalities to be satisfied e.g. point-to-point task or as areas of satisfaction e.g. the joint range. This paper proposes a complete solution to solve multiple least-square quadratic problems of both equality and inequality constraints ordered into a strict hierarchy. Our method is able to solve a hierarchy of only equalities 10 times faster than the iterative-projection hierarchical solvers and can consider inequalities at any level while running at the typical control frequency on whole-body size problems. This generic solver is used to resolve the redundancy of humanoid robots while generating complex movements in constrained environments.
492 citations
"Kinematic Control of Redundant Mani..." refers methods in this paper
..., matrix decomposition and Gaussian elimination, have been applied to these problems to obtain numerical solutions [8]....
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TL;DR: A new prioritized task-regulation framework based on a sequence of quadratic programs (QP) that removes the limitation of inequality constraints and is implemented and illustrated in simulation on the humanoid robot HRP-2.
Abstract: Redundant mechanical systems like humanoid robots are designed to fulfill multiple tasks at a time. A task, in velocity-resolved inverse kinematics, is a desired value for a function of the robot configuration that can be regulated with an ordinary differential equation (ODE). When facing simultaneous tasks, the corresponding equations can be grouped in a single system or, better, sorted in priority and solved each in the solutions set of higher priority tasks. This elegant framework for hierarchical task regulation has been implemented as a sequence of least-squares problems. Its limitation lies in the handling of inequality constraints, which are usually transformed into more restrictive equality constraints through potential fields. In this paper, we propose a new prioritized task-regulation framework based on a sequence of quadratic programs (QP) that removes the limitation. At the basis of the proposed algorithm, there is a study of the optimal sets resulting from the sequence of QPs. The algorithm is implemented and illustrated in simulation on the humanoid robot HRP-2.
377 citations
"Kinematic Control of Redundant Mani..." refers methods in this paper
...To overcome the problems with pseudoinverse-based solutions, later works [6], [7] formulated the control problem as a quadratic programming problem to find an optimal solution with minimal kinematic energy consumption under physical constraints....
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