Redundancy Resolution Of Robot Manipulators Research Articles

An L₁-Norm Based Optimization Method for Sparse Redundancy Resolution of Robotic Manipulators

For targeted motion control tasks of manipulators, it is frequently necessary to make use of full levels of joint actuation to guarantee successful motion planning and path tracking. Such way of motion planning and control may keep the joint actuation in a non-sparse manner during motion control process. In order to improve sparsity of joint actuation for manipulator systems, a novel motion planning scheme which can optimally and sparsely adopt joint actuation is proposed in this brief. The proposed motion planning strategy is formulated as a constrained <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> norm optimization problem, and an equivalent enhanced optimization solution dealing with bounded joint velocity is proposed as well. A new primal dual neural network with a new solution set division is further proposed and applied to solve such bounded optimization which can sparsely adopt joint actuation for motion control. Simulation and experiment results demonstrate the efficiency, accuracy and superiority of the proposed method for optimally and sparsely adopting joint actuation. The average sparsity (i.e., - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\|\dot \theta \|_{p}$ </tex-math></inline-formula> where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula> denotes the joint angle) of the joint motion of the manipulator can be increased by 39.22% and 51.30% for path tracking tasks in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X - Y$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X - Z$ </tex-math></inline-formula> planes respectively, indicating that the sparsity of joint actuation can be enhanced.

A Predictive Approach to Redundancy Resolution for Robot Manipulators

Abstract In this paper, we propose a new method for the online redundancy resolution of robot manipulators, which implements a predictive strategy to calculate the optimal control action. In this way, it is possible to obtain a more efficient handling of the constraints, which represents one of the main issues in online resolution methods. The predictive model has been obtained by considering every joint as a k th-order integral system, and the predictive equations are derived from a continuous-time formulation. This allows the use of an irregular distribution of the prediction and control time instants and, as a consequence, longer prediction and control horizons can be obtained, without increasing the computational complexity of the algorithm. Finally, joint hard bounds are easily included in a linear-model-predictive-like framework, and the optimal control action is calculated by solving a linear quadratic problem. Simulation results for a 4-degree-of-freedom planar arm show the effectiveness of the method compared to purely local resolution techniques.

Modified ZNN for Time-Varying Quadratic Programming With Inherent Tolerance to Noises and Its Application to Kinematic Redundancy Resolution of Robot Manipulators

For quadratic programming (QP), it is usually assumed that the solving process is free of measurement noises or that the denoising has been conducted before the computation. However, time is precious for time-varying QP (TVQP) in practice. Preprocessing for denoising may consume extra time, and consequently violates real-time requirements. Therefore, a model with inherent noise tolerance is urgently needed to solve TVQP problems in real time. In this paper, we make progress along this direction by proposing a modified Zhang neural network (MZNN) model for the solution of TVQP. The original Zhang neural network model and the gradient neural network model are employed for comparisons with the MZNN model. In addition, theoretical analyses show that, without measurement noise, the proposed MZNN model globally converges to the exact real-time solution of the TVQP problem in an exponential manner and that, in the presence of measurement noises, the proposed MZNN model has a satisfactory performance. Finally, two illustrative simulation examples as well as a physical experiment are provided and analyzed to substantiate the efficacy and superiority of the proposed MZNN model for TVQP problem solving.

Pseudoinverse-type bi-criteria minimization scheme for redundancy resolution of robot manipulators

SUMMARYIn this paper, a pseudoinverse-type bi-criteria minimization scheme is proposed and investigated for the redundancy resolution of robot manipulators at the joint-acceleration level. Such a bi-criteria minimization scheme combines the weighted minimum acceleration norm solution and the minimum velocity norm solution via a weighting factor. The resultant bi-criteria minimization scheme, formulated as the pseudoinverse-type solution, not only avoids the high joint-velocity and joint-acceleration phenomena but also causes the joint velocity to be near zero at the end of motion. Computer simulation results based on a 4-Degree-of-Freedom planar robot manipulator comprising revolute joints further verify the efficacy and flexibility of the proposed bi-criteria minimization scheme on robotic redundancy resolution.

Equivalence of velocity-level and acceleration-level redundancy-resolution of manipulators

The equivalence of velocity-level and acceleration-level redundancy resolution of robot manipulators is investigated in this Letter. Theoretical analysis based on gradient-descent method and computer simulations based on PUMA560 robot manipulator both demonstrate the equivalence of redundancy-resolution schemes at different levels.

Redundancy resolution of robotic manipulators with neural computation

This letter presents a neural-network-based computational scheme for redundancy resolution of manipulators. The Tank-Hopfield (TH) network is adopted for pseudoinverse and inverse kinematics calculations and it can provide joint velocity and joint acceleration solutions within a time frame of the order of hundreds of nanoseconds. Incorporating the TH network into the redundancy resolution scheme allows planning algorithms to be implemented in real time. Simulation results for a three-link planar manipulator are presented to demonstrate that the proposed approach is efficient and practical.

Redundancy Resolution of Robotic Manipulators Using Normalized Generalized Inverses

A dynamical formulation based upon the undetermined force method is presented for analyzing redundant robotic manipulators. The equivalence between this dynamical formulation and the general solution of kinematic constraint equations is then obtained through use of a normalized generalized inverse. This leads to a special form of the dynamical equations, called the N-inverse form of the dynamical equations. A class of problems, associated with the optimization of quadratic objective functions, are then studied. We find that the N-inverse form of the dynamical equations is the solution of this class of problems. Examples, including local minimization of joint torques and global minimization of kinetic energy, are presented.

Identification and resolution of structural and algorithmic singularity in redundancy control of serial manipulations

AbstractA major difficulty that has haunted most researchers in the process of optimal redundancy resolution of robotic manipulators is the instability observed in even very simple numerical simulations. This numerical instability is not related to the structurally singular configurations of the manipulators, and in the literature has been referred to as “algorithmic singularity,” “artificial singularity,” or “unavoidable singularity.” In this work, conditions on both structural and algorithmic singularities are studied based on the Singular Value Decomposition of the Jacobian matrix, and, hence, a singularity‐free control algorithm for redundant manipulators is developed and resolved as the Lagrange problem of optimal control. It is shown that many well‐known methods for optimal redundant manipulation in the literature, including the Extended Jacobian Technique, most of constraint function‐based methods, and most of the previously reported methods on global optimization techniques, are all special cases of the formulation provided here. Further, the necessary conditions of the global optimality for this general formulation are derived in explicit form and the source of “algorithmic singularity” is rigorously identified and resolved. © 2995 John Wiley &amp; Sons, Inc.

A local solution with global characteristics for the joint torque optimization of a redundant manipulator

AbstractIn this article, a stable local solution with global characteristics is developed for the joint torque optimization problem in redundant robotic manipulators. It is shown that the local optimization of the inertia inverse weighted dynamic torque corresponds to the global kinetic energy minimization problem. The proposed local‐global alternative to the joint torque optimization problem is compared for stability and torque optimality with five different methods used for redundancy resolution of robotic manipulators at the acceleration level. The proposed local‐global solution has been implemented and tested on a planar four‐DOF kinematically redundant lab robot which was designed and built at Southwest Research Institute (SWRI). Several numerical simulations confirm the positive advantages of solutions which have a local as well as a global interpretation. In addition, a “dynamic manipulation index” is introduced to monitor the stability of an optimization problem in a kinematically redundant robot.

Global versus Local Optimization in Redundancy Resolution of Robotic Manipulators

In redundancy resolution of robotic manipulators with more than the required degrees of freedom at the kinematic level, the minimization of the Euclidean norm of the joint velocities at the dynamic level, and the minimization of the kinetic energy of the manipulator at any moment of the task execu tion have long been suggested in the literature. In this paper the global optimization of the above characteristics are worked out by using integral-type criteria. The results are in surprisingly simple and elegant forms and give new insights to the redundancy resolution of robotic manipulators. The relations between local and global optimization are discussed.

Some Results on Generalized Inverses

B = S0B + (I S?S)Y, where Y is an arbitrary matrix of appropriate dimensions. The matrix S0 is called a generalized inverse of S and has the property SSgs = S. Four types of generalized inverses can be defined as follows: DEFINITION 1. Sg is said to be a generalized inverse of S if (1.1) SSgS = S. DEFINITION 2. Sr is said to be a reflexive generalized inverse of S if (1.2) SSrS = S and SrSSr = Sr. DEFINITION 3. Sn is said to be a normalized generalized inverse of S if (1.3) SS'S = , S) SS = S', and (SS')* = SS'. DEFINITION 4. St is said to be the pseudoinverse of S if