Four-link Planar Manipulator Research Articles

Spring Configurations and Attachment Angles Determination for Statically Balanced Planar Articulated Manipulators

Abstract Admissible spring configurations for statically balanced planar articulated manipulators have been investigated in previous studies. However, in these spring configurations, springs are only identified by the connection between links. The attachment angles and distance for springs to be properly installed remain unaddressed. In this study, a method to determine attachment angles and distance for springs is developed to ensure all the springs are acting for the benefit of static balancing. Here, the gravitational and elastic potential energies are represented in stiffness matrix form, it is shown that term by term compatibility exists between the first row of gravitational stiffness matrix and the first row of the elastic stiffness matrix. In accordance with these compatibility conditions, the admissible spring attachment angles are found to ensure all the ground-connected springs are acting for the benefit of gravity balancing. And the remained components below the first row of the elastic stiffness matrix are offset by the non-ground-connected springs. In accordance with the compatibility between the remained components and the elastic stiffness matrix of non-ground-connected springs, the spring attachment angles to ensure all the non-ground-connected springs acting for the benefit of elastic balancing are found. The determination of the admissible spring configurations is revisited in addition to the connection between links, and the attachment angles of springs are also specified. The admissible spring configurations of statically balanced planar articulated three- and four-link manipulators are derived. A four-link planar manipulator is used as an example for illustration.

Bi-criteria Acceleration Level Obstacle Avoidance of Redundant Manipulator.

In this paper, an improved obstacle-avoidance-scheme-based kinematic control problem in acceleration level for a redundant robot manipulator is investigated. Specifically, the manipulator and obstacle are abstracted as mathematical geometries, based on the vector relationship between geometric elements, and the Cartesian coordinate of the nearest point to an obstacle on a manipulator can be found. The distance between the manipulator and an obstacle is described as the point-to-point distance, and the collision avoidance strategy is formulated as an inequality. To avoid the joint drift phenomenon of the manipulator, bi-criteria performance indices integrating joint-acceleration-norm minimization and repetitive motion planning is adopted by assigning a weighing factor. From the perspective of optimization, therefore, an acceleration level quadratic programming (QP) problem is eventually formulated. Considering the physical structure of robot manipulators, inherent joint angle, speed, and acceleration limits are also incorporated. To solve the resultant QP minimization problem, a recurrent neural network based neural dynamic solver is proposed. Then, simulation experiments performing on a four-link planar manipulator validate the feasibility and effectiveness of the proposed scheme.

Two DTZNN Models of O(τ4) Pattern for Online Solving Dynamic System of Linear Equations: Application to Manipulator Motion Generation

In this paper, firstly, a high accuracy one-step-ahead numerical differentiation formula with O(τ 4 ) pattern is proposed for discretization. Meanwhile, a high precision first-order derivative formula of the backward difference rule with O(τ 4 ) pattern error is given to approximate the derivative information. Then, two high accuracy discrete-time zeroing-type models (HADTZTM) with O(τ 4 ) pattern, i.e., HADTZTM with derivative information known (HADTZTM-K) and HADTZTM with derivative information unknown (HADTZTM-U), are developed, analyzed and investigated for online solving the dynamic system of linear equations (DSLEs). In addition, the 0-stability, consistency, and convergence of the HADTZTM-K and HADTZTM-U are verified for DSLEs. From a theoretical/numerical viewpoint, the classical models are revisited and analyzed for online solving DSLEs. Ultimately, simulation experiment including an application to the path-tracking of the four-link planar manipulator is conducted to demonstrate the efficiency and superiority of the HADTZTM-K and HADTZTM-U, where the HADTZTM-U overcomes the difficulty of derivative information unknown in practical applications.

Repetitive motion of redundant robots planned by three kinds of recurrent neural networks and illustrated with a four-link planar manipulator’s straight-line example

In this paper, a dual neural network, LVI (linear variational inequalities)-based primal-dual neural network and simplified LVI-based primal-dual neural network are presented for online repetitive motion planning (RMP) of redundant robot manipulators (with a four-link planar manipulator as an example). To do this, a drift-free criterion is exploited in the form of a quadratic performance index. In addition, the repetitive-motion-planning scheme could incorporate the joint physical limits such as joint limits and joint velocity limits simultaneously. Such a scheme is finally reformulated as a quadratic program (QP). As QP real-time solvers, the aforementioned three kinds of neural networks all have piecewise-linear dynamics and could globally exponentially converge to the optimal solution of strictly-convex quadratic-programs. Furthermore, the neural-network based RMP scheme is simulated based on a four-link planar robot manipulator. Computer-simulation results substantiate the theoretical analysis and also show the effective remedy of the joint angle drift problem of robot manipulators.

Influence of trajectories on the joint torques of kinematically redundant manipulators

This paper presents an algorithm for solving the inverse dynamics problem of redundant manipulators using MAPLE software. The method has the advantage of generating efficient symbolic solutions which reduces the computational cost. The influence of trajectories on the joint torques of redundant manipulators is considered. The theory is illustrated by the numerical simulation of a redundant four-link planar manipulator.

Collision-free motion planning for redundant robots using neural-network processing

A computationally efficient obstacle-avoidance algorithm for redundant robots is presented in this paper. The algorithm incorporates Tank-Hopfield networks and the J function in the framework of resolved motion rate control, which is well suited for real-time implementation. Robot-arm kinematic control is carried out by the TH network. The connection weights of the network can be directly obtained from the known matrices at each sampling time, and joint velocity commands are generated from the outputs of the network. The obstacle-avoidance task can be achieved by formulating the performance criterion J > J min ( J min represents the minimal distance between the redundant robot and obstacles), and by using a null space to ensure that this criterion is satisfied. Several simulation cases for a four-link planar manipulator are given, to demonstrate how the proposed collision free trajectory planning scheme works.

A real-time planning algorithm for obstacle avoidance of redundant robots

A computationally efficient, obstacle avoidance algorithm for redundant robots is presented in this paper. This algorithm incorporates the neural networks and pseudodistance function Dp in the framework of resolved motion rate control. Thus, it is well suited for real-time implementation. Robot arm kinematic control is carried out by the Hopfield network. The connection weights of the network can be determined from the current value of Jacobian matrix at each sampling time, and joint velocity commands can be generated from the outputs of the network. The obstacle avoidance task is achieved by formulating the performance criterion as Dp>dmin (dmin represents the minimal distance between the redundant robot and obstacles). Its calculation is only related to some vertices which are used to model the robot and obstacles, and the computational times are nearly linear in the total number of vertices. Several simulation cases for a four-link planar manipulator are given to prove that the proposed collision-free trajectory planning scheme is efficient and practical.

On controlling robots with redundancy in an environment with obstacles

This paper presents a method to solve the problem of obstacle avoidance for a redundant manipulator so that it closely tracks the desired end-effector trajectory and simultaneously avoids workspace obstacles. The proposed method introduces the describing function J to indicate whether collision occurs between the robot and obstacles. The obstacle avoidance task is achieved by formulating the performance criterion J >Jmin (Jmin represents the minimal distance between the redundant robot and obstacles), and by using configuration control to ensure that this criterion is satisfied. The calculation of J function is only related to some vertices which are used to generate and model the robot and obstacles, and the computational times are nearly linear with the total number of vertices. The configuration control algorithm which achieves end-effector motion and obstacle avoidance does not require either a complex dynamic model or complicated inverse kinematics transformations of the robot. Several simulation cases for a four-link planar manipulator are given to prove that the proposed collision-free trajectory planning scheme is efficient and practical.