Three-link Planar Manipulator Research Articles

Modeling the workspace of a three-link planar manipulator

A study of the working space of a three-link planar manipulator was carried out. The basis is taken from analytical dependencies that allow solving the direct problem of kinematics, i.e. determine the coordinates of the gripper center point using three generalized coordinates of the manipulator. The analysis performed made it possible to give a geometric interpretation of the dependencies. It has been established that the workspace of the manipulator is a three-parameter set of points. On a plane, this set of points is represented in the form of two disks consisting of ring cells, for which the corresponding analytical dependencies are obtained. The geometric image of this set is a three-dimensional torus. The resulting models are visualized, which facilitates the solution of this problem. To determine the values of the generalized coordinates of the gripper center points, a mapping was carried out by orthogonal projection of the families of circles obtained in the work into four-dimensional space. As a result, three-dimensional hypersurfaces in four-dimensional space were obtained. It is proposed to study them by constructing hypersurface sections models by hyperplanes. Such models in visualization mode allow solving direct and inverse kinematics problems of the manipulator under study.

Evaluating the Maximum Directional Kinematic Capability of a Redundant Manipulator Based on Allowable Velocity and Force

In this study, a new concept of allowable velocity and force is proposed to precisely evaluate the maximum directional kinematic capability of a redundant manipulator. For a general redundant manipulator, an optimization problem is formulated to determine the maximum achievable velocity and force projected along the base direction at any target position in the workspace. This provides quantitative information on allowable (i.e., maximum directional) velocity and force to be precisely visualized in 2D and 3D complicated shapes, which conventional manipulability ellipsoid cannot provide. As application examples, allowable velocity and force are evaluated for a distributed actuation mechanism (DAM)-based three-link planar manipulator, 3RRR planar parallel manipulator, and the UR5 robot (a spatial manipulator with 6 degrees of freedom). The simulation and experimental results validate that the proposed method can precisely determine allowable velocity and force, thereby contributing to planning the optimal operation for a given task.

Model-based, Distributed, and Cooperative Control of Planar Serial-link Manipulators

In this paper, we propose a novel distributed control scheme for a planar serial-link manipulator with revolute joints. The control scheme is based on the conventional model-based nonlinear control scheme that achieves linearization by feedback. A dedicated controller controls each joint of the manipulator, as in the case of the decentralized manipulator control scheme. However, in the proposed control scheme, the joint-level controllers communicate and cooperate to account for the nonlinear dynamic coupling between the links. The proposed control scheme can achieve the performance level of that of the model-based nonlinear control scheme, and at the same time, reduce the computational lead-time by distributing the computational load associated with the control law among the joint-level controllers. We design a distributed cooperative control law for a three-link planar manipulator and demonstrate its trajectory tracking performance using simulation experiments.

Multi‐model switching‐based fault tolerant control for planar robot manipulators

This study addresses the fault-tolerant tracking control issue for a class of planar manipulators with various actuator and sensor faults. Firstly, a set of linear models are constructed to approximate the original non-linear model at the different joint angular positions, which explicitly reveal the coupling effects among sub-manipulators. Secondly, a family of decentralised fault-tolerant controllers are proposed with each one being related to one linear model respectively, which does not require the information exchange among sub-manipulators and thus lightens the communication burden. Finally, a switching law is proposed among controllers such that the system remains stable in the presence of controller switching. An example of a three-link planar robot manipulator is taken to illustrate the effectiveness of the proposed methods.

Nonlinear Regulators in the Position Stabilization Problem of the Holonomic Mechanical System

The application of nonlinear proportional-integral and proportional-integro-differential regulators in the program position stabilization problem of a holonomic mechanical system is investigated. To this end, the method of Lyapunov functionals is developed in the stability problem of Volterra integro-differential equations. As an example, the global regulation problem of a three-link planar manipulator is solved.

A Velocity-Level Bi-Criteria Optimization Scheme for Coordinated Path Tracking of Dual Robot Manipulators Using Recurrent Neural Network.

A dual-robot system is a robotic device composed of two robot arms. To eliminate the joint-angle drift and prevent the occurrence of high joint velocity, a velocity-level bi-criteria optimization scheme, which includes two criteria (i.e., the minimum velocity norm and the repetitive motion), is proposed and investigated for coordinated path tracking of dual robot manipulators. Specifically, to realize the coordinated path tracking of dual robot manipulators, two subschemes are first presented for the left and right robot manipulators. After that, such two subschemes are reformulated as two general quadratic programs (QPs), which can be formulated as one unified QP. A recurrent neural network (RNN) is thus presented to solve effectively the unified QP problem. At last, computer simulation results based on a dual three-link planar manipulator further validate the feasibility and the efficacy of the velocity-level optimization scheme for coordinated path tracking using the recurrent neural network.

On position/force tracking control problem of cooperative robot manipulators using adaptive fuzzy backstepping approach

In this paper, the position and force tracking control problem of cooperative robot manipulator system handling a common rigid object with unknown dynamical models and unknown external disturbances is investigated. The universal approximation properties of fuzzy logic systems are employed to estimate the unknown system dynamics. On the other hand, by defining new state variables based on the integral and differential of position and orientation errors of the grasped object, the error system of coordinated robot manipulators is constructed. Subsequently by defining the appropriate change of coordinates and using the backstepping design strategy, an adaptive fuzzy backstepping position tracking control scheme is proposed for multi-robot manipulator systems. By utilizing the properties of internal forces, extra terms are also added to the control signals to consider the force tracking problem. Moreover, it is shown that the proposed adaptive fuzzy backstepping position/force control approach ensures all the signals of the closed loop system uniformly ultimately bounded and tracking errors of both positions and forces can converge to small desired values by proper selection of the design parameters. Finally, the theoretic achievements are tested on the two three-link planar robot manipulators cooperatively handling a common object to illustrate the effectiveness of the proposed approach.

Trajectory planning with residual vibration suppression for space manipulator based on particle swarm optimization algorithm

Space manipulator suffers from vibration problems mainly due to the flexibility of joints and links in a microgravity environment. This article presents a new optimization method of trajectory planning with minimum residual vibration for space manipulator system which is modeled by absolute coordinate-based method. First, absolute nodal coordinate formulation, which can describe large rotation and large deformation of flexible bodies precisely, is used to describe the deformation of flexible links, and natural coordinate formulation with nonlinear torsion stiffness function is used to model flexible joints. Then, joint rotation trajectory resulting from the planned end-effector trajectory by inverse kinematics theory is discrete through the proposed cosine-based function that has been validated to suppress the residual vibration. The particle swarm optimization algorithm is employed to achieve minimum residual vibration by optimizing redundant coefficients of movement derived from inverse kinematics theory. The effectiveness of the proposed method is illustrated via simulation of a planar three-link manipulator taking large deformation and large rotation into account. Results show that the optimized method can exhibit better features for the residual vibration suppression as compared to those of the original cosine-based trajectory.

A simple and quick control strategy for a class of first-order nonholonomic manipulator

This paper presents a simple and quick control strategy for a class of first-order nonholonomic manipulator: planar n-link manipulator with a passive first joint (no gravity). The control target is driving its endpoint from any initial position to any target position. First, we reduce the planar n-link manipulator to a planar three-link one by maintaining the states (angles and angular velocities) of n-3 active links in the initial value all the time. That is, we only adjust the states of the remaining two active links in the whole control process, and these two adjusted active links are chosen to guarantee that the target position is in the reachable region of the planar n-link manipulator by using the enumeration method. Then, we divide the whole control process into two stages for the reduced planar three-link manipulator. In each stage, the manipulator becomes a planar two-link one by maintaining the states of one adjusted active link to be the constant value. The state constraint existing between the passive first link and the adjusted active link is obtained by using the integral characteristics of a planar two-link manipulator. Meantime, the geometric constraint between the position of the endpoint and angles of all joints is obtained based on the homogeneous coordinate transformation method. According to the above two kinds of constraint, the target angles of the two adjusted active links are calculated by employing the particle swarm optimization algorithm. When the two adjusted active links are controlled to their target angles in turn, the control target of the planar n-link manipulator is completed. Finally, simulation results demonstrate that the proposed control strategy is valid and rapid.

Dynamic analysis and parameter estimation of coupled three-link planar manipulator with flexible belt-drive system

The coupled three-link planar manipulator mechanism is widely adopted in panel handling robots for the realization of straight-line translational motion of the end-effector with a single actuator and three belt-drive systems. This research analyzes and models the complex dynamics of the coupled three-link planar manipulator including the flexible belt systems. Equations of the motion of the manipulator are derived mathematically by using Lagrange method and the coupling constraints between the links are modeled and appropriately represented in the mathematical model. Also, joint friction is modeled with static, Coulomb and viscous models. Using the mathematical model a numerical simulation program is developed. The system parameters, including joint friction and belt damping, for the highly nonlinear model are estimated using the genetic algorithm that is one of the global optimization techniques. The validity of the simulation model is verified by comparing the simulation results with the experimental results.

Neural Network based Inverse Kinematics Solution for Trajectory Tracking of a Robotic Arm

Planar two and three-link manipulators are often used in Robotics as testbeds for various algorithms or theories. In this paper, the case of a three-link planar manipulator is considered. For this type of robot a solution to the inverse kinematics problem, needed for generating desired trajectories in the Cartesian space (2D) is found by using a feed-forward neural network.

On the Damping-Induced Self-Recovery Phenomenon in Mechanical Systems with Several Unactuated Cyclic Variables

The damping-induced self-recovery phenomenon refers to the fundamental property of underactuated mechanical systems: if an unactuated cyclic variable is under a viscous damping-like force and the system starts from rest, then the cyclic variable will always move back to its initial condition as the actuated variables come to stop. The regular momentum conservation phenomenon can be viewed as the limit of the damping-induced self-recovery phenomenon in the sense that the self-recovery phenomenon disappears as the damping goes to zero. This paper generalizes the past result on damping-induced self-recovery for the case of a single unactuated cyclic variable to the case of multiple unactuated cyclic variables. We characterize a class of external forces that induce new conserved quantities, which we call the damping-induced momenta. The damping-induced momenta yield first-order asymptotically stable dynamics for the unactuated cyclic variables under some conditions, thereby inducing the self-recovery phenomenon. It is also shown that the viscous damping-like forces impose bounds on the range of trajectories of the unactuated cyclic variables. Two examples are presented to demonstrate the analytical discoveries: the planar pendulum with gimbal actuators and the three-link planar manipulator on a horizontal plane.

Adaptive neural controller for cooperative multiple robot manipulator system manipulating a single rigid object

In this article, an adaptive neural controller is developed for cooperative multiple robot manipulator system carrying and manipulating a common rigid object. In coordinated manipulation of a single object using multiple robot manipulators simultaneous control of the object motion and the internal force exerted by manipulators on the object is required. Firstly, an integrated dynamic model of the manipulators and the object is derived in terms of object position and orientation as the states of the derived model. Based on this model, a controller is proposed that achieves required trajectory tracking of the object as well as tracking of the desired internal forces arising in the system. A feedforward neural network is employed to learn the unknown dynamics of robot manipulators and the object. It is shown that the neural network can cope with the unknown nonlinearities through the adaptive learning process and requires no preliminary offline learning. The adaptive learning algorithm is derived from Lyapunov stability analysis so that both error convergence and tracking stability are guaranteed in the closed loop system. Finally, simulation studies and analysis are carried out for two three-link planar manipulators moving a circular disc on specified trajectory.

Control of a class of underactuated mechanical systems

In this paper a new control methodology for underactuated mechanical systems is proposed. The basic idea of this method is to combine passive velocity field control with decoupling vector field. In order that the underactuated mechanical systems can be stabilized at the desired position after settling on the desired velocity vector field, novel control strategies are proposed. Proposed control strategies are applied to the underactuated planar three-link manipulator and underactuated planar body. Simulations demonstrate the usefulness and effectiveness of the proposed control methodology.

Real-Time Motion Planning for a Volleyball Robot Task Based on a Multi-Agent Technique

This paper takes the volleyball robot task as an example of a dynamic manipulation task and presents a multi-agent-based motion-planning framework for it. Each subtask in the motion planning is defined as an agent. The motion planning is accomplished by the solution of each agent activated by a blackboard. It is convenient to extend the module and enable real-time control compared to the hierarchy and subsumption architecture. In the solution of each subtask, one difference from the motion planning of other ball-playing robots is that simple fuzzy rules are adopted to determine the hitting position, which leads to smaller hitting velocities beneficial for task control. The other difference is that the task-based directional manipulability measure (TDMM) is used to optimize the robot configuration on the basis of optimal hitting path, so as to improve the manipulating ability on task direction. The simulation of a planar three-link manipulator ball-hitting task is implemented by the MATLAB/Simulink tool. The virtual target of the hitting motion is validated on the ABB manipulator by the ball-catching experiment.

Design of Dissipative and Stable Assist Robots

This paper presents a methodology for design of dissipative assist robots with proven stability during set-point control. A dissipative assist robot is defined as one where the actuators continuously dissipate energy from the robot until the robot reaches the desired set point. We have discussed in this paper that, under well known control laws, it is hard to characterize dissipativity of a general assist robot. However, by appropriately designing the robot through inertia redistribution, the dynamic equations can be modified so that the control laws can now be proven to be both dissipative and stable under set-point control. The proposed method is demonstrated through simulation of a three-link planar manipulator used as an assist robot to modify human functional movements in a vertical plane.

Control of a three-link manipulator driven by three spinning disks

This work deals with the modelling and control of a planar three-link manipulator driven by three spinning disks. The motion of the manipulator+disks' system is described by six angles. The first three of them describing the motion of the manipulator, and the rest describing the motion of the spinning disks. A torque i is applied on Disk i, i = 1,2,3, respectively. Thus, the system is underactuated.

Multiple tasks manipulation for a robotic manipulator

Robotic manipulators can execute multiple tasks precisely at the same time and, thus, the task-priority scheme plays an important role in implementing multiple tasks. Until now, several algorithms for task-priority have been used in solving the inverse kinematics for redundant manipulators. In this paper, through the comparative study of existing algorithms, we will propose a new method for task-priority manipulation in terms of two important criteria—algorithmic singularity and task error. This manipulation scheme will be applied to a planar three-link manipulator to demonstrate its effectiveness.

Path design of redundant flexible robot manipulators to reduce residual vibration in the presence of obstacles

A method is presented for generating the path that significantly reduces residual vibration of the redundant, flexible robot manipulator in the presence of obstacles. The desired path is optimally designed so that the system completes the required move with minimum residual vibration, avoiding obstacles. The dynamic model and optimal path are effectively formulated and computed by using a special moving coordinate, called VLCS, to represent the link flexibility. The path to be designed is developed by a combined Fourier series and polynomial function to satisfy both the convergence and boundary condition matching problems. The concept of correlation coefficients is used to select the minimum number of design variables. A planar three-link manipulator is used to evaluate this method. Results show that residual vibration can be drastically reduced by selecting an appropriate path, in the presence of obstacles.

Time-optimal control of kinematically redundant manipulators with limit heat characteristics of actuators

In this study, we present a time-optimal control scheme for kinematically redundant manipulators to track a predefined geometric path, subject to the limit heat characteristics of actuators (a DC motor was assumed to be the actuator used). Constraints due to the rated torque and the rated velocity of the motor would not be valid for continuous use of manipulators, since the required mechanical output of the actuator (DC motor) exceeds its maximum power capacity and far more exceeds its heat-converted power limit. The heat-converted power limit of the DC motor is thus considered as the actuation bound of the actuator and the time-optimal trajectories are generated by using the phase-plane analysis and the linear programming technique subject to this bound. Computer simulation was also executed on a three-link planar rotary manipulator to demonstrate the effectiveness of the proposed scheme.