Multi-link Robot Manipulators Research Articles

Prescribed performance tracking control of multi-link robotic manipulator with uncertainties

<p style='text-indent:20px;'>This paper addresses the trajectory tracking problem with prescribed performance for a multi-link robotic manipulator subject to unknown dynamics and external disturbances. A predefined performance function is adopted to describe tracking errors' desired transient and steady-state performance. Then, the output error dynamics with performance constraints are transformed into an equivalent unconstrained system, whose stabilization is sufficient to guarantee the prescribed performance of the original system. An extended state observer with a friction model is designed to approximate unknown dynamics together with the unmeasurable velocity state, which extends the applicability of the proposed controller to manipulators with only position signals available. The friction model is lumped into it to improve the precision and velocity of estimation. It is proved via Lyapunov analysis that the proposed controller can theoretically guarantee the satisfaction of prescribed performance in the presence of uncertainties. The simulation results verify the reliability and effectiveness of the proposed method.</p>

Trajectory tracking controller of a robotized arm with joint constraints, a direct adaptive gain with state limitations approach

Motion restrictions in robotic devices may introduce complex requirements for any closed-loop control design, mainly when the robot joints must track reference trajectories that force the end-effector to perform planned motions. This study summarizes the comprehensive technical design of an adaptive state feedback controller for multi-link robotic manipulators that consider the effect of position and velocity restrictions on the tracking trajectory control approach. The proposed design is less conservative than other methods because of the explicit inclusion of state restrictions in the control gain dynamics. A logarithm barrier Lyapunov function class supports the design of the adaptive gain for the manipulator. Sufficient conditions based on a Riccati equation simplify the implementation of the adaptive controller with gains depending on the distance between the current state and the restriction sets. Numerical simulations show the advantages of the proposed controller with adaptive gains concerning a similar adaptive controller that does not consider the restrictions and a proportional–integral–derivative form. An implementation for the motion control of a robotic arm is presented to demonstrate the development by implementing the proposed gain, which confirms the suggested improvements enforced by the proposed controller. The performed comparison shows the advantages of the suggested adaptive gain control form, inducing better tracking of reference trajectories and smaller control energy applications.

FEATURES OF KINEMATICS AND CONTROL OF MULTI-LINK MANIPULATOR ROBOTS

The subject of research is multi-link manipulators, their kinematics and methods of controlling multi-link manipulator robots. To improve the accuracy of movement of each link and their synergy of work with each other during operation. In addition, the subject of the research is the analysis of the requirements for multi-link robot manipulators and the improvement of the kinematics of the robot-manipulator movements based on the comparison of mathematical methods in operating conditions. In different operating conditions manipulators and the automation of the production line is a big step for industry. Instead of a traditional industrial robot, a multi -link manipulator robot can be a good intermediate solution. It is more maneuverable, flexible, and has more complex movements for working on serial production. Multi-link robots provide a quick replacement of skilled labor in case of a shortage of employees or when production needs to be accelerated. As with any revolutionary technology, it is necessary to be critical of its implementation. The most decisive advantage of a robot over a single-link industrial robot is flexibility. Especially since the production environment needs to be able to adapt to handle the work with small volumes and a large number of different tasks. Such robots are more mobile and take up less space than traditional industrial robots. They are easier to reprogram to perform different jobs or product variants. However, it is worth noting that programming a traditional robot, which in its specialized environment requires deep knowledge and endless settings. When using a robot, the entry barrier for operators is significantly reduced, while deployment and ROI are accelerated. The aim of the work is to determine how the project context affects the choice of motion techniques and to determine the dependencies between requirements discovery methods. The article solves the following tasks: to study the trajectory of robots and compare mathematical control methods. Requirements in industry, create and draw a parallel regarding the practice of using demonstration robots and requirements in real conditions of using multi-link structures, determine the preferences of practitioners regarding detection methods and determine how the project context affects the choice of requirements detection techniques, determine dependencies between requirements detection methods. The task using such a method as a parametric form of the task is to prove that: the mathematical model of motion trajectories is the most reliable. Development and improvement of kinematic movements of manipulators with synergy of movements between manipulators. The following results were obtained: The best detection methods were identified and compared with other comprehensive studies. Conclusion: It was concluded that the choice of the shape of the wave-like trajectory of the movement; a traveling wave in a coordinate system moving along this sine wave form should be used as a control program for an automatic drive system. The assignment of a form in the form of a sine wave appears unsuitable for this task, because the obvious disadvantage of the sine wave is a continuous change in curvature and greater curvature at the peaks at large amplitudes.

PID controllers with delay in a problem of stabilization of robotic manipulators’ desired motions

Proportional-integro-differentiating (PID) controllers are widely used in solving control problems of technical systems, including mechanical ones. For this case, most of works are limited to the study of stabilization problem for steady motions and states; such studies are based on the analysis of model equations in a linear approximation. On the other hand, one of the urgent problems of controlled-motion mechanics is the problem of using PID controllers in tracking the trajectories of multi-link robotic manipulators with semi-global or global stabilization in a non-linear formulation. Practically little studied is the problem of justifying the applicability of such controllers taking into account possible delay in the feedback structure. This paper deals with such a problem. As an application of the theory developed in this paper, the control for a motion of a six-link manipulator is obtained.

Решение обратной задачи кинематики для последовательных роботов- манипуляторов на основе нечетких численных методов

Nowadays the introduction of robotic systems is one of the most common forms of the technological operations automation in various spheres of human activity. Among the robotic systems a special place is occupied by sequential multi-link robotic manipulators (SRM). SRM have become widespread due to relatively small dimensions and high maneuverability, which makes their use indispensable to solve various tasks. In practice, the effectiveness of the functioning of the SRM can be influenced by various types of external environment fuzzy factors. Among the external factors there is a group affecting the ability to determine the exact target position. Such factors often affect technical vision systems. This problem is especially relevant for special purpose mobile robots operating in aggressive environmental conditions. A situation similar to the described one also occurs when a medical robot manipulator is used for minimally invasive surgery, when the role of the control and monitoring system is assumed by an operator. In this regard, the organization of effective control taking into account influence of the external fuzzy factors, that prevent the correct recognition of the target position of the SRM instrument, is an urgent problem. The authors consider the solution of the inverse kinematics problem for SRM based on the use of fuzzy numerical methods, taking into account the possible occurrence of singular configurations in the process of solving.

Hierarchical multiloop MPC scheme for robot manipulators with nonlinear disturbance observer.

This paper addresses the robust enhancement problem in the control of robot manipulators. A new hierarchical multiloop model predictive control (MPC) scheme is proposed by combining an inverse dynamics-based feedback linearization and a nonlinear disturbance observer (NDO) based uncertainty compensation. By employing inverse dynamics-based feedback linearization, the multi-link robot manipulator was decoupled to reduce the computational burden compared with the traditional MPC method. Moreover, an NDO was introduced into the input torque signal to compensate and correct the errors from external disturbances and uncertainties, aiming to enhance the robustness of the proposed controller. The feasibility of the proposed hierarchical multiloop MPC scheme was verified and validated via simulation of a 3-DOF robot manipulator. Results demonstrate that the proposed controller provides comparative accuracy and robustness and extends the existing state-of-the-art algorithms for the trajectory tracking problem of robot manipulators with disturbances.

On the steady motions control of viscoelastic joined robotic manipulators

In this paper, the control problem of the serial multi-link robotic manipulators with rigid and viscoelastic joints is considered. The manipulators structure is such that only the rigid joints are controlled by DC motors. It is shown that such robotic manipulators can make so called stationary motions wherein the part of the generalized coordinates does’t change in time and the others change according to a linear law. The robust output feedback controllers are obtained for the robotic manipulators such that the stationary motion is locally, semi-globally, and globally asymptotically stable.

Design of gain scheduled fuzzy PID controller for multi-link robot manipulators

Gain Scheduling (GS) controller is one of the most popular approaches to nonlinear control design. Commonly, Gain Scheduling (GS) controllers have better performance than robust ones. In this paper, the structure of a proposed gain scheduled PID fuzzy controller (GS-PIDF) designed and analyzed. The Fuzzy PID controller gains weighted through gain scheduling designed system to grantee both the stability and the best performance of a multi links robot manipulator system. The overall designed controller system is applied to two links robot manipulator system, which is subject to modelling using Lagrangian dynamics method and simulation vie MatLab and Simulink package to minimize the vibration and acquire best performance.

Non‐linear optimal control for multi‐DOF electro‐hydraulic robotic manipulators

A non-linear optimal (H-infinity) control approach is proposed for the dynamic model of multi-degree-of-freedom (DOF) electro-hydraulic robotic manipulators. Control of electro-hydraulic manipulators is a non-trivial problem because of their non-linear and multi-variable dynamics. In this study, the considered robotic system consists of a multi-link robotic manipulator that receives actuation from rotary electro-hydraulic drives. The article's approach relies first on approximate linearisation of the state-space model of the electro-hydraulic manipulator, according to first-order Taylor series expansion and the computation of the related Jacobian matrices. For the approximately linearised model of the manipulator, a stabilising H-infinity feedback controller is designed. To compute the controller's gains, an algebraic Riccati equation is solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. The proposed control method retains the advantages of typical optimal control, i.e. fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.

Mathematical Modeling of the Dynamics of 3-DOF Robot-Manipulator with Software Control

Abstract The paper presents a general method for constructing a mathematical model of multi-link robot-manipulators. For the 3-DOF manipulator, kinematic equations and differential equations of dynamics are obtained. To study mathematical models of the dynamics of robotic manipulators and applications in software control systems, it is necessary to develop special analytical methods for solving systems of differential equations. An analytical method of transformations applied for the study of mathematical models of the dynamics of 3-DOF robot-manipulators. The method allows to obtain a solution in an analytical form, taking into account all nonlinear components of the system of differential equations. The software package for study of nonlinear mathematical models was developed and implemented. The problem of software control of electric drives of 3-DOF robot-manipulator is considered and control actions are determined that ensure the fulfillment of a given trajectory by the manipulator. The method for constructing and analyzing a mathematical model of manipulators presented in this work can be used to study a wide class of multi-link manipulators with many degrees of freedom.

Trajectory tracking of quadrotor flying manipulators using [formula omitted] adaptive control

This paper concerns with tracking control of an unmanned quadrotor vehicle equipped with a multi-link robotic manipulator. We present an analytic model of the system that formulates unknown interactions between the aerial platform and the manipulator in the form of nonlinear time-varying uncertainties. Based on the proposed model, a novel trajectory tracking scheme is synthesized by combining two inner feedback linearization loops to stabilize the nominal quadrotor and manipulator dynamics and a master L1 adaptive loop to systematically compensate for uncertainties and realize the desired closed-loop behavior. We show that this scheme leverages predictable transient and steady state performance in the presence of coupling effects and given a specified reference trajectory. Simulation studies have shown the effectiveness of the proposed aerial manipulator control method.

Feedforward fuzzy trajectory compensator with robust adaptive observer at input trajectory level for uncertain multi-link robot manipulators

This paper presents an inverse dynamics controller plus feedforward fuzzy trajectory compensator suitable for the trajectory tracking control of uncertain multi-link robot manipulators. To address the issue of unavailable normalization factor, a feedforward fuzzy trajectory compensator is proposed and assembled at the input trajectory level of the inverse dynamics controller rather than at the joint drive torque position. The compensator serving as a low-pass filter is implemented outside the inner control loop by adjusting the desired characteristic trajectory. Due to the nearly unchanged internal control algorithm, the adaptive fuzzy compensator is feasible to implement, and is robust when varying the feedback gain in the inner control loop. Moreover, a robust adaptive fuzzy state observer with loose constraints on the position of uncertain function is designed to assess some unmeasurable state parameters, and a robust term is designed to reduce the influence of the lumped uncertainties. By such design, the observer no longer imposes strict limitations on the position of the nonlinear function and the canonical form of unknown robotic dynamic model. To validate the effectiveness of the proposed controller, simulations and experiments are conducted for a desired characteristic trajectory, and the performance of the proposed controller has been compared with conventional controllers and recently developed controllers to illustrate the usefulness and efficiency of the proposed controller.

A new adaptive fuzzy sliding mode observer for a class of MIMO nonlinear systems

In this paper, a new adaptive fuzzy sliding mode (AFSM) observer is proposed which can be used for a class of MIMO nonlinear systems. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. In this method, a fuzzy system is designed to estimate the nonlinear behavior of the observer. The output of fuzzy rules are tuned adaptively, based on the observer error. The output connection matrix is used to combine the observer errors of individual subsystems. A robust term, which is designed based on the sliding mode theory, is added to the observer to compensate the fuzzy estimation error. The estimation error bound is adjusted by an adaptive law. The main advantage of the proposed observer is that, unlike many of the previous works, the measured outputs is not limited to the first entries of a canonical-form state vector. The proposed observer estimates the closed-loop state tracking error asymptotically, provided that the output gain matrix includes Hurwitz coefficients. The chattering is eliminated by using boundary layers around the sliding surfaces and the observer convergence is proved using a Lyapunov-based approach. The proposed method is applied on a real multilink robot manipulator. The performance of the observer shows its effectiveness in the real world.

Inertia-related coupling torque compensator for disturbance observer based position control of robotic manipulators

We propose an inertia-related coupling torque (IRCT) compensator for disturbance observer (DOB)-based position control of multi-link robotic manipulators. The proposed compensator reduces the DOB estimation error that is due to input with high-frequency components. To analyze the compensated system, the state space model is converted to singular perturbation form and the stability of the proposed system is also addressed. Numerical simulations and experimental results show the effectiveness of the proposed compensator.

Optimal Parameter Estimation for Long-Term Prediction in the Presence of Model Mismatch

For nonlinear multi-input multi-output (MIMO) systems such as multilink robotic manipulators, finding a correct, physically derived model structure is almost impossible, so that significant model mismatch is nearly inevitable. Moreover, in the presence of model mismatch, the use of least-squares minimization of the one-step-ahead prediction error (residual error) to estimate unknown parameters in a given model structure often leads to model predictions that are extremely inaccurate beyond a short time interval. In this paper, we develop a method for optimal parameter estimation for accurate long-term prediction models in the presence of significant model mismatch in practice. For many practical cases, where a correct model and the correct number of degrees of freedom for a given model structure are unknown, we combine the use of long-term prediction error with frequency-based regularization to produce more accurate long-term prediction models for actual MIMO nonlinear systems.

Nonsingular Terminal Neural Network Sliding Mode Control for Manipulator Joint Based on Backstepping

A new method of nonsingular terminal neural network sliding control based on backstepping for tracking control of multi-link robot manipulators with modeling error and external disturbances is introduced.Nonsingular terminal sliding mode surface is used which has property of finite-time convergence.According to sliding mode control theory,backstepping is used to design nonsingular terminal sliding mode controller.To confirm the upper bound of uncertainties in sliding-mode control system,a proper radial basis function neural networks controller is designed to estimate uncertain upper boundary on line.The system stability is proved by Lyapunov principle simulation results verify that this method improves the performances of trajectory tracking,enhances the robustness to modeling error and external disturbances and reduces chattering.

3次元ロボットマニピュレータの多数制約最適制御

This paper presents a generic method for optimal motion planning for three-dimensional 3-DOF multi-link robotic manipulators. We consider the operation of the manipulator systems, which involve constrained payload transportation/ capture/release, which is a subject to the minimization of the user-defined objective function, enabling for example minimization of the time of the transfer and/or actuation efforts. It should be stressed out that the task is solved in the presence of arbitrary multiple additional constraints. The solutions of the associated nonlinear differential equations of motion are obtained numerically using the direct transcription method. The direct method seeks to transform the continuous optimal control problem into a discrete mathematical programming problem, which in turn is solved using a non-linear programming algorithm. By discretizing the state and control variables at a series of nodes, the integration of the dynamical equations of motion is not required. The Chebyshev pseudospectral method, due to its high accuracy and fast computation times, was chosen as the direct optimization method to be employed to solve the problem. To illustrate the capabilities of the methodology, maneuvering of RRR 3D robot manipulators were considered in detail. Their optimal operations were simulated for the manipulators, binded to move their effectors along the specified 2D plane and 3D spherical and cylindrical surfaces (imitating for example, welding, tooling or scanning robots).

Multi-Constrained Optimal Control of 3D Robotic Arm Manipulators

This paper presents a generic method for optimal motion planning for three-dimensional 3-DOF multi-link robotic manipulators. We consider the operation of the manipulator systems, which involve constrained payload transportation/ capture/release, which is a subject to the minimization of the user-defined objective function, enabling for example minimization of the time of the transfer and/or actuation efforts. It should be stressed out that the task is solved in the presence of arbitrary multiple additional constraints. The solutions of the associated nonlinear differential equations of motion are obtained numerically using the direct transcription method. The direct method seeks to transform the continuous optimal control problem into a discrete mathematical programming problem, which in turn is solved using a non-linear programming algorithm. By discretizing the state and control variables at a series of nodes, the integration of the dynamical equations of motion is not required. The Chebyshev pseudospectral method, due to its high accuracy and fast computation times, was chosen as the direct optimization method to be employed to solve the problem. To illustrate the capabilities of the methodology, maneuvering of RRR 3D robot manipulators were considered in detail. Their optimal operations were simulated for the manipulators, binded to move their effectors along the specified 2D plane and 3D spherical and cylindrical surfaces (imitating for example, welding, tooling or scanning robots).

Block synthesis for manipulator under uncertainties

In this paper a decompose synthesis procedures are proposed for tracking problem of multilink robotic manipulator, functioning under uncertainties and external disturbances. On the assumption that external disturbances and control object components are belong to smooth functions, and only link positions are measured the complex solution of tracking and observation problems is presented using block approach.

On-line Adaptive T-S Fuzzy-Neural Control for A Class of General Multi-Link Robot Manipulators

nonlinear systems. In [4-6], the authors proved that the T-S fuzzy system can approximate any continuous function to any precision. This paper proposes a novel method of on-line modeling and control through the Takagi-Sugeno (T-S) fuzzy-neural model for a class of general n-link robot manipulators. Compared with previous methods, this paper has two unique aspects: first, a more general n-link robot system using on-line adaptive T-S fuzzy-neural controller is investigated, and second, the complete proof of the controller is given. The general robot systems are linearized via the mean value theorem, and then the T-S fuzzy-neural model can approximate the linearized system. Also, we propose an on-line identification algorithm and put significant emphasis on robust tracking controller design using an adaptive scheme for the robot systems. Finally, an example including two cases is provided to demonstrate the feasibility and robustness of the proposed method.