Control Law For Robot Manipulators Research Articles

Visual Based Control Scheme for a Robotic Manipulator with Duality of Task-space Information and Friction Compensation

This paper presents a new control technique for a robot manipulator with dual task-space information and friction compensation. The control scheme allows the end effector to transit smoothly from Cartesian-space feedback to vision-space feedback when the target is inside the vicinity of the camera. An adaptive term is integrated into the proposed controller to compensate the uncertainty associated with parameters in the friction model, including the Stribeck effect. A Lyapunov-like function is presented for stability analysis of the proposed control law. Numerical simulations are presented to demonstrate the performance of the proposed control law for robot manipulator.

Pseudo-inverse Jacobian control with grey relational analysis for robot manipulators mounted on oscillatory bases

Interest in complex robotic systems is growing in new application areas. An example of such a robotic system is a dexterous manipulator mounted on an oscillatory base. In literature, such systems are known as macro/micro systems. This work proposes pseudo-inverse Jacobian feedback control laws and applies grey relational analysis for tuning outer-loop PID control parameters of Cartesian computed-torque control law for robotic manipulators mounted on oscillatory bases. The priority when modifying controller parameters should be the top ranking importance among parameters. Grey relational grade is utilized to investigate the sensitivity of tuning the auxiliary signal PID of the Cartesian computed-torque law to achieve desired performance. Results of this study can be feasible to numerous mechanical systems, such as mobile robots, gantry cranes, underwater robots, and other dynamic systems mounted on oscillatory bases, for moving the end-effector to a desired Cartesian position.

Canonical transformations used to derive robot control laws from a port-controlled Hamiltonian system perspective

This paper addresses the problem of deriving control laws for robot manipulators in the framework of port-controlled Hamiltonian systems via canonical transformations and passivity-based control. The control design is focused on the presentation of a new energy-shaping methodology for tracking control based on the introduction of virtual non-homogeneous fields where a desired energy is defined to compensate for the actual energy of the robot manipulator while a virtual field forces the system to track a general reference trajectory. This requires use of the Legendre–Fenchel transformation and allows for the derivation standard control laws in the robotics field such as PD control with gravity compensation or PD with precompensation. Finally, the passivity of the input–output mapping of the non-autonomous Hamiltonian system is analyzed in detail, resulting in new Lyapunov candidate functions having their roots in physics.

Uniform Bounds of the Coriolis/Centripetal Matrix of Serial Robot Manipulators

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Many control laws for robot manipulators assume uniform boundedness of the Coriolis/centripetal matrix to insure global stability. In this paper, a new procedure to derive explicitly uniform bounds of the Coriolis/centripetal matrix is proposed. This procedure has the advantage with respect to other methods of avoiding the computation of the Christoffel symbols of first order involved in the derivation of the dynamics of the whole mechanism. To this end a new description of the Coriolis/centripetal matrix has been introduced based on fundamental matrices which exhibit structural properties of commutation and representation. </para>

A Natural Saturating Extension of the PD-With-Desired-Gravity-Compensation Control Law for Robot Manipulators With Bounded Inputs

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper proposes a natural saturating extension of the proportional-derivative (PD) with desired gravity compensation (PD<emphasis emphasistype="boldital">d</emphasis>gc) control law for the global regulation of robot manipulators with bounded inputs. Compared with other algorithms previously proposed under the same analytical framework, it proves to be advantageous in several senses. First, it involves a single saturation function at each joint. Second, it does not need to discriminate the terms that shall be bounded, since these are simply all of them included within the only saturation involved at every joint. Experimental results show the effectiveness of the proposed scheme. As far as the authors are aware, no such type of natural saturating extension (i.e., involving only one saturation function at each joint, where all the terms of the controller are embedded) to the bounded input case had been previously proposed for the PD<emphasis emphasistype="boldital">d</emphasis>gc scheme. Furthermore, it is shown how the proposed approach may be conceived within the framework of the energy shaping plus damping injection methodology. </para>

A CONTROL LAW FOR ROBOTIC MANIPULATORS BASED ON A FILTERED SIGNAL TO GENERATE PD ACTION AND VELOCITY ESTIMATES

This paper deals with an adaptive control law for robotic manipulators based on a filtered signal to generate both the PD action and velocity estimates of the joints, suitable for trajectory tracking tasks, with the particular aim of reducing the harmonic content ofthe mechanical torques developed at the joints and thus avoiding excitation of unmodelled dynamics and instability.

Simple extensions of the PD-with-gravity-compensation control law for robot manipulators with bounded inputs

This brief proposes two alternative approaches for the global regulation of robot manipulators with input saturations. They prove to be simple extensions of the PD-with-gravity-compensation (PDgc) control law to the bounded-input case. Moreover, they turn out to be in a better position to approach (within the restricted range of the control variables) a PDgc control signal than other algorithms previously proposed under the same analytical framework. Closed-loop performance improvements are, therefore, obtained through their implementation. This is corroborated through experimental results

Discussion on: “Application of Logarithmic-based Parameter and Upper Bounding Estimation Rules to Adaptive-Robust Control of Robot Manipulators”

This paper presents a new adaptive-robust control law for robot manipulators with parametric uncertainty. The control law for n-link robot manipulators using the Lyapunov-based theory of guaranteed stability of uncertain system is derived by means of analytical approach. The proposed adaptive-robust control law includes an adaptive dynamic compensation, robust feedforward compensators with an adaptive upper bounding function and a PD feedforward part, and both system parameters and robust feedforward compensator are updated in time. As distinct from similar studies, the manipulator parameters are updated with a logarithmic function depending on manipulator kinematics, inertia parameters and tracking error and on the other hand, robust compensator is updated as a function of uncertainty bound, robot kinematics and tracking error. The developed approach has the advantages of both adaptive and robust control laws, and besides it eliminates disadvantages of them.

Application of Logarithmic-based Parameter and Upper Bounding Estimation Rules to Adaptive-Robust Control of Robot Manipulators

This paper presents a new adaptive-robust control law for robot manipulators with parametric uncertainty. The control law for n-link robot manipulators using the Lyapunov-based theory of guaranteed stability of uncertain system is derived by means of analytical approach. The proposed adaptive-robust control law includes an adaptive dynamic compensation, robust feedforward compensators with an adaptive upper bounding function and a PD feedforward part, and both system parameters and robust feedforward compensator are updated in time. As distinct from similar studies, the manipulator parameters are updated with a logarithmic function depending on manipulator kinematics, inertia parameters and tracking error and on the other hand, robust compensator is updated as a function of uncertainty bound, robot kinematics and tracking error. The developed approach has the advantages of both adaptive and robust control laws, and besides it eliminates disadvantages of them.

Variable Upper Bounding Approach for Adaptive-Robust Control in Robot Control

This paper presents a new adaptive-robust control law for robot manipulators with parametric uncertainty. Stability of the uncertain system has been guaranteed using the Lyapunov theory and the control law is derived by means of analytical approach. In this scheme, the manipulator parameters are determined with an estimation law, and both adaptive gain and additional control input are also updated as a function of the estimated value. The proposed adaptive control input includes a parameter estimation law as an adaptive controller and an additional control input vector as a robust controller. The developed approach has the advantages of both adaptive and robust control laws, and besides it eliminates the disadvantages of them.

Stability analysis of a robust PD control law for robot manipulators

The purpose of this article is to examine the stability of a robust and decentralized PD control law for robot manipulator control. The control law, which was developed by the authors, has been shown experimentally to be extremely simple to implement and highly accurate for position and force tracking in the presence of robot model uncertainty and payload variation. However, stability analysis has been difficult due to the nonlinearity of robot dynamics and the use of time-delayed measurements of joint torques and joint accelerations in the control law. A rigorous stability analysis is presented in this article using Popov's hyperstability theory. A sufficient condition for global stability is obtained that supports previous theoretical and experimental results. © 1996 John Wiley & Sons, Inc.

Sliding Mode Block Control of Uncertain Nonlinear Plants

This paper combines the block control, sliding mode and high gain robust control techniques to form a stabilising control law for nonlinear systems with matched and unmatched uncertainties. A generalised observer is presented to cater for plants subjected to an unknown matched disturbance. The approach is applied to form a non-chatiering sliding-mode observer-based control law for robotic manipulators driven by DC motors.

Robust adaptive control for robot manipulators

A composite adaptive control law for robot manipulators in task space, which uses both the tracking error and the prediction error to drive parameter estimation, is developed in this paper. It is shown that global stability and convergence can be achieved for the adaptive control algorithm in the ideal case, and furthermore that the algorithm can be easily modified by using parameter projection to achieve robustness with respect to a class of unmodelled dynamics. In addition, the algorithm has the advantage that no requirement is needed for the inverse of the jacobian matrix or for the bounded inverse of the estimated inertia matrix. A simulation example is provided for performance demonstration.

Exponentially stable robust control law for robot manipulators

Robust control has a chattering problem since the control laws are discontinuous functions. To improve this, a boundary layer can be introduced; however the system then loses asymptotical stability and is only globally stable. An exponentially stable robust nonlinear control law for robot manipulators, based on Lyapunov stability theory, is presented. The robust control law is designed using a special Lyapunov function which includes both tracking errors and an exponentially convergent additional term, making the stability proof easy, and guarantees that the tracking errors decrease exponentially to zero. For bounded input disturbances, the control laws, with little modification, maintain satisfactory system performance. The results of a computer simulation for a 2-link manipulator are presented, demonstrating the benefits and robustness of the proposed algorithm.

Design of a robust adaptive control law for robotic manipulators

AbstractIn this article, a robust adaptive control scheme for robotic manipulators is designed based on the concept of performance index and Lyapunov's second method. Compensators are selected for a given feedback system by using a quadratic performance index. Then the stability of the system is proven based on Lyapunov's method, where a Lyapunov function and its time‐derivative are derived from the selected compensators. In the process of stabilization, stability bounds are obtained for disturbances, control gains, adaptation gains, and desired trajectories, in the presence of feedback delay due to digital computation and first‐order hold in the control loop. © 1994 John Wiley &amp; Sons, Inc.

Robust Adaptive Control for Robot Manipulators in Task Space

A new adaptive control law for robot manipulators in task space is developed in this paper. It is shown that global stability and convergence can be achieved for the adaptive control algorithm in the ideal case, and furthermore, the algorithm can be simply modified using parameter estimate projection to achieve robustness with respect to a class of unmodelled dynamics. In addition, the algorithm has the advantage that no requirement is needed for the inverse of Jacobian matrix or for the bounded inverse of the estimated inertia matrix.

Design of robust PD‐type control laws for robotic manipulators with parametric uncertainties

AbstractIn this article, design of a simple robust control law that achieves desired positions and orientations for robotic manipulators with parametric uncertainties is studied. A discontinuous control law is proposed, which consists of a high‐gain linear proportional plus derivative (PD) term and additional terms that compensate for the effect of gravitation. The stability of the robotic system under the proposed control law is proved by LaSalle's stability theorem. Furthermore, by the theory of singularly perturbed systems, it is shown that if the proportional and derivative gain matrices are diagonal with large positive elements then the system is decoupled into a set of first‐order linear systems. Simulation results are presented to illustrate the application of the proposed control law to a two‐link robotic manipulator.

Minimum-time control laws for robotic manipulators

This work addresses the problem of minimum-time control (MTC) for rigid robotic manipulators with point-to-point motion subject to 'hard' constraints on the control torques. A hamiltonian canonical formulation of the robot dynamic equations is used. A perturbation-based transformation algorithm is applied to solve this category of the MTC problem. In this algorithm, the original MTC problem, possibly a partially singular one, is converted into a totally non-singular optimal control problem by introducing a perturbed energy term into the original objective functional. It is shown that in the limiting case the solution to the transformed problem is convergent to that of the original MTC problem. The numerical solutions to several example manipulators are presented to verify the theoretical result on the structure of the MTC law. Some of the characteristics of the resulting optimal trajectories are analyzed by using a dynamic scaling approach. The result provides new insight into the dynamic characteristics of robot arms, pertaining to both path planning and design specifications.

Program Package for Generation of Control Laws for Robot Manipulators in Symbolic Form

Abstract This paper presents a new program package for the generation of control laws for robot manipulators in symbolic form. Since the computational efficiency of the generated control laws is extremely high, the real-time implementation become possible even on low-cost microcomputers. This program package represents an extension of the previously developed program package SYM which is designed to generate efficient manipulator models (Timcenko, Kircanski, Vukobratovic 1991). The basic algorithm belongs to the class of customized algorithms that reduce the computational burden by taking into account the specific characteristics of the manipulator to be controlled. It generates the high-level program code for computing various control laws based on inverse robot dynamics. The program code is highly optimized from the standpoint of numerical complexity. It represents a series of assignment statements with simple float variables and constants. Matrix and vector computations, loops, and conditional branches are avoided. The software modules for generation of various kinds of control laws as well as for simulation of robot moving along a defined path are incorporated into SYM software package and demonstrated in this paper. Generated models and control laws are implemented in several robot controllers designed to drive a 6 degrees of freedom robots.

Adaptive motion control of robot manipulators: A unified approach based on passivity

AbstractThis paper presents a unified approach to direct adaptive motion control laws for robot manipulators that have been studied during the last few years by several authors. It provides a general approach based on sensivity to demonstrate the global asymptotic stability of adaptive schemes applied to rigid multilinked manipulators. It is shown that most of the schemes fit within this framework, which presents the advantage of being more systematic than other techniques and therefore will enable a unified presentation of the several schemes proposed to date and will increase our understanding of adaptive control of robot manipulators.