Kinematic Control of Robots With Joint Constraints

This paper proposes a flexible enhanced power quality strategy for a multi-function distributed generation (DG) in an aggregated system. Being a multi-function DG system, the grid-interfaced inverter can provide very sinusoidal current and harmonic compensating current simultaneously. Different from the classic strategy where the compensating current is directly calculated by the measured harmonic content in the load current, the proposed power quality control strategy presents a more flexible way using a voltage-controlled approach based on the virtual impedance theory. As a result, each individual DG can provide harmonic compensation functionality independently and the power quality of grid current can be enhanced. This paper first develops an aggregated DGs model using continuous timedomain equivalent circuit. The classic and proposed power quality control strategies can then be derived from the developed models. The proposed control strategy is performed by the virtual harmonic impedance method, which can promote the output current of each individual DG itself and compensate harmonics caused by the other DGs. The proposed control strategy can be seamlessly incorporated into the conventional PR control scheme, and maintain both the stead-state and transient performance within the control bandwidth. Moreover, the proposed control strategy is less sensitive to the variable of the grid frequency. Experimental results are provided to validate the correctness of the proposed power quality strategy.

This paper presents an event-triggered model predictive control (MPC) strategy with learning terminal cost for robotic manipulators containing model uncertainty and input constraints. In the proposed MPC structure, an adaptive predictive model for the robotic system is established by radial basis function neural networks (RBFNNs) firstly. Then, a terminal cost adjusted by the global learning mechanism is constructed. Both global steady-state optimization and transient fast convergence are achieved by adding the learning terminal cost to the MPC scheme. After that, a triggering condition of the MPC solving is developed based on the predictive model’s weights and the predictive tracking error. Besides, the condition to avoid Zeno behavior is obtained. The recursive feasibility of the proposed MPC strategy is verified, and the ultimately uniformly boundedness (UUB) of all variables is proved according to the Lyapunov theorem. Finally, experiments based on an xMate7 Pro robot are conducted to demonstrate the effectiveness of the presented method. Note to Practitioners—The tracking control of robotic manipulators is a common and important problem in industrial applications, such as grasping, loading, unloading, et al. There exist some limitations in existing control methods. For example, general control strategies such as adaptive control, sliding mode control neglect the balance between control costs and expected performance; existing optimal control approaches rarely consider global steady-state optimization and transient fast convergence under the influence of model uncertainty. This paper is motivated by these limitations of robotic control design and inspired by model predictive control and optimal control theory. It develops a novel strategy for tracking control of robotic manipulators, which includes three following items: (1) adopt an approximation model constructed by neural networks as the predictive model for estimating the robotic system; (2) introduce a critic network into the terminal cost of the objective function of MPC for learning global optimal solution; (3) establish an event-triggered mechanism for solving of the optimization problem. The proposed method is verified by experimental results. In our future work, the proposed control strategy will be applied to more industrial processes.

PurposeThis paper aims to present an iterative path-following method with joint limits to solve the problem of large computation cost, movement exceeding joint limits and poor path-following accuracy for the path planning of hyper-redundant snake-like manipulator.Design/methodology/approachWhen a desired path is given, new configuration of the snake-like manipulator is obtained through a geometrical approach, then the joints are repositioned through iterations until all the rotation angles satisfy the imposed joint limits. Finally, a new arrangement is obtained through the analytic solution of the inverse kinematics of hyper-redundant manipulator. Finally, simulations and experiments are carried out to analyze the performance of the proposed path-following method.FindingsSimulation results show that the average computation time is 0.1 ms per step for a hyper-redundant manipulator with 12 degrees of freedom, and the deviation in tip position can be kept below 0.02 mm. Experiments show that all the rotation angles are within joint limits.Research limitations/implicationsCurrently , the manipulator is working in open-loop, the elasticity of the driving cable will cause positioning error. In future, close-loop control based on real-time attitude detection will be used in in combination with the path-following method to achieve high-precision trajectory tracking.Originality/valueThrough a series of iterative processes, the proposed method can make the manipulator approach the desired path as much as possible within the joint constraints with high precision and less computation time.

This paper proposes an optimal control method based on adaptive dynamic programming (ADP) for manipulators with joint limitation under input saturation. The asymmetric input saturation problem is solved by introducing a smooth function, by which the saturation and nonsmooth issues of the input caused by the actuators can be handled. Joint limitation of the manipulator is transformed through a transfer function, which is incorporated into the cost function of the whole robotic system, to guarantee the joint limitation will not be violated. Meanwhile, due to the difficulty in solving Hamilton-Jacobi-Bellman (HJB) equation, the critic network is constructed utilising radial basis function neural networks (RBFNNs) to approximate the cost function. This approach effectively overcomes the curse of dimensionality problem associated with dynamic programming. Subsequently, an ADP-based optimal controller is designed for the robotic system. Lyapunov synthesis is used in the stability analysis to prove all the signals are convergent and ultimately uniformly bounded (UUB). Simulations are conducted on a planar 3-DOF manipulator to validate the effectiveness of the proposed method. The results demonstrate the improved performance and feasibility of the developed ADP-based optimal control strategy in handling joint limitations and input saturation challenges in robotic systems.

Real-time motion planning and control of multi-joint robot manipulators are studied using neural networks. The proposed neural network approach consists of two modules: one for real-time collision-free motion planning, the other for real-time fine control of the robot manipulators. The motion planning module is a biologically inspired, parallel connected, topologically organised neural network, where each neuron is characterised by a shunting equation, whose state space is the robot configuration joint space. This module is capable of planning a real-time optimal path for robot manipulators through the dynamic activity landscape of the neural network. The motion control module involves of a feedforward neural network together with a traditional PD feedback loop. It is capable of achieving real-time fine motion control of robot manipulators under significant uncertainties and without any prior knowledge of the robot dynamics. This module can quickly compensate sudden changes in the robot dynamics. The real-time fine control of robot manipulators is achieved through the online learning of the neural network. Both the motion planning and motion control modules are computationally efficient, and their global stabilities are proved using Lyapunov stability theory.

Kinematic control of manipulators with joint physical constraints, such as joint limits and joint velocity limits, has received extensive studies. Many studies resolved this problem at the second-order kinematic level, which may suffer from the self-motion instability in the presence of persistent self-motion or unboundedness of joint velocity. In this paper, a unified approach is proposed to control a manipulator with both joint limits and joint velocity limits at the second-order kinematic level. By combining the weighted least-norm (WLN) solution in the revised joint space and the clamping weighted least-norm (CWLN) solution in the real joint space, the unified approach ensures the joint limits and joint velocity limits at the same time. A time-variant clamping factor is incorporated into the unified approach to suppress the self-motion when the joint velocity diverges, or the end-effector stops, which improves the stability of self-motion. The simulations in contrast to the traditional dynamic feedback control scheme and the new minimum-acceleration-norm (MAN) scheme have been made to demonstrate the advantages of the unified approach.

A dual neural network is presented for the bi-criteria kinematic control of redundant manipulators. To diminish the discontinuity of minimum infinity-norm solutions, the kinematic-control problem is formulated in the bi-criteria of the infinity and Euclidean norms. Physical constraints such as joint limits and joint velocity limits are also incorporated simultaneously into the proposed kinematic control scheme. The single-layer dual neural network model with a simple structure is developed for bi-criteria redundant resolution of redundant manipulators subject to robot physical constraints. The dual neural network is shown to be globally convergent to optimal solutions in the bi-criteria sense, and is demonstrated to be effective in controlling the PA10 robot manipulator.

This paper presents two kinds of adaptive control schemes for robot manipulator which has the parametric uncertainties. In order to compensate these uncertainties, we use the NN (neural network system) that has the capability to approximate any nonlinear function over the compact input space. In the proposed control schemes, we need not derive the linear formulation of robot dynamic equation and tune the parameters. We also suggest the robust adaptive control laws in all proposed schemes for decreasing the effect of approximation error. To reduce the number of neural of network, we consider the properties of robot dynamics and the decomposition of the uncertainty function. The proposed controllers are robust not only to the structured uncertainty such as payload parameter, but also to the unstructured one such as friction model and disturbance. The validity of the control scheme is shown by computer simulations and experiment of dual-arm robot manipulator.

In this paper, the problem of robust control of robot manipulators which perform noncontact and contact tasks is considered. Using the hybrid control strategy, two variable structure control algorithms are developed in task space. One of the algorithms is developed for control of robot manipulators in constrained motion; the other is proposed for control of manipulators in unconstrained and constrained motion. Computer simulation results are presented for illustration. >

An approach to force and visual control of robot manipulators in contact with a partially known environment is proposed in this article. The environment is modeled as a rigid object of known geometry but of unknown and time-varying position and orientation. An algorithm for online estimation of the object pose is adopted, based on visual data provided by a camera as well as on forces measured during the interaction. This information is used by a force/position control scheme, in charge of managing the interaction. Simulation and experimental results are presented for the case of an industrial robot manipulator.

This paper focuses on the issue of hybrid force/position control of the robots with oscillatory base. The purpose of controlling a system is to control the contact force between the environment and object in the constrained directions. The auxiliary control input laws with adaptive network-based fuzzy inference system (ANFIS) tuning methodology was successfully applied for robot manipulators mounted on oscillatory bases for hybrid position/force control purpose. The principal advantage is that the proposed control scheme only needs to select control inputs for task space trajectory tracking; that is, one does not need to redesign a vibration damping controller for such a system. Experiments are conducted to confirm the efficiency of the proposed control design. The results of this study can be feasible to various mechanical systems, such as mobile robot, gantry cranes, underwater robot, and other dynamic systems mounted on oscillatory bases during on constraint motion tasks.

This book is the second edition of a textbook published in 1996 by McGraw Hill and originates from a graduate level course given by the authors at the University of Naples. The topics include kinematics, statics and dynamics of robot manipulators together with trajectory planning and active control. There are only minor additions the first edition, which are mainly the use of quaternion to describe the orientation of the end effector and a short description of a closed chain architecture for a manipulator (parallelogram arm). The book is largely devoted to serial manipulators, with special developments about active control including adaptative control, robust controls and stability analysis. Another strength of this book is the great number of problems proposed at the end of each chapter, together with a list of references related to it. The fundamental features covered by the text are illustrated on simple examples of serial manipulators (two-link planar arm, parallelogram arm) including analytical results and numerical tests.The book has nine chapters followed by three appendices. The first appendix is devoted to linear algebra, the second recalls some fundamental aspects of rigid body mechanics and the third gives some basic principles of feedback control of linear systems.Chapter one is an introduction to the study of robot manipulators, giving an interesting classification of their architectures, the corresponding workspace and describes the tasks for which theyare used. After some standard examples of industrial manipulators, bibliographical reference texts are proposed, including textbooks on modelling and control of robots, general books on robotics, specialized texts, scientific robotic reviews and some international conferences on robotics.Chapters two, three and four are devoted to mechanical modelling of robot manipulators. The fundamental basics of kinematics are given in chapter two, including the representation of finite rotations by Euler angles or unit quaternions, homogeneous transformations, Denavit-Hartenberg parameters and workspace. The direct and inverse kinematical problems are solved in analytical form for some typical manipulator structures. The differential kinematics of robots are presented in chapter three, with an introduction to the geometric and analytic Jacobian matrices, kinematic singularities and redundancy. The inverse kinematic problem is presented, with special attention to the case of redundant robots where the solution is obtained by a linear optimization problem leading to the introduction of the pseudo-inverse Jacobian matrix and to the solution of several objectives such as avoidance of collision with an obstacle or moving away from singularities. Several inverse kinematics algorithms are given wih an interesting application to a three-link planar arm. Finally, a property of kineto-statics duality is deduced from the principle of virtual work applied to an equilibrium configuration of the robot. Chapter four is a standard presentation of the derivation of the dynamical model by Lagrange formulation and then by the Newton-Euler method. In the Lagrange formulation method, the linearity with respect to inertial parameters is shown and a detailed formulation of the dynamical model is obtained for a two-link Cartesian arm, a two-link planar arm and a parallelogram arm. The problem of dynamic parameter identification is also briefly presented from a numerical point of view. The recursive algorithm constructed from the Newton-Euler formulation is presented and illustrated by considering a two-link planar arm. Finally, the operational space dynamic model is introduced.In chapter five, paths and trajectory planning in joints and in operational spaces are presented; several classical methods of interpolation are described.Chapter six is an extensive study of active control of manipulators. Several methods are presented, involving classical independent joint control, non-linear centralized control, robust control and adaptative control. Both joint-space control and operational-space control are studied together with stability analysis by using Liapounoff functions. An interesting application to the two-link planar arm already used shows the comparison between various control schemes.Chapter seven deals with interaction control of serial manipulators with the working environment. Several strategies involving compliance control, impedance control, force control and hybrid control are presented.Chapter eight describes the actuators and the sensors used in robotics. Several types of servomotors (electric and hydraulic) are presented, together with the model giving their input/output relationship. Several kinds of sensors are also described including encoders, tachometers, force and vision sensors.The last chapter gives a short presentation of the functional architecture of a robot's control system, including characteristics of the programing environment and the hardware architecture.In conclusion, the book provides a good insight about simulation and control of robot manipulators, with a detailed study of the various control strategies and several interesting and pedagogical applications. This book is an excellent review of the standard knowledge needed not only for graduate students but also for researchers interested in robot manipulators.M Pascal

Presents an approach to the design and real-time implementation of an adaptive controller for a robotic manipulator based on digital signal processors. The Texas Instruments DSP (TMS320C31) chips are used in implementing real-time adaptive control algorithms to provide enhanced motion control performance for robotic manipulators. In the proposed scheme, adaptation laws are derived from the direct model reference adaptive control principle based on the improved Lyapunov second method. The proposed adaptive controller consists of an adaptive feedforward and feedback controller and PI-type time-varying auxiliary control elements. The proposed control scheme is simple in structure, fast in computation, and suitable for real-time control. Moreover, this scheme does not require any accurate dynamic modeling nor values of manipulator parameters and payload. Performance of the proposed adaptive controller is illustrated by simulation and experimental results for an industrial robot with four joints in the joint space and Cartesian space.

Safety-Oriented Control of Robotic Manipulators – a Kinematic Approach

This brief presents a contouring control scheme for robotic manipulators. The geometric properties of the desired contour are incorporated in the controller design phase, and the resulting controller has been structured as a two-layered hierarchical control scheme that consists of an outer loop and an inner loop. The outer loop is formed by kinematic control system in operational space, which can be designed to assign different dynamics to the tangential, normal, and binormal direction of the desired contour. It is shown that the outer loop can provide a joint velocity reference signal to the inner one. The inner loop is used to implement a velocity servo control system at the robot joint level. Meanwhile, a radial basis function network is adopted to compensate for the nonlinear dynamics of the robotic manipulator, where a robust control strategy is used to suppress the modeling error of neural networks. Experimental results on the Zebra-Zero robotic manipulator have demonstrated the effectiveness of the proposed control scheme in comparison with other control strategies.