Modelling and Control of Robot Manipulators

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.

Further results on adaptive iterative learning control of robot manipulators

Radial basis function network (RBFN) is used in this paper for predefined trajectory control of both one-link and two-link robotic manipulators. The updating equations for the RBFN parameters were derived using the gradient descent principle. The other advantage of using this principle is that it shows the clustering effect in distributing the radial centres. To increase the complexity, the dynamics of robotic manipulator is assumed to be unknown, and hence, simultaneous control and identification steps were performed using the RBFNs. The performance of the RBFN is compared with the multilayer feed-forward neural network (MLFFNN) in terms of mean square error, tolerance to disturbance and parameter variations in the system. The efficacy of RBFN as a controller and identification tool is verified by performing the simulation study, and the results obtained reveal the superior performance of RBFN over MLFFNN in both identification and control aspects for one-link and two-link robotic manipulators.

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. >

A new nonlinear optimal control method is proposed for solving the problem of control and stabilization of a two-link robotic manipulator where the first link is rigid and the second link is flexible. The dynamic model of this robot describes both the rotational motion of the two links and the vibration modes which are excited at the flexible link. The control and stabilization problem of this 2-DOF rigid-flexible robot is nontrivial due to complex nonlinear dynamics and underactuation. To apply the proposed nonlinear optimal control method, the dynamic model of the two-link rigid-flexible robotic manipulator undergoes first approximate linearization around a temporary operating point that is updated at each iteration of the control algorithm. The linearization takes place through first-order Taylor series expansion and through the computation of the Jacobian matrices of the flexible manipulator’s state-space description. For the approximately linearized model of the two-link rigid-flexible robot, an H-infinity feedback controller is designed. Actually, the H-infinity controller stands for the solution of the optimal control problem for the rigid-flexible robot under uncertainty and external perturbations. For the computation of the feedback gains of the H-infinity controller, an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control algorithm are proven through Lyapunov analysis. First, it is shown that the control scheme achieves H-infinity tracking performance which signifies robustness for the control loop of the two-link rigid-flexible robot under uncertainties and external perturbations. Next, it is also shown that the control loop of the 2-DOF rigid-flexible robot is globally asymptotically stable. The proposed control method achieves fast and accurate tracking of setpoints under moderate variations of the control inputs. The concept of the proposed nonlinear optimal control method has been to approximate locally and at each sampling interval the nonlinear dynamics of the rigid-flexible robotic manipulator by an equivalent linear state-space description and to solve the H-infinity control problem for the linearized model. Finally, the control inputs are applied to the initial nonlinear dynamics and stability proof is given for the initial nonlinear state-space model.

In this paper, the results of several experiments made on the control of oscillations of a single module of the I-Support manipulator are presented. The I-Support is a soft continuum robotic manipulator composed of several similar modules, designed and built for assisting disabled users during a showering task. For these experiments, a single module is pneumatically actuated by three sets of bellow-like actuators, that allow controlled bending in any direction and also controlled extension. The actuators are made of latex and braided polyester components that, when pressurized, make up the load-carrying structure of the module. As motion control of even a single module is a complex non-linear problem, a stepwise approach was followed where several signal based control techniques were tested for feasibility. These techniques focus on the oscillation control itself, meaning that it is assumed that the inverse kinematics problem—the definition of the input signals that will allow the robot to reach a specified equilibrium position—is dealt with elsewhere. Results show that pre-filtering the input commands significantly reduces overshoot and settling time for a task in three-dimensional space. Also, closed-loop control based on feeding back the error from the equilibrium position showed promising results but has for now only been applied to one-dimensional problems.KeywordsFlexible robotsSoft robotsVibration controlFlexible structures

Robotics is a relatively new and evolving technology being applied to manufacturing automation and is fast replacing the special-purpose machines or hard automation as it is often called. Demands for higher productivity, better and uniform quality products, and better working environments are primary reasons for its development. An industrial robot is a multifunctional and computer-controlled mechanical manipulator exhibiting a complex and highly nonlinear behavior. Even though most current robots have anthropomorphic configurations, they have far inferior manipulating abilities compared to humans. A great deal of research effort is presently being directed toward improving their overall performance by using optimal mechanical structures and control strategies. The optimal design of robot manipulators can include kinematic performance characteristics such as workspace, accuracy, repeatability, and redundancy. The static load capacity as well as dynamic criteria such as generalized inertia ellipsoid, dynamic manipulability, and vibratory response have also been considered in the design stages. The optimal control problems typically involve trajectory planning, time-optimal control, energy-optimal control, and mixed-optimal control. The constraints in a robot manipulator design problem usually involve link stresses, actuator torques, elastic deformation of links, and collision avoidance. This paper presents a review of the literature on the issues of optimum design and control of robotic manipulators and also the various optimization techniques currently available for application to robotics.

This paper presents the current state of the art in the adaptive control of single rigid robotic manipulators in the constrained motion tasks. A complete mathematical model of a single rigid robotic manipulator in contact with dynamic environment is presented. The basic approaches in deriving the environment model are given. The significance of the dynamic environment in the scope of the stability problem of the whole system robot-dynamic environment is emphasized. A classification of the adaptive contact control concepts in manipulation robotics is presented. The main characteristics of the most important adaptive strategies in constrained manipulation are given. The advantages and the drawbacks of the presented methods are emphasized. The paper covers results published a few years ago, as well as some recent trends in this field. One important result in the stability analysis of robotic manipulators in the constrained motion tasks is reported. Finally, some concluding remarks are given and possible future investigation trends in adaptive control of robotic manipulators are indicated.

In this paper we present the development of a hybrid constraint space dynamics modeling technique and position/force controller for robotic manipulator control in constrained environments. The method utilizes a constraint space dynamic model in which the model coordinates are displacement along the constraint trajectory and the normal force between the manipulator end-effector and the environment. The dynamic model is constructed by transforming the conventional joint space manipulator dynamics equations into their constraint space equivalents through the application of mapping functions, which relate differential displacements and velocities in the constraint space coordinate system to the joint space coordinate system. Control algorithms may then be applied to the simplified dynamic structure of the constraint space equations of motion in order to produce a vector of manipulator joint torques which will satisfy both position and force requirements along the environmental constraint. Actuator constraints and momentum compensating techniques are also used to ensure that the position and force control problems are completely decoupled from one another. A computer torque control algorithm is then applied to a two-degrees-of-freedom prismatic robot and simulations are carried out with two different constraint surfaces, i.e. a planar, and a concave circular environment. The results of these simulations show that the controller, implemented in hybrid constraint space provides good position and force control.

This paper proposes a novel reward based Single Network Adaptive Critic (SNAC) architecture for optimal kinematic control of a redundant robot manipulator. At first, the closed-loop positioning task is formulated as a discrete-time input affine system. The optimal controller is then derived for the reward based cost function with the adaptive critic. The notion of goal-directed optimal behavior is captured by defining a performance measure or cost function in terms of discounted reward function. The reward function is chosen to deliberately speed up convergence of the closed loop positioning error. The performance of the proposed reward based SNAC architecture is compared with standard quadratic cost based SNAC for kinematic control of the redundant robot manipulator. The results show faster convergence of the overall trajectory cost. The proposed kinematic solution has been validated in simulations and experimentally executed using 6 degrees of freedom (DOF) Universal Robot (UR) 10 robot manipulator for both regulation and tracking.

Super-twisting ZNN for coordinated motion control of multiple robot manipulators with external disturbances suppression

Enhanced tracking control for n-DOF robotic manipulators: A fixed-time terminal sliding mode approach with time delay estimation

Trajectory planning and tracking are crucial tasks in any application using robot manipulators. These tasks become particularly difficult when obstacles are present in the manipulatorpsilas workspace. In this paper it is assumed that the obstacles can be approximated in a conservative way with discs. The goal is to represent the obstacles in the robot configuration space, in order to allow an efficient and accurate trajectory planning and tracking. Moreover, the paper provides the methods for checking the collision between the n-joint manipulator and the obstacles. Trajectory planning depends on tracking accuracy. In this paper an adequate tracking accuracy is guaranteed assuming the use of a suitably designed robust controller.

In this paper we continue the investigations begun in [13] and [14] on the control of robot manipulators. Using the theory of uncertain dynamical systems developed in [4], [5], [16], [17] we derive a robust nonlinear control strategy with guaranteed tracking properties which can be quantified given bounds on the extent of model uncertainty, sensor noise, input disturbances, etc. We also extend the class of pointwise optimal control strategies of [13] to the case of systems with uncertainty in order to treat the problem of input constraints within the context of uncertain systems.

ABSTRACTIn this article, we give some comments on the article ‘A new terminal sliding mode control for robotic manipulators’. The article presents a new terminal sliding mode control approach for global finite-time tracking of robotic manipulators. We point out a serious error occurred through the article, leading to the ineffectiveness of the proposed approach. A correction is proposed. Comparisons are presented.