Adaptive control of robot manipulators based on passivity

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.

SUMMARYIn most dynamic adaptive control simulation of robotic manipulators, the Langrange–Euler (L–E) dynamic equations are first piecewise linearized about the desired reference and then discretized and rewritten in a state space form. This makes things very complicated and it is easy to make errors. What is more is that with a different reference this work must be done again. A new simulation scheme – Backward Recursive Self-Tuning Adaptive (BRSTA) – as it will be called, is suggested in this paper for adaptive controller design of robot manipulators. A two degree of freedom robot manipulator is used to verify the scheme in the condition of highly nonlinear and highly coupled system. A one degree of freedom robot manipulator is used for comparing both the forward and backward methods. The main advantages of this scheme include that it can be used for evaluating the self-tuning adaptive control laws and provide the initial process parameters for real-time control. And it is concluded here that the Newton–Euler (N–E) dynamic equations are equally well qualified as the Langrange–Euler (L-E) equations for the simulation of self-tuning adaptive control of robot manipulators.

This paper studies the multiple-model based adaptive control of a robot manipulator moving in varying environments. The research problem is divided into two parts: the modeling of the system consisting of the robot manipulator and the varying environment, and the multiple-model based adaptive control of the robot manipulator. This paper considers the added mass, added moment of inertia, drag, and buoyancy as the environmental factors. In these dynamic models, the environmental factors and the mass, moment of inertia, and gravity of the robot are unknown parameters. By the linearity in the parameters property, we can write these parameters independently of the robot joint variables and thus can be estimated using an adaptive control law. After obtaining the system model, we adopt a multiple-model based adaptive control scheme. When the model of the robot changes, the parameter estimates can rapidly convert to a relatively closer one for the new true values. With a multiple-model based adaptive controller, the asymptotic tracking of the robot and the parameter boundedness are achieved, and the tracking is not disturbed by the variance of the environment parameters in the multiple model control case, which has better performance than the single model case.

Thus far, most research in adaptive control of robotic manipulators has assumed that models of regressor matrix and kinematics are known exactly. To overcome these drawbacks, we propose in this paper a task-space adaptive law for setpoint control of robots with uncertainties in gravity regressor matrix and kinematics. In addition, we investigate the stability problem when an estimated task-space velocity is used in the feedback loop. Sufficient conditions for choosing the feedback gains, gravity regressor, and Jacobian matrix are presented to guarantee the stability.

Adaptive control of robot manipulator is reviewed in this paper. General structure of the adaptive algorithms is presented with reference to the research carried out in recent years. General approach to the stability analysis of algorithms is highlighted. Extensive simulation study confirms the potential of adaptive control theory in dealing with the highly nonlinear, uncertain and complex robot arm dynamics.

Adaptive control of robot manipulators based on the use of a sliding variable and the passivity property of the dynamic equations was originally designed and successfully applied to task tracking in joint space few decades ago. Surprisingly, no extension is available to date for the multi-task case such that the controller tends towards enforcing strict task priorities as the parameters tend to their real values. Given the importance of both multi-task control and adaptive algorithms, an approach that deals with this situation has an important impact in the robotic field. This letter provides a solution to this problem leveraging on our recent formulation of hierarchical multi-task impedance control for trajectory tracking and on geometric methods for model identification. Experiments are used to validate the stability analysis.

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.

This paper presents a robust adaptive fuzzy neural controller (AFNC) suitable for motion control of multilink robot manipulators. The proposed controller has the following salient features: (1) self-organizing fuzzy neural structure, i.e., fuzzy control rules can be generated or deleted automatically according to their significance to the control system and the complexity of the mapped system and no predefined fuzzy rules are required; (2) fast online learning ability, i.e., no prescribed training models are needed for online learning and weights of the fuzzy neural controller are modified without any iterations; (3) fast convergence of tracking errors, i.e., manipulator joints can track the desired trajectories very quickly; (4) adaptive control, i.e., structure and parameters of the AFNC can be self-adaptive in the presence of disturbances to maintain high control performance; and (5) robust control, where asymptotic stability of the control system is established using the Lyapunov theorem. Experimental evaluation conducted on an industrial selectively compliant assembly robot arm demonstrates that excellent tracking performance can be achieved under time-varying conditions.

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.

A new formulation of the impedance control problem which is suitable for passivity based adaptive controllers for robot manipulators is proposed. A reference model architecture leading to a desired error dynamics and an adaptation procedure which is independent of the initial state error is used. The reference model dynamics represents the desired dynamics relationship between position error, velocity error and external force. It also allows for the adaptation procedure to be tuned independently of the desired impedance behavior of the manipulator. The proposed control algorithm is shown to be globally stable, computationally simple and easy to implement. The theoretical results are verified through computer simulations.

The practical applicability of recently developed adaptive neurocontrol algorithms for poorly modeled robotic systems depends crucially upon the accuracy and efficiency of the neural network used to approximate the functions required for accurate control of the system. Recently, an algorithm has been developed which dynamically varies the actual structure of the network concurrently with its associated parameters, in the process stably evolving a minimal network which still provides the required accuracy. In this paper, we extend these ideas to the adaptive control of robot manipulators, providing a formal proof of the stability and convergence properties of our new algorithm. A main feature of the proof is the demonstration that the stability properties of the algorithm are independent of the specific mechanism used to vary the structure of the network, allowing great flexibility in the design of the structure adaptation mechanism. A specific structural adaptation mechanism is suggested, and its performance is then demonstrated on a simulation of a free-floating space robotic manipulator.

Variable-order stochastic adaptive control of robotic manipulators with a flexible forearm

A decentralized adaptive control scheme is proposed for the trajectory tracking of a general n‐degree‐of‐freedom robot manipulator. The robot is considered as a set of decoupled second‐order systems with disturbances. The controller consists of feedforward from the desired trajectory based on the “inverse system” of the model, PID feedback from the actual trajectory, and auxiliary input for the compensation of the neglected terms in modeling in each subsystem. The gain is derived in diagonal matrix form, and is adjusted by the model reference adaptive control theory based on the Lyapunov's direct method. The result is high accuracy in path tracking despite the high speed, load change, and sudden torque disturbances. Numerical simulations on.a planar two‐link robot manipulator are presented to show the performance under various practical considerations.

Predefined performance adaptive control of robotic manipulators with dynamic uncertainties and input saturation constraints

This paper investigates fuzzy approach to the adaptive control of robot manipulators. Adaptive fuzzy systems are trained to approximate the robot dynamic; then, based on the estimated model, a certainty equivalent control is designed to ensure the tracking of a stable reference model. It is proven, using Lyapunov stability, that this adaptive scheme is robust against uncertainty, external disturbance and approximation error, and achieves asymptotic tracking of a stable reference model. The effectiveness of the proposed fuzzy approach is demonstrated, by simulation, on a two-link robot model.